Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018): Volume 2 [1st ed.] 978-981-13-3133-6, 978-981-13-3134-3

Table of contents :
Front Matter ....Pages i-xviii
Front Matter ....Pages 1-1
Spatial and Temporal Variability of Some Coastal Water Parameters at Selected Locations on the East Coast of India (R. Gayathri, V. Ranga Rao, P. Madeswaran, V. Padmavathi, R. ManjuPriya, M. Arunvel et al.)....Pages 3-11
Laboratory Investigations on the Effect of Fragmentation and Heterogeneity of Coastal Vegetation in Wave Height Attenuation (Kiran G. Shirlal, Beena Mary John, Subba Rao)....Pages 13-23
Measurement of Surf Zone Hydrodynamics Along the Coastline of Pondicherry, India (R. Balaji, M. V. Ramana Murthy, J. Satheeshkumar)....Pages 25-34
Beach Morphology Near the Inlet of Chilika Lagoon (Subhasis Pradhan, Pratap K. Mohanty, Rabindro N. Samal, Rabindra K. Sahoo, Rakesh Baral, Shraban K. Barik et al.)....Pages 35-47
Study of Bamboo Bandalling Structures in the Tidal River for River Bank Erosion (Md. Lutfor Rahman)....Pages 49-57
Development of Predictive Tool for Coastal Erosion in Arctic—A Review (Mohammad Saud Afzal, Raed Lubbad)....Pages 59-69
Evaluation of Hydrodynamic Performance of Quarter Circular Breakwater Using Soft Computing Techniques (N. Ramesh, A. V. Hegde, Subba Rao)....Pages 71-88
Statistical Analysis of Coastal Currents from HF Radar Along the North-Western Bay of Bengal (Samiran Mandal, Saikat Pramanik, Subrota Halder, Sourav Sil)....Pages 89-97
Numerical Modelling and Experimental Investigation on the Effect of Wave Attenuation Due to Coastal Vegetation (S. Hemavathi, R. Manjula, N. Ponmani)....Pages 99-110
Studies on the Morphological Changes by Numerical Modeling Along Kakinada Coasts (N. Sharmila, R. Venkatachalapathy, M. Mugilarasan)....Pages 111-138
Desk Studies and Modelling Sedimentation Pattern in Gulf of Khambhat (L. R. Ranganath, A. V. Sriram, M. Karthikeyan)....Pages 139-157
Wave Climate and Nearshore Sediment Transport Pattern Along the SE Coast of India (V. Ranga Rao, Akhil Kolli, K. Stephen Raju, D. Kumaresan)....Pages 159-171
Nondimensional Methods to Classify the Tidal Inlets Along the Karnataka Coastline, West Coast of India (N. Amaranatha Reddy, Vikas Mendi, Jaya Kumar Seelam, Subba Rao)....Pages 173-184
Study of Dynamic Changes Through Geoinformatics Technique: A Case Study of Karwar Coast, West Coast of India (Arunkumar Yadav, Basavanand M. Dodamani, G. S. Dwarakish)....Pages 185-197
An Experimental Study on Surface Wave Modulation Due to Viscoelastic Bottom (Dharma Sree, Adrian Wing-Keung Law, Hayley H. Shen)....Pages 199-206
Spectral AB Simulations for Coastal and Ocean Engineering Applications (R. Kurnia, P. Turnip, E. van Groesen)....Pages 207-217
Nearshore Hydrodynamics Near an Open Coast Harbour at Gopalpur, Central East Coast of India (U. K. Pradhan, P. Mishra, P. K. Mohanty, U. S. Panda, M. V. Ramana Murthy)....Pages 219-237
Improving Hydraulic Conditions to Preserve Mangroves at Hazira (V. B. Sharma, A. K. Singh, Prabhat Chandra)....Pages 239-250
Hydrodynamic Modelling for Development of a Port in an Estuary (A. K. Singh, L. R. Ranganath, M. Karthikeyan)....Pages 251-264
Wave Interaction with Multiple Submerged Porous Structures (V. Venkateswarlu, D. Karmakar)....Pages 265-279
Beyond the Data Range Approach to Soft Compute the Reflection Coefficient for Emerged Perforated Semicircular Breakwater (Suman Kundapura, Arkal Vittal Hegde, Amit Vijay Wazerkar)....Pages 281-292
Design of a Reef for Coastal Protection (P. V. Chandramohan)....Pages 293-302
Assessment of Littoral Drift and Shoreline Changes for Fisheries Harbour on East Coast of India (S. N. Jha, J. Sinha)....Pages 303-313
Impact of Flow-Driven Debris on Coastal Structure During Tsunami Bore (S. Harish, V. Sriram, V. Sundar, S. A. Sannasiraj, I. Didenkulova)....Pages 315-326
Wave Transformation Around Submerged Breakwaters Made of Rubble Mound and Those Made of Geosynthetic Tubes—A Comparison Study for Kadalur Periyakuppam Coast (M. Kalyani, A. S. Kiran, Vijaya Ravichandran, V. Suseentharan, Basanta Kumar Jena, M. V. Ramana Murthy)....Pages 327-336
Study on Stability of Eden Navigational Channel in Hooghly River Estuary (N. Saichenthur, K. Murali, V. Sundar)....Pages 337-352
Study on Maintenance Dredging for Navigable Depth Assurance in the Macro-tidal Hooghly Estuary (V. Maheshvaran, K. Murali, V. Sundar, K. Chitra)....Pages 353-367
Migration of Chilika Lake Mouth (R. Sundaravadivelu, P. Shanmugam, A. K. Patnaik, P. K. Suresh)....Pages 369-380
Front Matter ....Pages 381-381
Coupled Dynamics of Deep Water Tension Leg Platforms Under Steep Regular Waves (R. Jayalekshmi, R. Sundaravadivelu, V. G. Idichandy)....Pages 383-393
Residual Strength of Cracked Tubular Joint Using Nonlinear Finite Element Analysis (Natarajan Vignesh Chellappan, Seeninaidu Nallayarasu)....Pages 395-416
Wave Transformation Due to Floating Elastic Thick Plate over Changing Bottom Topography (K. M. Praveen, D. Karmakar)....Pages 417-430
Installation Analysis of Monopile for Offshore Wind Data Collection Platform in High Tidal Environment (Devender Gujjula, Satya Kiran Raju Alluri, G. Dhinesh, R. Panneer Selvam, M. V. Ramana Murthy)....Pages 431-440
Analysis and Design of Guyed 120 m-Long Offshore Met Mast Supported on Suction Piles (Mallela Mounika, C. R. Suribabu, Satya Kiran Raju Alluri, M. V. Ramana Murthy)....Pages 441-450
Reliability-Based Multi-objective Optimization of Offshore Jacket Structures (Vishnu Murali)....Pages 451-461
Dynamic Behaviour of Inverted Catenary Cold Water Pipelines for Seawater Desalination Project (R. Saravanan, S. K. Bhattacharya, M. V. Ramana Murthy)....Pages 463-477
Optimization Study of Eight-Legged Fixed Offshore Jacket Platform (V. Suryaprakash, N. Sunil Kumar)....Pages 479-486
Front Matter ....Pages 487-487
Comparative Study of Breaking Wave Forces on a Quasi-Prototype Recurved Seawall (R. Ravindar, V. Sriram, Stefan Schimmels, Dimitris Stagonas)....Pages 489-501
Optimisation of Layout of Semi-enclosed Basin in Micro Tidal Region to Minimise Siltation for Mega Ship by FEM (Anil Anant Purohit, Mandar Mohan Vaidya)....Pages 503-520
Evolving Fishing Harbour Layout by Wave Tranquility Study Using Mathematical Model—A Case Study (J. D. Agrawal, H. C. Patil, Sagar Chanda, T. Nagendra)....Pages 521-533
Shoreline Change Associated with Coastal Structures at Gopalpur Port, Odisha, East Coast of India (Prabin Kumar Kar, Pratap Kumar Mohanty, Balaji Behera)....Pages 535-547
Experimental Studies on Hydrodynamic Performance of an Artificial Reef ( Lokesha, S. A. Sannasiraj, V. Sundar)....Pages 549-558
Prediction of Wave Transmission over an Outer Submerged Reef of Tandem Breakwater Using RBF-Based Support Vector Regression Technique (Geetha Kuntoji, Subba Rao, Manu)....Pages 559-570
Assisting Pumps for Dredging (Mridul K. Sarkar, Sritama Sarkar)....Pages 571-579
A Study to Identify Locations Suitable of Deep Sea Port Operations in the State of West Bengal (Bal Krishna, B. Chaudhuri, P. K. Bhaskaran)....Pages 581-598
Interaction of Wave with an Open Caisson (Yan-Xiang Lin, Da-Wei Chen, Jiahn-Horng Chen)....Pages 599-613
Layout, Foundation Design, and Dredging Methodology of Multipurpose Terminal (R. Sundaravadivelu, M. Sasirekha, S. Kreesa Kumaran, S. M. Madhumathy)....Pages 615-625
Front Matter ....Pages 627-627
Study on Suitable Electrode for Energy Harvesting Using Galvanic Cell in Seawater (G. Nithya Sivakami, V. T. Perarasu, S. Sakthivel Murugan)....Pages 629-638
Surrogate-Based Optimization of a Biplane Wells Turbine (Tapas K. Das, Abdus Samad)....Pages 639-648
Tidal Energy Estimation of Potential Tidal Inlets Along the East Coast of India (Vikas Mendi, N. Amaranatha Reddy, Jaya Kumar Seelam, Subba Rao)....Pages 649-674
Optimal Design of a Marine Current Turbine Using CFD and FEA (Thandayutham Karthikeyan, Lava Kush Mishra, Abdus Samad)....Pages 675-690
Offshore Energy for the Remote Islands of Lakshadweep (K. Srilakshmi, Satya Kiran Raju Alluri, Manu)....Pages 691-703
Control-Oriented Wave to Wire Model of Oscillating Water Column (R. Suchithra, Abdus Samad)....Pages 705-716
Hysteresis Behavior for Wave Energy Conversion Device Under Alternative Axial Flow Conditions (Paresh Halder, Tapas K. Das, Abdus Samad, Mohaned H. Mohamed)....Pages 717-723
Ocean Current Measurements and Energy Potential in the Islands of Andaman (Biren Pattanaik, D. Nagasamy, YVN Rao, Balaji Chandrakanth, Nitinesh Awasthi, Abhijeet Sajjan et al.)....Pages 725-736
Explicit Structural Response-Based Methodology for Assessment of Operational Limits for Single Blade Installation for Offshore Wind Turbines (Amrit Shankar Verma, Yuna Zhao, Zhen Gao, Nils Petter Vedvik)....Pages 737-750
Influence of Harbour Wall on Pressure Variation in an Oscillating Water Column (D. Daniel Raj, V. Sundar, S. A. Sannasiraj)....Pages 751-763
Evaluation of Natural Period of Offshore Tension Leg Platform Wind Turbine Experimental Studies (Madhuri Seeram, G. Satya Sravya, K. Venkateswara Rao)....Pages 765-774
Open Sea Trials on Floating Wave Energy Device Backward Bent Ducted Buoy and Its Performance Optimization (Biren Pattanaik, D. Nagasamy, A. Karthikeyan, D. Leo, Y. V. Narasimha Rao, K. S. Sajeev et al.)....Pages 775-791
Numerical Investigation of Semi-submersible Floating Wind Turbine Combined with Flap-Type WECs (A. K. Kumawat, D. Karmakar, C. Guedes Soares)....Pages 793-805
Effects of Power Take-Off Damping and Model Scaling on the Hydrodynamic Performance of Oscillating Water Column Device (S. John Ashlin, S. A. Sannasiraj, V. Sundar, Arun Kamath, Hans Bihs)....Pages 807-821
Offshore Wind Energy Potential Assessment of India Based on the Synergetic Use of QuikSCAT, OSCAT and ASCAT Scatterometers Data (Surisetty V. V. Arun Kumar, Jagdish Prajapati, Raj Kumar)....Pages 823-834
Hydrodynamic Study of Flow Past Cylinders with Different Diameters at High Reynolds Number (Kumar Narendran, Kumar Varma Kolahalam Vinay, Kantharaj Murali, Salem Kaushik)....Pages 835-855
Experimental Study on Heave and Yaw Motions of a 1:30 Spar Support for Offshore Wind Turbines (Carlo Ruzzo, Nilanjan Saha, Felice Arena)....Pages 857-868
Performance Simulation of Wave-Powered Navigational Buoy Using CFD and Experimental Study (Ashwani Vishwanath, Nitinesh Awasthi, Purnima Jalihal, Prasad Dudhgaonkar)....Pages 869-882
Performance Evaluation of Floating Two-Body Wave Energy Converter with Hydraulic Power Take-Off System (Sudharsan Kalidoss, Arindam Banerjee)....Pages 883-897
Pitch Motion Studies of Barge Supporting 5-MW-NREL Offshore Floating Wind Turbine with Gyrostabilizer (P. Manmathakrishnan, R. Panneer Selvam)....Pages 899-911
Wave Energy Conversion by Multiple Bottom-Hinged Surging WEC (A. K. Kumawat, D. Karmakar, C. Guedes Soares)....Pages 913-929

Citation preview

Lecture Notes in Civil Engineering

K. Murali V. Sriram Abdus Samad Nilanjan Saha   Editors

Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018) Volume 2

Lecture Notes in Civil Engineering Volume 23

Series editors Marco di Prisco, Politecnico di Milano, Milano, Italy Sheng-Hong Chen, School of Water Resources and Hydropower Engineering, Wuhan University, Wuhan, China Ioannis Vayas, National Technical University of Athens, Zografou Campus, Zografou, Greece Sanjay Kumar Shukla, School of Engineering, Edith Cowan University, Joondalup, Perth, Australia Giovanni Solari, University of Genoa, Genova, Italy Anuj Sharma, Iowa State University, Ames, IA, USA Nagesh Kumar, Department of Civil Engineering, Indian Institute of Science Bangalore, Bangalore, Karnataka, India Chien Ming Wang, School of Civil Engineering, The University of Queensland, St Lucia, QLD, Australia

Lecture Notes in Civil Engineering (LNCE) publishes the latest developments in Civil Engineering - quickly, informally and in top quality. Though original research reported in proceedings and post-proceedings represents the core of LNCE, edited volumes of exceptionally high quality and interest may also be considered for publication. Volumes published in LNCE embrace all aspects and subfields of, as well as new challenges in, Civil Engineering. Topics in the series include: – – – – – – – – – – – – – –

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More information about this series at http://www.springer.com/series/15087

K. Murali V. Sriram Abdus Samad Nilanjan Saha •

•

Editors

Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018) Volume 2

123

Editors K. Murali Department of Ocean Engineering Indian Institute of Technology Madras Chennai, Tamil Nadu, India

Abdus Samad Department of Ocean Engineering Indian Institute of Technology Madras Chennai, Tamil Nadu, India

V. Sriram Department of Ocean Engineering Indian Institute of Technology Madras Chennai, Tamil Nadu, India

Nilanjan Saha Department of Ocean Engineering Indian Institute of Technology Madras Chennai, Tamil Nadu, India

ISSN 2366-2557 ISSN 2366-2565 (electronic) Lecture Notes in Civil Engineering ISBN 978-981-13-3133-6 ISBN 978-981-13-3134-3 (eBook) https://doi.org/10.1007/978-981-13-3134-3 Library of Congress Control Number: 2018960240 © Springer Nature Singapore Pte Ltd. 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Organising Committee

Advisory Committee B. Ramamurthi, Director, IITM Patron and Chairman The Head, Department of Ocean Engineering, IITM Vice Chairman Director, CWPRS Member Chairman, CWC Member Chairman, Chennai Port Trust Member Chairman, Ennore Port Limited Member Vice Chancellor, Indian Maritime University Member Director, INCOIS and NIOT Member Director, NIO Member CMD, DCI Member Organizing Secretary, ICOE2018, Convener

Scientific Committee Shinji Sato, Japan Tomoya Shibayama, Japan Hitoshi Tanaka, Japan Kyung-Duck Suh, Korea Holger Schüttrumpf, Germany Peter Fröhle, Germany Qingwei Ma, UK Perumal Nithiarasu, UK M. R. Dhanak, USA Krish Thiagarajan, USA Zhenhua Huang, USA Felice Arena, Italy

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Roberto Tomasicchio, Italy P. Ferrant, France Ioan Nistor, Canada P. Lin, China Decheng Wan, China Adrian Law, Singapore Inigo-Losada, Spain T. E. Baldock, Australia Ron Cox, Australia Enrique Alvarez Del Rio, Mexico Janaka Wijetunga, Sri Lanka K. H. Kim, Korea Shin Hyung Rhee, Korea Richard Manasseh, Australia M. C. Deo, India R. Sundaravadivelu, India V. Sundar, India A. D. Rao, India P. K. Bhaskaran, India D. Sen, India Ira Didenkulova, Russia Efim Pelinovsky, Russia

Local Organizing Committee S. A. Sannasiraj, IITM, Chennai K. Murali, IITM, Chennai V. Sundar, IITM, Chennai R. Sundaravadivelu, IITM, Chennai V. Anantha Subramaniam, IITM, Chennai S. K. Bhattacharya, IITM, Chennai S. Nallayarasu, IITM, Chennai P. Ananthakrishnan, IITM, Chennai P. Krishnankutty, IITM, Chennai S. Surendran, IITM, Chennai R. Panneer Selvam, IITM, Chennai Srinivasan Chandrasekaran, IITM, Chennai G. Suresh Kumar, IITM, Chennai P. Shanmugam, IITM, Chennai Nilanjan Saha, IITM, Chennai Rajiv Sharma, IITM, Chennai Jitendra Sangwai, IITM, Chennai Rajesh Nair, IITM, Chennai

Organising Committee

Organising Committee

Abdus Samad, IITM, Chennai Deepak Kumar, IITM, Chennai V. Sriram, IITM, Chennai Tarun K. Chandrayadula, IITM, Chennai R. Vijayakumar, IITM, Chennai Suresh Rajendran, IITM, Chennai J. Purnima, NIOT, Chennai

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Preface

The Fourth International Conference in Ocean Engineering (ICOE2018) is organized by the Department of Ocean Engineering, Indian Institute of Technology Madras (IITM). The Department of Ocean Engineering has achieved significant success with a dynamic profile in terms of training graduate and postgraduate professionals for careers across the globe. The department is a centre of excellence in disciplines spanning across the areas of ship design, coastal and harbour structures, deep-water technologies, marine geo-techniques, energy and areas in oil and gas. The department organized its flagship conference ICOE in 1996, 2001 and 2009. This conference is aimed at bringing experts in the field to interact with young researchers. The main theme of the conference is “Emerging Opportunities and Challenges in Ocean Engineering”. It is aimed at addressing the upstream challenges in ocean engineering. Thus, the Fourth International Conference in Ocean Engineering 2018 (ICOE2018) offers an exciting platform for academicians, engineers from industry, policymakers and administrators from all over the globe to deliberate on various conference themes. The technical programme of the conference has been carefully planned with eight keynote addresses from experts from USA, UK, Norway, South Korea, India and Italy, 149 contributed papers and special sessions in the modernization of ports, hydrodynamics, ocean energy and naval architecture with invited speakers. All the papers accepted in this conference have been reviewed by experts in the procedure of blind peer review and subsequently revised by the authors incorporating the remarks and suggestions of the reviewers and thus improving the quality of the contributions. These papers will be published in two volumes in Springer book series “Lecture Notes in Civil Engineering”. The present second volume consists of papers in the areas of coastal, sediment and hydrodynamics; port, harbour and coastal structures; offshore structures and deep-water technology and ocean renewable energy. We would like to thank the members of the Advisory Committee, International Steering Committee, Local Organizing Committee and the reviewers, who have greatly contributed to the improvement of the quality of papers, providing constructive critical comments, corrections and suggestions to the authors. Finally, we ix

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Preface

wish to thank all the authors who submitted papers, making this conference possible. It is the quality of their contributions and presentations that really has made this conference a success and come up as a book volume. Chennai, India

Prof. K. Murali Dr. V. Sriram Dr. Nilanjan Saha Dr. Abdus Samad

Contents

Part I

Coastal, Sediment and Hydrodynamics

Spatial and Temporal Variability of Some Coastal Water Parameters at Selected Locations on the East Coast of India . . . . . . . . . . . . . . . . . . R. Gayathri, V. Ranga Rao, P. Madeswaran, V. Padmavathi, R. ManjuPriya, M. Arunvel and S. R. Kishore Baabu Laboratory Investigations on the Effect of Fragmentation and Heterogeneity of Coastal Vegetation in Wave Height Attenuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kiran G. Shirlal, Beena Mary John and Subba Rao Measurement of Surf Zone Hydrodynamics Along the Coastline of Pondicherry, India . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R. Balaji, M. V. Ramana Murthy and J. Satheeshkumar Beach Morphology Near the Inlet of Chilika Lagoon . . . . . . . . . . . . . . . Subhasis Pradhan, Pratap K. Mohanty, Rabindro N. Samal, Rabindra K. Sahoo, Rakesh Baral, Shraban K. Barik, Madan M. Mahanty and Sujit Mishra

3

13

25 35

Study of Bamboo Bandalling Structures in the Tidal River for River Bank Erosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Md. Lutfor Rahman

49

Development of Predictive Tool for Coastal Erosion in Arctic—A Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mohammad Saud Afzal and Raed Lubbad

59

Evaluation of Hydrodynamic Performance of Quarter Circular Breakwater Using Soft Computing Techniques . . . . . . . . . . . . . . . . . . . N. Ramesh, A. V. Hegde and Subba Rao

71

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xii

Contents

Statistical Analysis of Coastal Currents from HF Radar Along the North-Western Bay of Bengal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Samiran Mandal, Saikat Pramanik, Subrota Halder and Sourav Sil

89

Numerical Modelling and Experimental Investigation on the Effect of Wave Attenuation Due to Coastal Vegetation . . . . . . . . . . . . . . . . . . S. Hemavathi, R. Manjula and N. Ponmani

99

Studies on the Morphological Changes by Numerical Modeling Along Kakinada Coasts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 N. Sharmila, R. Venkatachalapathy and M. Mugilarasan Desk Studies and Modelling Sedimentation Pattern in Gulf of Khambhat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 L. R. Ranganath, A. V. Sriram and M. Karthikeyan Wave Climate and Nearshore Sediment Transport Pattern Along the SE Coast of India . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 V. Ranga Rao, Akhil Kolli, K. Stephen Raju and D. Kumaresan Nondimensional Methods to Classify the Tidal Inlets Along the Karnataka Coastline, West Coast of India . . . . . . . . . . . . . . . . . . . . 173 N. Amaranatha Reddy, Vikas Mendi, Jaya Kumar Seelam and Subba Rao Study of Dynamic Changes Through Geoinformatics Technique: A Case Study of Karwar Coast, West Coast of India . . . . . . . . . . . . . . . 185 Arunkumar Yadav, Basavanand M. Dodamani and G. S. Dwarakish An Experimental Study on Surface Wave Modulation Due to Viscoelastic Bottom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 Dharma Sree, Adrian Wing-Keung Law and Hayley H. Shen Spectral AB Simulations for Coastal and Ocean Engineering Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 R. Kurnia, P. Turnip and E. van Groesen Nearshore Hydrodynamics Near an Open Coast Harbour at Gopalpur, Central East Coast of India . . . . . . . . . . . . . . . . . . . . . . . 219 U. K. Pradhan, P. Mishra, P. K. Mohanty, U. S. Panda and M. V. Ramana Murthy Improving Hydraulic Conditions to Preserve Mangroves at Hazira . . . . 239 V. B. Sharma, A. K. Singh and Prabhat Chandra Hydrodynamic Modelling for Development of a Port in an Estuary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 A. K. Singh, L. R. Ranganath and M. Karthikeyan Wave Interaction with Multiple Submerged Porous Structures . . . . . . . 265 V. Venkateswarlu and D. Karmakar

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xiii

Beyond the Data Range Approach to Soft Compute the Reflection Coefficient for Emerged Perforated Semicircular Breakwater . . . . . . . . 281 Suman Kundapura, Arkal Vittal Hegde and Amit Vijay Wazerkar Design of a Reef for Coastal Protection . . . . . . . . . . . . . . . . . . . . . . . . . 293 P. V. Chandramohan Assessment of Littoral Drift and Shoreline Changes for Fisheries Harbour on East Coast of India . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 S. N. Jha and J. Sinha Impact of Flow-Driven Debris on Coastal Structure During Tsunami Bore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 S. Harish, V. Sriram, V. Sundar, S. A. Sannasiraj and I. Didenkulova Wave Transformation Around Submerged Breakwaters Made of Rubble Mound and Those Made of Geosynthetic Tubes—A Comparison Study for Kadalur Periyakuppam Coast . . . . . . . . . . . . . . 327 M. Kalyani, A. S. Kiran, Vijaya Ravichandran, V. Suseentharan, Basanta Kumar Jena and M. V. Ramana Murthy Study on Stability of Eden Navigational Channel in Hooghly River Estuary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 N. Saichenthur, K. Murali and V. Sundar Study on Maintenance Dredging for Navigable Depth Assurance in the Macro-tidal Hooghly Estuary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 V. Maheshvaran, K. Murali, V. Sundar and K. Chitra Migration of Chilika Lake Mouth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369 R. Sundaravadivelu, P. Shanmugam, A. K. Patnaik and P. K. Suresh Part II

Offshore Structures and Deepwater Technology

Coupled Dynamics of Deep Water Tension Leg Platforms Under Steep Regular Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 R. Jayalekshmi, R. Sundaravadivelu and V. G. Idichandy Residual Strength of Cracked Tubular Joint Using Nonlinear Finite Element Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 Natarajan Vignesh Chellappan and Seeninaidu Nallayarasu Wave Transformation Due to Floating Elastic Thick Plate over Changing Bottom Topography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417 K. M. Praveen and D. Karmakar Installation Analysis of Monopile for Offshore Wind Data Collection Platform in High Tidal Environment . . . . . . . . . . . . . . . . . . . 431 Devender Gujjula, Satya Kiran Raju Alluri, G. Dhinesh, R. Panneer Selvam and M. V. Ramana Murthy

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Contents

Analysis and Design of Guyed 120 m-Long Offshore Met Mast Supported on Suction Piles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441 Mallela Mounika, C. R. Suribabu, Satya Kiran Raju Alluri and M. V. Ramana Murthy Reliability-Based Multi-objective Optimization of Offshore Jacket Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451 Vishnu Murali Dynamic Behaviour of Inverted Catenary Cold Water Pipelines for Seawater Desalination Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463 R. Saravanan, S. K. Bhattacharya and M. V. Ramana Murthy Optimization Study of Eight-Legged Fixed Offshore Jacket Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 V. Suryaprakash and N. Sunil Kumar Part III

Port, Harbour and Coastal Structures

Comparative Study of Breaking Wave Forces on a Quasi-Prototype Recurved Seawall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489 R. Ravindar, V. Sriram, Stefan Schimmels and Dimitris Stagonas Optimisation of Layout of Semi-enclosed Basin in Micro Tidal Region to Minimise Siltation for Mega Ship by FEM . . . . . . . . . . . . . . . . . . . . 503 Anil Anant Purohit and Mandar Mohan Vaidya Evolving Fishing Harbour Layout by Wave Tranquility Study Using Mathematical Model—A Case Study . . . . . . . . . . . . . . . . . . . . . . 521 J. D. Agrawal, H. C. Patil, Sagar Chanda and T. Nagendra Shoreline Change Associated with Coastal Structures at Gopalpur Port, Odisha, East Coast of India . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535 Prabin Kumar Kar, Pratap Kumar Mohanty and Balaji Behera Experimental Studies on Hydrodynamic Performance of an Artificial Reef . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549 Lokesha, S. A. Sannasiraj and V. Sundar Prediction of Wave Transmission over an Outer Submerged Reef of Tandem Breakwater Using RBF-Based Support Vector Regression Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559 Geetha Kuntoji, Subba Rao and Manu Assisting Pumps for Dredging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571 Mridul K. Sarkar and Sritama Sarkar A Study to Identify Locations Suitable of Deep Sea Port Operations in the State of West Bengal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581 Bal Krishna, B. Chaudhuri and P. K. Bhaskaran

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Interaction of Wave with an Open Caisson . . . . . . . . . . . . . . . . . . . . . . 599 Yan-Xiang Lin, Da-Wei Chen and Jiahn-Horng Chen Layout, Foundation Design, and Dredging Methodology of Multipurpose Terminal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615 R. Sundaravadivelu, M. Sasirekha, S. Kreesa Kumaran and S. M. Madhumathy Part IV

Ocean Renewable Energy

Study on Suitable Electrode for Energy Harvesting Using Galvanic Cell in Seawater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629 G. Nithya Sivakami, V. T. Perarasu and S. Sakthivel Murugan Surrogate-Based Optimization of a Biplane Wells Turbine . . . . . . . . . . 639 Tapas K. Das and Abdus Samad Tidal Energy Estimation of Potential Tidal Inlets Along the East Coast of India . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 649 Vikas Mendi, N. Amaranatha Reddy, Jaya Kumar Seelam and Subba Rao Optimal Design of a Marine Current Turbine Using CFD and FEA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675 Thandayutham Karthikeyan, Lava Kush Mishra and Abdus Samad Offshore Energy for the Remote Islands of Lakshadweep . . . . . . . . . . . 691 K. Srilakshmi, Satya Kiran Raju Alluri and Manu Control-Oriented Wave to Wire Model of Oscillating Water Column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705 R. Suchithra and Abdus Samad Hysteresis Behavior for Wave Energy Conversion Device Under Alternative Axial Flow Conditions . . . . . . . . . . . . . . . . . . . . . . . . 717 Paresh Halder, Tapas K. Das, Abdus Samad and Mohaned H. Mohamed Ocean Current Measurements and Energy Potential in the Islands of Andaman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725 Biren Pattanaik, D. Nagasamy, YVN Rao, Balaji Chandrakanth, Nitinesh Awasthi, Abhijeet Sajjan, D. Leo, Prasad Dudhgaonkar and Purnima Jalihal Explicit Structural Response-Based Methodology for Assessment of Operational Limits for Single Blade Installation for Offshore Wind Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 737 Amrit Shankar Verma, Yuna Zhao, Zhen Gao and Nils Petter Vedvik Influence of Harbour Wall on Pressure Variation in an Oscillating Water Column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 751 D. Daniel Raj, V. Sundar and S. A. Sannasiraj

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Evaluation of Natural Period of Offshore Tension Leg Platform Wind Turbine Experimental Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765 Madhuri Seeram, G. Satya Sravya and K. Venkateswara Rao Open Sea Trials on Floating Wave Energy Device Backward Bent Ducted Buoy and Its Performance Optimization . . . . . . . . . . . . . . . . . . 775 Biren Pattanaik, D. Nagasamy, A. Karthikeyan, D. Leo, Y. V. Narasimha Rao, K. S. Sajeev, Prasad V. Dudhgaonkar and Purnima Jalihal Numerical Investigation of Semi-submersible Floating Wind Turbine Combined with Flap-Type WECs . . . . . . . . . . . . . . . . . . . . . . . 793 A. K. Kumawat, D. Karmakar and C. Guedes Soares Effects of Power Take-Off Damping and Model Scaling on the Hydrodynamic Performance of Oscillating Water Column Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 807 S. John Ashlin, S. A. Sannasiraj, V. Sundar, Arun Kamath and Hans Bihs Offshore Wind Energy Potential Assessment of India Based on the Synergetic Use of QuikSCAT, OSCAT and ASCAT Scatterometers Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823 Surisetty V. V. Arun Kumar, Jagdish Prajapati and Raj Kumar Hydrodynamic Study of Flow Past Cylinders with Different Diameters at High Reynolds Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835 Kumar Narendran, Kumar Varma Kolahalam Vinay, Kantharaj Murali and Salem Kaushik Experimental Study on Heave and Yaw Motions of a 1:30 Spar Support for Offshore Wind Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . 857 Carlo Ruzzo, Nilanjan Saha and Felice Arena Performance Simulation of Wave-Powered Navigational Buoy Using CFD and Experimental Study . . . . . . . . . . . . . . . . . . . . . . . . . . . 869 Ashwani Vishwanath, Nitinesh Awasthi, Purnima Jalihal and Prasad Dudhgaonkar Performance Evaluation of Floating Two-Body Wave Energy Converter with Hydraulic Power Take-Off System . . . . . . . . . . . . . . . . 883 Sudharsan Kalidoss and Arindam Banerjee Pitch Motion Studies of Barge Supporting 5-MW-NREL Offshore Floating Wind Turbine with Gyrostabilizer . . . . . . . . . . . . . . . . . . . . . . 899 P. Manmathakrishnan and R. Panneer Selvam Wave Energy Conversion by Multiple Bottom-Hinged Surging WEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 913 A. K. Kumawat, D. Karmakar and C. Guedes Soares

About the Editors

Prof. K. Murali is Professor in the Department of Ocean Engineering, IITM. He has authored about 100 publications in international conferences and journals and is the recipient of the Endeavour Research Fellowship from the Australian Government. He received a major research grant from ISRO for developing coastal research models after the Indian Ocean Tsunami. His field of research specialization is computational hydrodynamics. He has more than 20 years of consultancy experience in coastal and port engineering. He has completed 50 coastal protection design works in and around India. Dr. V. Sriram is Associate Professor in the Department of Ocean Engineering, IITM. He received the prestigious Newton International Fellowship (from the Royal Society, UK) in 2009, Alexander von Humboldt Fellowship (from AvH foundation, Germany) in 2011, DST INSPIRE Faculty Award (from DST) and RJ Garde Research Award (from Indian Society of Hydraulics). He is Visiting Researcher at City, University of London and Visiting Professor at Leibniz Universität Hannover, Germany. He has published more than 60 papers in international journals and conferences. His research work focuses on computational hydrodynamics. He has developed state-of-the-art numerical models applied to ocean engineering, particularly coastal and offshore engineering. Dr. Abdus Samad is Associate Professor in the Department of Ocean Engineering, IITM, working in the areas of marine energy, fluid mechanics and optimization. He has received several awards from various bodies, has published more than 100 articles in a number of journals and conferences and has filed several patents. He was Knowledge Transfer Associate in the UK from 2008 to 2010 and was a Brainpool Invited Scientist in South Korea during his sabbatical leave in 2016.

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About the Editors

Dr. Nilanjan Saha is Associate Professor in the Department of Ocean Engineering, IITM. He has published 20 papers in international journals and is the recipient of the IEI Young Engineer Award—Marine 2013 from the Institution of Engineers, India; Young Researcher Award—2013 from Ministry of Earth Sciences; and Hari Om Ashram Prerit Research Award. His interest includes stochastic analysis of marine structures. He is currently applying his knowledge in offshore renewable energy with an emphasis on extremes.

Part I

Coastal, Sediment and Hydrodynamics

Spatial and Temporal Variability of Some Coastal Water Parameters at Selected Locations on the East Coast of India R. Gayathri, V. Ranga Rao, P. Madeswaran, V. Padmavathi, R. ManjuPriya, M. Arunvel and S. R. Kishore Baabu

Abstract Seawater quality status of shore and offshore areas of four selected locations (Visakhapatnam, Kakinada, Ennore, and Pondicherry) along the east coast of India were studied based on the analysis of various water quality parameters (Temperature, pH, Dissolved Oxygen, Biological Oxygen Demand, Suspended Sediment Concentration, Nitrate, Phosphate, and Fecal Coliforms collected during 1993–2014 under the COMAPS program of ICMAM-PD, Ministry of Earth Sciences, Govt. of India. The National Sanitation Foundation Water Quality Index was used to estimate the indices for different seasons. The water quality parameters have strong seasonal and spatial variability along the coast. Higher concentration of BOD and SSC toward shore waters and lower concentration toward offshore is noticed. In Visakhapatnam and Kakinada, the nitrate and phosphate concentration was comparatively higher than Ennore and Pondicherry. The Fecal Coliform counts in the shore waters were significantly high for all the four locations. Computation of Water Quality Index based on different water quality parameters reveals that the water quality along these sites varied from ‘medium’ to ‘good’ depending on the location and the season. The analysis of the data clearly emphasize the need for continuous monitoring of these water quality parameters to maintain and preserve the water quality as well as the related coastal ecosystem productivity of the Indian coast. Further, comprehensive studies are required for the Indian coastal water to determine the relative weightages of various water quality parameters and to develop an optimum WQI index methodology. Keywords Temperature · Dissolved oxygen · Nitrates · Water quality index

R. Gayathri (B) · V. Ranga Rao · P. Madeswaran ICMAM-PD, NIOT Campus, Pallikaranai, Chennai 600100, India e-mail: [email protected] V. Padmavathi · R. ManjuPriya · M. Arunvel · S. R. Kishore Baabu Institute of Ocean Management, Anna University, Sardar Patel Road, Guindy, Chennai 600025, India © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_1

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1 Introduction Degradation of coastal water quality due to sewage runoff from land is a raising concern in the emerging scenario of urbanization and industrialization. The increase in temperature due to global warming, the excess nutrients from the sewage and fertilizers, and the chemicals from industries could adversely affect the water quality which, in turn, affects the health and wealth of marine biological production. Therefore, to achieve a sustainable management solution for improving the productivity of coastal and marine ecosystems, the assessment of coastal water quality is essential. As an initiation in this direction, ICMAM-PD, Ministry of Earth Sciences, Chennai is monitoring the coastal water quality parameters at regular monthly intervals along the Indian coast since 1993 under its COMAPS (Coastal Ocean Monitoring and Prediction System) and SWQM (Sea Water Quality Monitoring) programs. Extensive field data on various water quality parameters as per the standard COMAPS protocol [1] is being collected at selected locations along the Indian coast. In the present study, some of these data for selected coastal stations (Visakhapatnam, Kakinada, Ennore, and Pondicherry) was utilized to study the spatial and temporal variability of water quality along the east coast of India. A comparative study of these coastal water parameters for the four sites was carried out and presented in this paper.

2 Study Locations The four study locations (Fig. 1) chosen for the present study have different anthropogenic and natural influences due to urbanization and industrialization. Sewage is a major influence on coastal waters along all of these four locations. The Kakinada city located on the deltaic coast with major river influence and mangrove forest, which is rich in small water bodies and most of the adjacent agricultural lands are dependent on these water sources. Ennore is located on the northeast of Chennai and consists of alluvial tracts, beach dunes, tidal flats, and creeks. Ennore comprises lagoons, with salt marshes and backwaters, which are submerged under water during high tide and forms an arm of the sea opening into the Bay of Bengal. Puducherry historically known as Pondicherry is a tourist spot with intense urbanization facing various environmental problems especially erosion and sewage.

3 Data and Methodology The data for the present study was extracted from the COMAPS database, collected during the period 1993–2014, covering the shore and offshore areas of the selected locations of the Indian coast. In order to study the seasonal variability, all the collected data over different years have been segregated month wise and finally made into four

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Fig. 1 Study area and station locations

subdivisions of a year, i.e., (i) Pre monsoon (March, April, and May), (ii) Southwest monsoon (June, July, August, and September), (iii) Post monsoon (October and November), and (iv) Northeast monsoon (December, January, and February). The data of each parameter was seasonally averaged based on the available data period to obtain a representative value for each season. Based on this data, a detailed analysis of the seasonal variability of water quality parameters including temperature, pH, Dissolved Oxygen (DO), Biological Oxygen Demand (BOD), Suspended Sediment Concentration (SSC), Nitrate, Phosphate, and Fecal Coliforms (FC) was carried out. Further, the Water Quality Index (WQI) based on these parameters was computed by adopting the methodology of National Sanitation Foundation (NSF) [2, 3].

4 Results and Discussions 4.1 Spatial and Temporal Variations The seasonal variation in the mean values of various water quality parameter is presented elaborately in this section. Comparison of various sea water quality parameters of shore and offshore regions at the four selected stations on the east coast of India for different seasons are shown in Fig. 2a–i. In general, it is observed that BOD, SSC, Nitrate, Phosphate, and FC have higher concentrations inshore compared to that of the offshore region at all the four locations. This is a clear indication of the influence

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Fig. 2 2a–c—Distribution of water quality parameters (water temperature, salinity and pH) at shore and offshore areas of selected locations (Visakhapatnam, Kakinada, Ennore, and Puducherry) along the east coast of India; 2d–f—Distribution of water quality parameters (DO, BOD, and SSC) at shore and offshore areas of selected locations (Visakhapatnam, Kakinada, Ennore, and Puducherry) along the east coast of India; 2g–i—Distribution of water quality parameters (Nitrate, Phosphate, and FC) at shore and offshore areas of selected locations (Visakhapatnam, Kakinada, Ennore, and Puducherry) along the east coast of India

of land-derived material and their dispersion in the coastal waters. Along the shore, the comparatively higher temperature was observed. The variability in temperature (Fig. 2a–c) between shore and offshore peaked to about 1.5 °C during pre monsoon due to hot weather conditions. During winter, the lowest temperature was noticed

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Fig. 2 (continued)

in Kakinada and one of the possible reasons for this can be the advection of the freshwater from the rivers north of the location. As heat influences the chemical process and consequent life cycle of organisms, the water temperature controls the distribution of marine organisms and fishes [4], and therefore seasonal variations of water temperature may play a major role in biological production along the coast. However, the parameters such as salinity, pH exhibits relatively higher values in offshore waters compared to that inshore waters and hence they are influenced mostly by neritic waters. Visakhapatnam and Kakinada coastal waters show higher variability in pH between shore and offshore waters and thus it clearly indicates the impact of land-derived pollutants have an influence on water quality along these two

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Fig. 2 (continued)

coastal sites. However, at Ennore and Pondicherry, there is no significant variation in pH between shore and offshore waters. In general, the pH range at the four stations is within the range of 7.6–8.6 with a highest offshore value of 8.6 at Visakhapatnam. The DO concentration along the coastal water was within a range of 3–7 mg/l with no significant variability in the shore and offshore waters. The highest DO concentration was noted in the offshore waters during SW Monsoon and Post Monsoon. Similar to DO, the higher concentration of BOD was also observed during the SW Monsoon and Post Monsoon. The BOD values peaked to nearly 8 mg/l in the shore waters of Visakhapatnam, whereas the values were less than 3 mg/l for the rest of the locations. The nutrient distribution also indicated a higher concentration in Visakha-

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patnam and Kakinada. Compared to the Pondicherry and Ennore, the nitrate and phosphate values are several folds higher at these locations. This is undoubtedly the effect of the land runoff. Further, the effect of land runoff can be noted in the FC concentrations also.

4.2 Water Quality Status In order to study the status of water quality along the four locations, the data discussed above was utilized to calculate WQI. The index provides a single number (like a grade) that expresses overall water quality at a certain location and time based on several water quality parameters. WQI based on a few very important parameters can provide a simple indicator of water quality. It gives the public a general idea about the possible problems with the water in the region. Total Eight water quality parameters (DO, FC, pH, BOD, temperature change, total phosphate, nitrate, and total solids) were utilized to derive the index. The FC concentration of the coastal water was quite higher and hence the computed sub-index values were very low. Therefore separate calculation of WQI with and without FC was carried out. This type of WQI derived for the four locations Visakhapatnam, Kakinada, Ennore, and Pondicherry is shown in Fig. 3. The results indicate that without FC sub-index, except Visakhapatnam all the other three locations (Kakinada, Ennore, and Puducherry) showed good water quality along their respected coasts both inshore and offshore regions. However, Visakhapatnam coast showed medium water quality especially in the shore region which indicates clearly the influence of land-derived material along the coast. It can be expected as Visakhapatnam is one of the fast developing cities with most anthropogenic influence both in terms of urbanization and industrialization when compared to other three locations. The water quality status showed evident variations FC index was considered. The shore water quality shifted to medium from good water quality. This variability showed the importance of each parameter and their relative weightage in affecting the water quality. Therefore, the choice of water quality index method, the parameters and their relative weightage for a location need further investigation.

5 Conclusion Significant spatial and seasonal variability was noticed among various water quality parameters at Visakhapatnam, Kakinada, Ennore, and Pondicherry coastal waters. The variation of the parameters in the shore, and offshore locations clearly indicate that for parameters like temperature, suspended sediment concentration, and oxygen, the spatial variability for post monsoon was found negligible, however, there is a strong spatial variability for pH and BOD. The spatial distribution of nitrate throughout the season clearly indicated a higher concentration in the shore water and

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Fig. 3 Water quality index without FC(left panel) and with FC(right panel) for four seasons (Pre monsoon, SW monsoon, Post monsoon, and NE monsoon) along the four selected locations (Visakhapatnam, Kakinada, Ennore, and Pondicherry) along the east coast of India (dashed lines in the figure indicate the limits of appropriate water quality status, i.e., GOOD or MEDIUM)

it gradually decreased towards the offshore. An average value was computed from the shore, and offshore values and then the water quality index (WQI) was determined. The WQI based on the different parameters falls within a range of 60–90 indicating MEDIUM to GOOD coastal water quality. Without considering the FC, only the shore waters of Visakhapatnam showed MEDIUM water quality unlike the GOOD water quality of other locations. Though the present study indicated a good WQI, a regular assessment of the water quality is mandatory to maintain and preserve the coastal water quality and related ecosystem. Acknowledgements The authors wish to express their sincere thanks to Dr. M. Rajeevan, Secretary, Ministry of Earth Sciences, and Dr. M. V. Ramana Murthy, Head, ICMAM, for their keen interest and encouragement. The four authors (V. Padmavathi, R. ManjuPriya, M. Arunvel and S. R. Kishore Baabu) express their gratitude to Prof. S. Srinivasalu, Director, IOM (Anna University) and to Dr. P. Madeswaran, and Dr. V. Ranga Rao for providing the necessary permissions and facilities to do an internship at ICMAM for a period of 2 months in the field of seawater quality studies. The authors are thankful to ICMAM for providing the required data for the present study.

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References 1. ICMAM (2012) COMAPS water quality measurement protocol. Accessed on Sept 2017. http:// www.icmam.gov.in/pub.htm 2. Brown RM, McClelland NI, Deininger RA, Tozer RG (1970) A water quality index—do we dare 3. Mitchell MK, Stapp William B (2000) Field manual for water quality monitoring 4. Reddy MPM (2001) Descriptive physical oceanography 5. Calculating NSF water quality index. Des Moines River Water Quality Network: Annual Reports, 26 April 2011. home.eng.iastate.edu/~dslutz/dmrwqn/water_quality_index_calc.htm

Laboratory Investigations on the Effect of Fragmentation and Heterogeneity of Coastal Vegetation in Wave Height Attenuation Kiran G. Shirlal, Beena Mary John and Subba Rao

Abstract It has long been known that “bio-shields” do function as a sustainable solution for preserving our coasts. The presence of gaps in the “bio-shield”, that is, the forest cover, referred to as patchiness, is a common phenomenon in natural habitats. Various anthropogenic and natural causes can result in such gaps in coastal forests. This paper presents the results of a physical model investigation carried out with a fragmented heterogeneous vegetation model in a wave flume 50 m long, 0.71 m wide and 1.1 m deep. The heterogeneous meadow is modelled as a combined body of artificial submerged seagrass, rigid vegetation and emergent vegetation. To study the effect of fragmentation in vegetation, transverse gaps of varying widths are introduced in the heterogeneous model. The material used for modelling is polyethylene and nylon. The test runs were carried out with monochromatic waves of heights ranging from 0.08 to 0.16 m in water depths of 0.40 and 0.45 m, and wave periods 1.8 and 2 s. The wave height measurements at different locations within the vegetated meadow exhibit an exponential decay of wave heights. The presence of gaps in vegetation does not have a significant effect on wave height reduction. However, the experimental study revealed that heterogeneous vegetation showed a great promise leading to considerable wave attenuation, thus offering a good level of protection to life and property on the leeside. Keywords Coastal vegetation · Heterogeneity · Fragmentation · Gap Wave attenuation

K. G. Shirlal (B) · B. M. John · S. Rao National Institute of Technology Karnataka, Surathkal, Mangalore 575025, Karnataka, India e-mail: [email protected] S. Rao e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_2

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1 Introduction In the past decades, the world has witnessed a series of disasters in the form of storm surges, erosion, cyclones and tsunamis. Reports of coastal bio-shields protecting lives and settlements from the 1999 Odisha super cyclone [1] and the 2004 Indian Ocean tsunami [2–4], led to the widespread acceptance of ecosystem-based coastal protection measures to reduce the vulnerability of coastal communities from natural hazards. Coastal ecosystems such as seagrasses, mangroves, kelp forests, dune vegetation, coral reefs and many others do play a significant role in protecting the shoreline from intense wave activity, erosion and other hazards. Numerous theoretical, experimental and field studies have established the role of seagrasses and mangroves in attenuating the incident wave heights [5–10]. Seagrasses and mangroves are two different species of angiosperms which have colonized the sea, despite the hostile environments they live in; high salinity, wave action and fluctuating water levels [11]. Seagrass beds and mangrove habitats may be closely linked: “seagrass beds often grow in close proximity to mangroves and coral reefs, and the ecosystems are often closely linked through fluxes of carbon and other materials” [11]. They also share some of the fauna and these faunal movements provide an important functional link between these ecosystems. The ability of individual natural habitats such as seagrasses, coral reefs, salt marshes and mangroves to protect the shoreline against the fury of intense wave activity and storm surges is well known, but it is still uncertain how these habitats can complement each other in containing these impacts on the shoreline [12]. This study attempts to quantify the wave height attenuation due to the heterogeneous vegetation. Another noticeable phenomenon in natural coastal habitats is the presence of gaps in the forest cover. This may be due to the impacts of climate change scenarios or increased anthropogenic activities. These fragmented vegetated meadows may alter its hydrodynamics. Fragmentation and heterogeneity of the vegetated meadow results in wave height attenuation, which is investigated in this study.

2 Objective The present experimental investigation aims to determine the wave height attenuation, expressed in terms of percentage reduction in wave heights, through the fragmented heterogeneous vegetation models of varying gap widths.

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3 Materials and Methods An experimental study with fragmented heterogenous vegetation consisting of a combination of simulated submerged seagrass model, submerged rigid vegetation model and an emergent trunk model with roots, with transverse gaps of varying widths is conducted in the wave flume of Marine Structures Laboratory of the Department of Applied Mechanics and Hydraulics, National Institute of Technology Karnataka, Surathkal to study the wave height attenuation characteristics. The experiments are performed in a 50 m × 0.71 m × 1.1 m wave flume. This flume facility has a wave-generating chamber with a bottom-hinged paddle at one end and a porous beach which absorbs the wave energy at the other end. The paddle is controlled by an induction motor of 11 kW power at 1450 rpm, regulated by an inverter drive (0–50 Hz), rotating with a speed range of 0–155 rpm. The motor is linked to the flap by means of a flywheel and a bar-chain. Capacitance-type wave probes, along with its amplification units are used for collecting the data during the experimental runs. The spacing between probes is adjusted approximately to one-third of the wavelength as per the method proposed by [13]. Corresponding to each wave period, wave heights of 0.08, 0.10, 0.12, 0.14 and 0.16 m are generated. The wave surface elevation, measured by the wave probes are converted to electrical signals and is stored in digital form by a software controlled 12-bit A/D converter. The test model is a fragmented heterogeneous vegetation model, which consists of three sections: a submerged seagrass model of width 2 m, a submerged rigid vegetation model of width 2 m and an emergent trunk model with roots of width 2 m, separated by transverse gaps of varying widths. The seagrass model consists of simulated seagrass plants with stipes of height 0.01 m and leaves of length 0.21 m. Each simulated plant is composed of 4–5 polyethylene leaves, which is attached to a 0.5 m × 0.73 m × 0.02 m concrete slab. The rigid plant model, of plant density 394 trunks/m2 , consists of rigid nylon rods of 0.21 m length and 0.010 m diameter fixed in holes drilled in concrete slabs of 0.5 m × 0.73 m × 0.04 m. The emergent trunk model with roots consists of trunks of 0.016 m diameter and 0.50 m length. The roots are 0.010 m in diameter and length 0.25 m for Root Type I and 0.006 m in diameter and length 0.21 m for Root Type II. The density of trunks, root type I and root type II is 107 trunks/m2 , 300 roots/m2 and 300 roots/m2 respectively. This model is fabricated by fixing rigid nylon rods of varying dimensions specified above, in holes drilled in 0.5 m × 0.73 m × 0.04 m concrete slabs. The construction details of the simulated plant meadows are indicated in Fig. 1. The wave flume and the wave probes are calibrated before the start of the experimental runs. The 1:30 scale simulated heterogeneous model fabricated in the laboratory is placed at 30 m away from the generator flap. Gaps of varying widths are provided between the individual models of seagrass, submerged rigid vegetation and emergent trunks with roots. The experimental setup is as schematized in Fig. 2.

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Fig. 1 Construction details of simulated plant meadows. a Seagrass, b rigid submerged vegetation, c emergent trunks with roots (side and top view)

Fig. 2 Schematic representation of experimental setup

The test model is subjected to monochromatic waves of heights 0.08–0.16 m and wave periods ranging from 1.4 to 2 s in water depths of 0.40–0.45 m. To study the effect of fragmented heterogeneous vegetation on wave height attenuation, gaps of width (wgap ) 1.5–2.25 m are introduced in the heterogeneous model. The gap width parameter, given by wgap /w, for the above three cases is correspondingly equal to 0.25–0.375. Here, w is the width of the heterogenous model which is equal to 6 m. The photographs of model setup to investigate the wave height attenuation over a fragmented heterogeneous model is as shown in Fig. 3 and the vegetation characteristics and the experimental conditions are described in Table 1.

4 Results As the wave propagates through the initial stretch of submerged seagrass, the leaves of the seagrass interfere with the particle orbital velocities, which lead to wave height attenuation. As the propagating wave further encounters a gap, that is, a zone free of vegetation, there is no significant decrease in wave heights, which again gets attenuated while it passes through the submerged rigid vegetation. The wave again

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Fig. 3 Snapshots of model setup of a fragmented heterogeneous model Table 1 Plant characteristics and experimental conditions Simulated plant type

Vegetation model characteristics

Wave height (m)

Wave period, T (s)

Water depth, d (m)

Seagrass

Modulus of elasticity

0.6 GPa

0.08, 0.10, 0.12, 0.14, 0.16

1.4, 1.6, 1.8, 2

0.40, 0.45

Thickness of leaf

0.0001 m

Length of leaf

0.21 m

0.08, 0.10, 0.12, 0.14, 0.16

1.4, 1.6, 1.8, 2

0.40, 0.45

0.08, 0.10, 0.12, 0.14, 0.16

1.4, 1.6, 1.8, 2

0.40, 0.45

Rigid vegetation

Emergent trunk model with roots

Width of leaf

0.004 m

Plant density

10,000 shoots/m2

Modulus of elasticity

3 GPa

Length of rod

0.21 m

Diameter of rod

0.010 m

Density

394 plants/m2

Modulus of elasticity

3 GPa

Length of trunk

0.5 m

Diameter of trunk

0.016 m

Density of trunks

107 trunks/m2

Length of root 1

0.21 m

Diameter of root 1

0.010 m

Density of roots I

300 roots/m2

Length of root II

0.16 m

Diameter of root II 0.006 m Density of roots II

300 roots/m2

confronts a gap, which then passes over the emergent trunk model with roots, where there is a significant reduction of wave heights. This is due to the presence of emergent trunks as well as the roots of the model, which interferes with the particle orbital velocities, and an increased turbulence is observed which leads to an increased wave

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height attenuation. This attenuation is measured in terms of the percentage reduction in wave heights as the wave passes through the fragmented heterogeneous vegetation model. The variation of percentage reduction in wave heights with an increase in wave steepness parameter, Hi /gT2 for the simulated models of varying gap width parameters, wgap /w  0.25, 0.375 is discussed in the following paragraphs.

4.1 Gap Width Parameter, Wgap /W  0.25

Percentage reduction in wave heights

Percentage reduction in wave heights

For the fragmented heterogeneous model of gap width parameter, wgap /w  0.25 and relative plant height, hs /d  1.25, Fig. 4a–d depicts the influence of wave steepness parameter, Hi /gT2 on percentage wave height reduction.

80% 76% 72% 68% 64% 60% 0.004

0.006

76% 72% 68% 64% 60% 0.002

0.008

0.003

0.004

0.005

0.006

0.007

Hi/gT2

Hi/gT2

(a) for w/L = 2.508, T = 1.4 s

(b) for w/L = 2.142, T = 1.6 s

80%

Percentage reduction in wave heights

Percentage reduction in wave heights

0.002

80%

76% 72% 68% 64% 60% 0.002

0.003

0.004

0.005

0.006

Hi/gT2

(c) for w/L = 1.835, T = 1.8 s

80% 76% 72% 68% 64%

60% 0.002

0.003

0.004

0.005

Hi/gT2

(d) for w/L = 1.623, T = 2 s

Fig. 4 Variation of percentage wave height reduction with Hi /gT2 (hs /d  1.25, wgap /w  0.25)

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76%

72%

68%

64%

60% 0.004

0.006

0.008

Percentage reduction in wave heights

Percentage reduction in wave heights

It is noted that there is a decrease in wave height reduction from 75.00% to 70.00% as the wave steepness parameter, Hi /gT2 increases from 0.00416 to 0.00832 (w/L  2.508, T  1.4 s), from 73.75% to 67.50%, 72.50% to 65.00% and from 71.25% to 64.38% for wave steepness parameters ranging from 0.00318 to 0.00637 (w/L  2.142, T  1.6 s), 0.00251 to 0.00503 (w/L  1.835, T  1.8 s) and 0.00203 to 0.00407 (w/L  1.623, T  2 s), respectively. Figure 5a–d depicts the influence of wave steepness parameter, Hi /gT2 on percentage wave height reduction for the same fragmented heterogeneous model of relative plant height, hs /d  1.11. It is noted that there is a decrease in wave height reduction from 71.25% to 66.25% as the wave steepness parameter, Hi/gT2 increases from 0.00416 to 0.00832 (w/L  2.411, T  1.4 s), from 68.75% to 63.13%, 66.25% to 61.88% and from 65.00% to 59.38% for wave steepness parameters ranging from 0.00318 to 0.00637 (w/L  2.089, T  1.6 s), 0.00251 to 0.00503 (w/L  1.750, T  1.8 s) and 0.00203 to 0.00407 (w/L  1.546, T  2 s), respectively. 70% 68% 66% 64% 62% 60% 0.002 0.003 0.004 0.005 0.006 0.007

Hi/gT2

Hi/gT2

(b) for w/L = 2.089, T = 1.6 s Percentage reduction in wave heights

Percentage reduction in wave heights

(a) for w/L = 2.411, T = 1.4 s 70% 68% 66% 64% 62% 60% 0.002

0.003

0.004

0.005

Hi/gT2

(c) for w/L = 1.750, T = 1.8 s

68% 64% 60% 56% 52% 0.002 0.0025 0.003 0.0035 0.004 0.0045 Hi/gT2

(d) for w/L = 1.546, T = 2 s

Fig. 5 Variation of percentage wave height reduction with Hi /gT2 (hs /d  1.11, wgap /w  0.25)

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4.2 Gap Width Parameter, Wgap /W  0.375

Percentage reduction in wave heights

Percentage reduction in wave heights

As the gap width parameter, wgap /w increases from 0.25 to 0.375, the percentage wave height reduction increases for both relative plant heights, hs /d  1.25, 1.11 as depicted in Figs. 6 and 7. Figure 6a–d depicts the influence of wave steepness parameter, Hi /gT2 on percentage wave height reduction for the fragmented heterogeneous model of gap width parameter, wgap /w  0.375 and relative plant height, hs /d  1.25. It is noted that there is a decrease in wave height reduction from 76.25% to 70.63% as the wave steepness parameter, Hi /gT2 increases from 0.00416 to 0.00832 (w/L  2.508, T  1.4 s), from 75.00% to 69.38%, 73.75% to 67.50% and from 72.50% to 66.88% for wave steepness parameters ranging from 0.00318 to 0.00637 (w/L  2.142, T  1.6 s), 0.00251

80%

76%

72%

68%

0.002

0.004

0.006

80%

76%

72%

68%

0.002

0.008

76%

72%

68%

0.003

0.004

0.004

0.005

0.006

0.007

(b) for w/L = 2.142, T = 1.6 s Percentage reduction in wave heights

Percentage reduction in wave heights

(a) for w/L = 2.508, T = 1.4 s

0.002

0.003

Hi/gT2

Hi/gT2

0.005

Hi/gT2

(c) for w/L = 1.835, T = 1.8 s

76%

72%

68%

0.002 0.0025 0.003 0.0035 0.004 0.0045 Hi/gT2

(d) for w/L = 1.623, T = 2 s

Fig. 6 Variation of percentage wave height reduction with Hi /gT2 (hs /d  1.25, wgap /w  0.375)

76%

Percentage reduction in wave heights

Percentage reduction in wave heights

Laboratory Investigations on the Effect of Fragmentation …

72%

68%

0.004

0.006

72%

70%

68%

66%

0.008

0.002

Hi/gT2

66%

64%

0.004

0.004

0.005

0.006

0.007

0.005

Hi/gT2

(c) for w/L = 1.750, T = 1.8 s

(b) for w/L = 2.089, T = 1.6 s Percentage reduction in wave heights

Percentage reduction in waveheights

68%

0.003

0.003

Hi/gT2

(a) for w/L = 2.411, T = 1.4 s

0.002

21

66%

64%

62%

60% 0.002 0.0025 0.003 0.0035 0.004 0.0045 Hi/gT2

(d) for w/L = 1.546, T = 2 s

Fig. 7 Variation of percentage wave height reduction with Hi /gT2 (hs /d  1.11, wgap /w  0.375)

to 0.00503 (w/L  1.835, T  1.8 s) and 0.00203 to 0.00407 (w/L  1.623, T  2 s), respectively. For the same model of relative plant height, hs /d  1.11, it is noted from Fig. 7a–d that there is a decrease in wave height reduction from 72.50% to 68.13% as the wave steepness parameter, Hi /gT2 increases from 0.00416 to 0.00832 (w/L  2.411, T  1.4 s), from 70.00% to 67.50%, 67.50% to 65.00% and from 65.00% to 61.25% for wave steepness parameters ranging from 0.00318 to 0.00637 (w/L  2.089, T  1.6 s), 0.00251 to 0.00503 (w/L  1.750, T  1.8 s) and 0.00203 to 0.00407 (w/L  1.546, T  2 s), respectively. The findings from this study reveal that the heterogeneous model consisting of seagrass meadow, rigid submerged model as well as the emergent trunk model with roots shows a considerable reduction in wave heights and is, therefore, a viable option for providing a good level of protection of the shoreline from intense wave activity and storm surge events.

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5 Conclusions Based on the present experimental study, the following conclusions are drawn: • The important parameters that influence the wave height attenuation are: the relative plant height (hs /d), meadow width parameter (w/L) and gap width parameter (wgap /w). • As the relative plant height (hs /d) increases from 1.11 to 1.25 (12.6%), the simulated models exhibit an increased percentage wave height reduction ranging from 75.00% to 64.38% and from 76.25% to 66.88% for the fragmented heterogeneous vegetation model of gap width parameter, wgap /w  0.25 and 0.375, respectively. • The fragmented heterogeneous vegetation model with wgap /w  0.375 exhibits the highest wave height attenuation of 76.25% to 66.88% for hs /d  1.25, owing to the increase in meadow width due to the presence of gaps in vegetation. • The best vegetation model among the present sets of experimental investigations is, therefore, represented by the fragmented heterogeneous vegetation model of the gap with parameter, wgap /w  0.375.

References 1. Das S, Vincent JR (2009) Mangroves protected villages and reduced death toll during Indian super cyclone. Proc Natl Acad Sci 106(18):7357–7360 2. Jayakumar S, Ilangovan D, Naik KA, Gowthaman R, Tirodkar G, Naik GN, Ganeshan P, Mani Murali R, Michael GS, Ramana MV, Bhattacharya GC (2005) Run-up and inundation limits along southeast coast of India during the 26 December 2004 Indian Ocean tsunami. Curr Sci 88(11):1741–1743 3. Kathiresan K, Rajendran N (2005) Coastal mangrove forests mitigated tsunami. Estuar Coast Shelf Sci 67(3):601–606 4. Mascarenhas A, Jayakumar S (2008) An environmental perspective of the post-tsunami scenario along the coast of Tamil Nadu, India: role of sand dunes and forests. J Environ Manage 89(1):24–34 5. Asano T, Deguchi H, Kobayashi N (1992) Interaction between water waves and vegetation. In: Proceedings of 23rd international conference on coastal engineering, Venice, Italy, pp 2710–2723 6. Ciraolo G, Ferreri GB, Loggia LG (2006) Flow resistance of Posidonia oceanica in shallow water. J Hydraul Res 44(2):189–202 7. Fonseca MS, Cahalan JA (1992) A preliminary evaluation of wave attenuation by four species of seagrass. Estuar Coast Shelf Sci 35(6):565–576 8. Gambi MC, Nowell ARM, Jumars PA (1990) Flume observations on flow dynamics in Zostera marina (eelgrass) beds. Mar Ecol Prog Ser 61:159–169 9. Noarayanan L, Murali K, Sundar V (2012) Role of vegetation on beach run-up due to regular and cnoidal waves. J Coastal Res 28(1A):123–130 10. Sundar V, Murali K, Noarayanan L (2011) Effect of vegetation on run-up and wall pressures due to cnoidal waves. J Hydraul Res 49(4):562–567 11. Hogarth PJ (2015) The biology of mangroves and seagrasses. Oxford University Press

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12. Guannel G, Arkema K, Ruggiero P, Verutes G (2016) The power of three: coral reefs, seagrasses and mangroves protect coastal regions and increase their resilience. PLoS ONE 11(7):e0158094 13. Isaacson M (1991) Measurement of regular wave reflection. J Waterw Port Coast Ocean Eng ASCE 117:553–569

Measurement of Surf Zone Hydrodynamics Along the Coastline of Pondicherry, India R. Balaji, M. V. Ramana Murthy and J. Satheeshkumar

Abstract Surf zone is the most dynamic coastal region with spatially and temporally varying wave, current and sediment transport characteristics. The hydrodynamics along this surf zone is constantly changing and obtaining measurements of currents and waves in the surf zone has always been challenging. Any field measurement attempt along surf zone requires more planning to collect useful data. The present study focuses on the nearshore current mapping using a set of low-cost Global Navigation Satellite System (GNSS)-tracked surface drifters. An array of 10 drifters was deployed on the beach of Pondicherry coastline, where the coastal erosion has been a persistent problem and an artificial reef system is being constructed to regain the beach for the public. The longshore currents and drifter trajectories were recorded throughout the day during flooding and ebbing tide. The results reveal that waveinduced currents are moving toward south to north direction irrespective of any tidal variation. It clearly shows that wave direction plays a major role along this coastline and influences the movement of longshore currents and sediment particles. Simultaneous wave and current measurements were also taken on the same day using WTR and ADCP, the currents were compared with that obtained using drifters and found to be in good agreement. This paper describes the temporal and spatially varying currents along Pondicherry coastline and the results from field measurement campaign. Keywords Longshore currents · Surf zone hydrodynamics Low-cost GPS drifters

R. Balaji (B) · J. Satheeshkumar Indian Institute of Technology Bombay, Mumbai, India e-mail: [email protected]; [email protected] M. V. Ramana Murthy National Institute of Ocean Technology Pallikaranai, Chennai 600100, TN, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_3

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1 Introduction The surf zone is the very complicated zone in a coastal environment; it lies between the shoreface extending from the seaward boundary of wave breaking to the swash zone. The part of the beach in this zone is continuously exposed by breaking waves and it creates wave setup and set down. This is the most complicated zone in the coastal hydrodynamics, when wave breaking happens a lot of energy is dissipated along the beach still this phenomenon is not well understood by scientists and engineers. Breaking waves lead to a number of surf zone processes such as the creation of turbulent bores, wave setup, nearshore currents, and low-frequency motions. All these processes continuously create forces on the beach, which leads to longshore sediment transport. The understanding of the whole picture of the coastal hydrodynamic is always a challenge. Therefore, the temporal and spatial information of hydrodynamic parameters should be obtained simultaneously with fine enough resolution. Usually, the ocean data observation could be divided into two categories: Eulerian and Lagrangian approach. Eulerian method could give the temporally varying phenomena of hydrodynamic characteristics at some fixed locations. The Eulerian method is not satisfactory for coastal hydrodynamic applications because of the rapidly increasing cost when deploying a mass number of instruments spread out the domain to obtain the spatial information of hydrodynamic parameters. On the other hand, the Lagrangian method is used for continuous tracking to obtain temporal and spatial features of parameters simultaneously. For the sediment and material transport studies, the Lagrangian method may be more suitable. Since 1940, the Lagrangian method of data collection has been widely used by many researcher and scientist. The surface drifters were tracked by compass on boat or shore [8, 9, 11] or by swimmer [2, 10]. Besides, the aerial photography technique was employed to track the dye in water continuously [1, 6, 13]. In the last decade, the satellite-tracked surface drifters were widely used for water dispersion characteristics analysis [4, 7, 12]. In the present paper, we demonstrate the measurement of surface currents in a wave-dominated coastal region using low-cost GPS drifters An array of 10 drifters were released in the coastal region of Pondicherry on March 24, 2017, where the coastal erosion was addressed and beach nourishment plan has been proposed to regain the beach again. The currents were measured temporally and spatially throughout the day using drifter, also simultaneous wave and current measurements were taken on the same day using MIDAS WTR Wave and Tide Recorder (WTR) and Acoustic Doppler current profiler (ADCP).

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2 Study Area The area of interest in the present study is the coastal location off Pondicherry located on the east coast of India facing toward Bay of Bengal (Fig. 1). This coast experience two monsoons in a year in that northeast monsoon plays a major role compared to the southwest monsoon. Due to its geographical location, the frequency of cyclone is higher (5 per year), when compared to the west coast of India, where the frequency is low (2 per year) [5]. The bottom sediment strata off Puducherry coast is mainly composed of sand with a mixture of silt and clay. The study region is generally flat with an average elevation of 15 m above the mean sea level. Most of the coastal stretch of Pondicherry is occupied by sandy beach previously. The seabed contours were given in Fig. 2. However, after the development of fishing harbor on the southern coast, erosion has taken place in the northern part and hence the entire beach has been lost. In order to protect the coast short-term measures like seawalls and groin field were attempted by Puducherry government but the erosion problem shifted further north, with increased intensity. As part of shoreline management plan, the recent government has proposed to use soft measure techniques like beach nourishment to regain the lost beach from erosion. Figure 1 shows the detailed view of the Pondicherry coast with the existing coastal structures like seawall, groins, breakwater, and field data measurement location.

Fig. 1 View of the study area with field measurement locations

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Fig. 2 View of a cross section of seabed contour variations with instrument deployment location

3 Materials and Methods 3.1 Instruments Used The low-cost GPS-based RF drifters developed by National central university Taiwan [3] were used for the present study to measure surface current velocities temporally and spatially along Pondicherry coast. The whole system consists of three subsystems, i.e., 1. the drifter, 2. coastal relay station for data transmitting, 3. real-time data display and management system. The drifters are designed in a spherical shape with the diameter of 12 cm (Fig. 3) for continuous 96 h of deployment. The measured data immediately transmitted back to the shore station every 10-s interval via a digital RF network (Table 1). Each drifter on the sea can communicate with any other elements in the cluster; once the link is established, the data of the array can be downlink to the shore station. The real-time data display and management, a software has been developed for easy deployment and retrieval. Simultaneously, wave and current measurement were also carried out at two different locations using MIDAS WTR Wave and Tide Recorder (WTR) and Acoustic Doppler current profiler (ADCP).

3.2 Field Experiments A field experiment was carried out on March 23, 2017, and included the deployment of two WTR, ADCP, and ten GPS drifters. An array of 10 drifters was deployed on each experiment and most of them are continuously measured data during flood

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Fig. 3 Closer view of drifter and components

Table 1 Specification of drifters [3]

Diameter Weight

12 cm 600 g

Power

Alkaline battery

Lifetime

≥96 h

Positioning systems

GPS\GLONASS

Positioning accuracy

2.5 m CEP

Positioning precision

0.167 m

Sampling frequency

1–10 Hz

Transmitting frequency

0.1–1 Hz

Communication systems

RF

and ebb tidal cycles. These experiments were repeated many times in the predefined grid zone to obtain a high spatial resolution of currents. Simultaneously, wave and currents were recorded using the Eulerian approach. The waves measured using MIDAS WTR were deployed at 5 and 10 m water depth, around 200 and 700 m from the coastline. For currents, ADCP was installed at 10 m depth to get the current profile from bottom to surface. Figure 4 shows the deployment photo of ADCP and WTR.

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Fig. 4 View of deploying ADCP and WTR at 10 m water depth

4 Results The data were measured continuously throughout the day. The wave and tides are recorded 30 min interval at various water depth in order to get transformed wave characteristics in front of the study area. Measured wave characteristics of both locations have been presented in the form of time series plots in Fig. 5. From Fig. 5 it can be observed that significant wave height varies between 0.19 and 0.28 m, the peak wave periods are between 5 and 10 s and the wave directions are between 123° and 251° at 5 m of water depth. The waves at 10 m revealed that significant wave height varies between 0.12 and 0.26 m, the peak wave periods are between 5 and 9 s and the wave directions are between 113° and 127°. This shows the transformation effect on wave parameters when water depths decrease in the nearshore region. The ADCP was used to measure current profile at 10 m water depth. The measured data of different water column shown in the form of a time series plot in Fig. 6. It can be observed from the figure surface current speed is higher than the middle and bottom level. The measured current speed various between 0.1 and 0.45 m/s surface to bottom. The estimated depth-averaged velocity is around 0.3 m/s. Figure 7 shows the trajectories of drifter experiments and the color indicates measured current speed.

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Fig. 5 View of the measured wave characteristic at 5 and 10 m water depth

The results reveal that wave-induced currents are moving toward the south to north direction irrespective of any tidal variation. It clearly shows that wave direction plays a major role along this coastline and influence the movement of longshore currents and sediment particles. If we observe more closely Fig. 7, the average surface velocity in the range of 0.25–0.3 m/s which is almost close to ADCP measurements.

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Fig. 6 Time series graphs of currents measured by ADCP

5 Conclusion A low-cost GPS-based drifter has been used the measurement of surf zone hydrodynamics along the proposed beach nourishment site at Pondicherry. The same set of experiments has been conducted many times to measure high spatial and temporal currents. Simultaneously, wave and currents measurements been taken with regular conventional instruments like ADCP and WTR. The measured values are compared with drifter measurement and it shows good correlation with each other. It can be concluded from this study, low-cost GPS drifters are working well in surf zone environments.

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Fig. 7 View of spatially varying current velocity and drifter trajectories

References 1. Bowen A, Inman D (1974) Nearshore mixing due to waves and wave-induced currents. Rapp P-v Reun Cons Int Explor Mer 167:6–12 (Bianco Luna A/S, Copenhagen) 2. Brander R, Short A (2000) Morphodynamics of a large-scale rip current system at Muriwai Beach, New Zealand. Mar Geol 165:27–39 3. Chien H, Zong YZ, Cheng HY, Chang YC, Chang HM, Wei ST (2016) Lagrangian measurement of anthropogenic pollutants behavior in the estuaries of Taiwan. In: 38th ocean engineering conference in Taiwan, December 2016 4. Johnson D (2004) The spatial and temporal variability of nearshore currents. PhD thesis, University of Western Australia 5. Kudale MD, Kanetkar CN, Poonawala IZ (2004) Design wave prediction along the coast of India. In: 3rd Indian national conference on harbour and ocean engineering, NIO, Goa, 7–9 Dec 2004, India, pp 31–39 6. Rodriguez A, Snchez-Arcilla A, Redondo J, Bahia E, Sierra J (1995) Pollutant dispersion in the nearshore region: modelling and measurements. Water Sci Technol 32(9–10):169–178 7. Schmidt WE, Woodward BT, Millikan KS, Guza RT, Raubenheimer B, Elgar S (2003) A GPS-tracked surf zone drifter. J Atmos Ocean Technol 20(7):1069–1075 8. Shepard F, Inman D (1950) Nearshore water circulation related to bottom topography and wave refraction. Trans AGU 31:196–213

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9. Shepard F, Emery K, LaFond E (1941) Rip currents: a process of geological importance. J Geol 49:337–369 10. Short A, Hogan C (1994) Rip currents and beach hazards: their impact on public safety and implications for coastal management. J Coast Res SI.12:197–209 11. Sonu C (1972) Field observations of nearshore circulation and meandering currents. J Geophys Res 77:3232–3247 12. Spydell MS, Feddersen F, Olabarrieta M, Chen J, Guza RT, Raubenheimer B, Elgar S (2015) Observed and modeled drifters at a tidal inlet. J Geophys Res Oceans 120:4825–4844 13. Takewaka S, Misaki S, Nakamura T (2003) Dye diffusion experiment in a longshore current field. Coast Eng J 45(3):471–489

Beach Morphology Near the Inlet of Chilika Lagoon Subhasis Pradhan , Pratap K. Mohanty, Rabindro N. Samal, Rabindra K. Sahoo, Rakesh Baral, Shraban K. Barik, Madan M. Mahanty and Sujit Mishra

Abstract The sandy beach, which represents a transitional zone between terrestrial and oceanic environment, is always in motion and frequently changes its landform due to the exposure to wind, ocean waves, tide, and river discharge. In the present study, an attempt has been made to understand the complex dynamics of shorefront of Chilika and its spatiotemporal variability for effective management of its inlet system. To carry out beach morphology study, several observations were made which include seasonal beach profile and shoreline using RTK-GPS during December 2008–November 2013. Besides, the seasonal wave characteristics near the inlet are collected from ECMWF for understanding wave impact over the inlet system and the associated sandbars. Beach Morphology Analysis Package (BMAP) developed by Coastal Engineering Design Analysis System (CEDAS), Veritech Inc. is used to compute beach width and volume. Results of the above observation indicate that the spatiotemporal variability of beach morphology is mostly attributed to complex hydrodynamic conditions persistent near the inlet as well as to the occurrence of cyclonic events in the Bay of Bengal. Hence, understanding beach morphology and associated physical processes and their variability in spatiotemporal scales are very important for effective inlet management and conservation of the lagoon ecosystem. Keywords Beach morphology · Chilika Lagoon · Inlet · Cyclonic storm

Shraban K. Barik—Deceased. S. Pradhan (B) · R. N. Samal · R. Baral · S. Mishra Chilika Development Authority, C-11, BJB Nagar, Bhubaneswar 751014, Odisha, India e-mail: [email protected] P. K. Mohanty · R. K. Sahoo · S. K. Barik Department of Marine Sciences, Berhampur University, Berhampur 760007, Odisha, India M. M. Mahanty National Institute of Ocean Technology, Velachery-Tambaram Main Road, Narayanapuram, Pallikaranai, Chennai 600100, Tamil Nadu, India © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_4

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1 Introduction Coastal environments which represent the most dynamic and defensive system in terrestrial systems undergo several transformations due to frequent exposure with winds, waves, tides, relative sea level, and high freshwater river discharge. The wave transformation and its asymmetry caused by interaction with bottom sediment in the nearshore zone determines the degrees of beach morphology and also acts as one of the important factors for inlet migration [1, 2]. The sediment bypassing through the tidal inlet and alongshore sediment transport near coastal lagoon make the adjacent beach more complex [3, 4]. Besides, a periodic extreme phenomenon also plays a major role in the significant change in beach morphology. So far as coastal morphology is concerned, coastal erosion and accretion are two opposite physical processes in the annual morphological development of beach environment. The changes in beach morphology are generally considered as either addition or withdrawal of sediment resources or redistribution of sediment resources due to the activity caused by wind, wave, and tide. Along the world coastline, several studies have been registered, among which a few studies [5–9] are quite relevant to our study. Continuous and long-term observation of beach profile would be of immense help in evaluating the erosion and accretion status and longshore sediment transport along the coast, which, in turn, would be helpful for successful implementation of the coastal management plan. The present study is undertaken to understand beach morphological changes near Chilika Inlet during 2008–2013 and the associated factors.

2 Site Description Chilika, along the east coast of India, is a semi-enclosed tropical coastal lagoon bounded by latitudes 19° 28 N to 19° 54 N and longitudes 85° 5 E to 85° 38 E (Fig. 1). It is one of the biggest wetlands of international importance and was designated as a Ramsar site in 1981 for its rich biodiversity and beautiful ecosystem services. The lagoon is connected with the Bay of Bengal through multiple tidal inlet(s), which vary in number and position in due course of time. The opening of the lagoon to sea is largely controlled by sediment supply from the river systems as well as alongshore sediment transport. The coastal stretch of the lagoon is about 65 km in length extending from north of Rushikulya estuary to extreme north of the lagoon. The orientation of the shoreline is about 45°. The inlet channel of the lagoon is very irregular and divergent type towards its upstream region. The lagoon is connected with the sea with multiple inlet systems, which shows its ephemeral nature. These inlet systems, in due course of their operation, have merged and separated from each other with an island system. The lagoon was connected with one inlet during 2005 , while it was connected by two inlets during 2008 due to the opening of a new

Beach Morphology Near the Inlet of Chilika Lagoon

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Fig. 1 Study area showing inlet(s), spit(s) and the beach profile stations (S1–S3) on the south spit and north spit (N1 and N2) (Google Earth Image––June 1, 2009)

inlet near Gabakuda inlet as a result of the severe wave-tide interaction. Thereafter, these two inlets are operated for a couple of years and merged into one called as Gabakuda inlet. Until 2008, the inlet system of Chilika is classified as bar-passing by nature [10] due to excess alongshore sediment transport and less tidal prism. Beach near shorefront of Chilika is macro-tidal by nature and composed of sediments with median grain size diameter equivalent to fine sand [11].

3 Data and Methods Observations include seasonal beach profiles and shoreline using RTK-GPS over the sand spits (south, north, and middle spits) adjacent to the inlets of Chilika Lagoon during 2008–2013. Leica SR 1200 Real Time Kinematic (RTK) Global Positioning System (GPS) was used for beach profile and shoreline survey, which has the position accuracy of ±1 cm and elevation accuracy of ±2 cm. A base reference station was established at the southern end of the south spit. A total of five transects; three on the south spit (S1, S2, and S3) and two on the north spit (N1 and N2) were monitored. The distance between two consecutive transects was maintained at 500 m while observation across the profile was taken at 10 m interval in predefined transects inshore normal direction to the lowest low water mark (Fig. 1). The Beach Morphology Analysis Package (BMAP) version 2.0 of Coastal Engineering Design Analysis System (CEDAS), Veritech Inc. was used to compute beach width and volume. The ERAInterim reanalysis wave parameters of Chilika coast were downloaded for the period

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2008–2013 from European Centre for medium-range Weather Forecast (ECMWF) and the point series data were extracted for analysis.

4 Results and Discussion 4.1 Wave Characteristics The wave properties at the nearshore environment of Chilika lagoon (from December 2008 to December 2013) were obtained from ECMWF data center and analyzed for three seasons such as Pre-monsoon––PRM (February–May), Southwest monsoon––SWM (June–September), and Northeast monsoon–NEM (October–January) period. Figure 2 depicts the frequency distribution of significant wave height (Hs) and wave period (Tz). Hs varies from 0.36 to 2.85 m during PRM, 0.77 to 3.47 m during SWM and 0.42 to 4.15 m during NEM. Frequency distribution of wave parameters indicates the maximum occurrence of Hs in the range 1–2 m (81%) followed by

Fig. 2 Frequency distribution of wave characteristics along Chilika Coast a significant wave height (Hs) in meter and b wave period (Tz) in second

Beach Morphology Near the Inlet of Chilika Lagoon

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0–1 m (77%) while Hs in the range of 2–3 m is only 26%. Highest wave heights are observed during SWM. Considering the interannual variability, the highest magnitude of Hs is observed during 2013 followed by 2011, which is evident from the erosional trend of the spits (Fig. 5) in particular years. The frequency distribution of Tz indicates that maximum percentage of Tz occurs in the range 5–10 s followed by 10–15 s. Besides, Tz in the range of 5–10 s is predominant during PRM while Tz in the range 10–15 s is predominant during SWM. Interannual variability indicates that the maximum percentage of Tz in the range 5–10 s is observed during 2010 followed by 2009 and 2012. Similarly, the maximum percentage of Tz in the range 10–15 s is observed during 2009. Figure 3 depicts wave rose diagram from 2009 to 2013, which distinctly indicates round the year wave approach from SW to SSE, with predominant wave direction as SW. Interannual variability in wave direction shows that SSW to SSE waves is predominantly high during 2009 and low during 2012. On the other hand, SW to SSW wave approach is predominantly high during 2012 followed by 2013.

4.2 Shoreline The shoreline continually changes over time because of the littoral drift and dynamic wave climate along the coast. The shoreline of adjacent sand spits (south, middle, and north) near Chilika Inlet are monitored during 2008–2013 and the results are presented in Fig. 4. It is observed that the geomorphology of spits show significant spatiotemporal variability and the results agree with Pradhan et al. [4]. The south spit (S) gets accreted and elongated toward north direction while the middle (M) and north (N) spits get eroded (Fig. 4). To understand the exact depositional/erosional trend of the three spits, the temporal variation in the area is examined (Fig. 5). It is evident that south spit continuously shows a depositional trend with time while middle and north spit show erosional trend with time. North and middle spit existed up to November 2012 and later on split in north spit (to N1 and N2) is observed while middle spit completely vanished (Fig. 5). Spit N1 further divided into N11 and N12 due to the impact very severe cyclonic storm (VSCS) Phailin, which crossed the Odisha coast on October 12, 2013. The results of the present study agree with the observation made by Pradhan et al. [4]. Besides wave characteristics, spatial variability in longshore sediment transport, higher on the updrift side (i.e., south spit), and lower on the downdrift side(i.e., middle and north spit) is attributed as one of the important factors by Pradhan et al. [4] for the depositional (erosional) trend of the south(middle and north) spit.

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2009

2010

2011

2012

2013

Fig. 3 Wave rose diagram at the nearshore environment of Chilika Lagoon (2009–2013)

4.3 Beach Profile The morphodynamic variability of south and north spits near Chilika Inlet is monitored and the results are presented in Fig. 6. Three profiles (S1, S2, S3) on the south spit and two on the north (N1, N2) spits are presented for three seasons (PRM, SWM,

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Fig. 4 Shoreline positions of adjacent sand spits near Chilika Inlet [South Spit-S, Middle Spit-M, North Spit-N, North Spit divided-N1 and N2, N1 Spit divided-N11 and N12 (not to scale)]

NEM) from December 2008 to November 2013. Measurements for all profiles are made at a constant benchmark to the limit of lowest low water mark. The largest variance in the profile occurs around the bermline and swash zone. The beach profile at S1, located extreme south of south spit, follows a definite pattern maintaining a width of 153–197 m with the continued depositional trend, while at S2 and S3, advancement of bermline toward seaside with variable width is observed due to accretion during the interaction of ocean waves with beach environment (Fig. 6). Further, it is noticed that the beach profile during December 2008 is very gentle compared to June 2013. The gradual depositional process at south spit maintains the stability of the spit and acts as a defensive system against the cyclonic disturbances. On the contrary, beach profiles on the north spit (N1 and N2) show a declining trend in elevation even at the constant benchmark. The berm width at N1 drastically reduced from 60 to 30 m from 2008 to 2013 while the height reduced from 4 m during 2008 to 1.05 m by the end of September 2013. The profile was completely washed away due to the impact of

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Fig. 5 Variation in the area of adjacent sand spits near Chilika Inlet (South Spit-S, Middle Spit-M, North Spit-N, North Spit divided-N1 and N2, N1 Spit divided-N11 and N12)

VSCS Phailin during October 2013. Profile N2 existed till May 2009 and thereafter the benchmark was washed out and the shoreline position shifted towards lakeside. To understand the spatiotemporal variability, beach width and volume are computed and the change in width and volume with reference to December 2008 are presented in Table 1. It is noticed that change in beach width shows increasing pattern with time for S1, S2, and S3, albeit higher magnitude in S3. On the other hand, the width of N1 and N2 reduced (negative change as in Table 1) with time. Concomitant with beach width, beach volume of south spits show a significant increase from September 2010 to September 2013. The magnitude of beach width and volume changes are highest at S3 followed by S2 and S1. Change in volume of N1and N2 is distinctly negative with time indicating erosion.

4.4 Impact of Cyclonic Disturbances Figure 7 depicts three case studies showing the impact of the cyclonic disturbances on beach morphology. Case-I: It refers to the impact of cyclone Bijli and Aila as detailed in Table 2. Profiles of north spit (N1) during pre- and post-cyclonic events are compared, which distinctly indicate the significant impact of the cyclone Bijli and Aila with erosion predominantly in the midshore and foreshore region during post-cyclone period. Case-II: It refers to the impact of depression during September 2011 (Table 2). The pre- and post-depression profiles are compared at both south

Beach Morphology Near the Inlet of Chilika Lagoon

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Fig. 6 Seasonal changes in beach profiles at adjacent sand spits of Chilika inlet [S1, S2, and S3 are at South Spit and N1 and N2 are at North Spit]

(S2) and north (N1) spits. On the north spit, the profiles show steep slope and severe erosion after depression while on the south spit, the profiles show distinct ridge in the midshore, stiff cut in the foreshore, erosion in the backshore and midshore, and deposition in the foreshore. Case-III: It refers to the impact of the VSCS Phailin (Table 2) on the south spit (S2). The pre- and post-cyclone profiles show ridge in the midshore, deposition in the backshore and severe erosion on the foreshore.

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Table 1 Seasonal variation in beach volume (cu.m/m) and beach width (m) (*reference month) S1

S2

S3

N1

N2

Beach width (m) December 2008

157.7*

197.5*

187.0*

63.2*

40.9*

May 2009

−4.6

9.6

5.9

−6.7

−0.5

September 2009

−1.3

13.1

2.2

−7.4

December 2009

−2.4

19.1

19.8

−15.1

May 2010

2.3

29.4

56.1

−17.8

September 2010

18.2

52.5

52.6

−7.2

December 2010

19.6

44.7

56.2

−17

June 2011

24.5

49.8

89

−18.5

October 2011

22.3

42.5

104.6

−29

December 2011

21.8

61.3

98.7

−31.1

February 2012

25.9

61.6

102.1

−32.9

August 2012

21.9

55.1

109.3

−25

November 2012

35.2

58.4

98

−34.1

June 2013

38.8

64.3

106.2

−32

September 2013

37.8

69.8

105.8

−32.3

November 2013

19.2

59.8

80.6

−63.2

Beach volume (cu.m/m) December 2008

415.7*

507.2*

540.0*

146.5*

101.4*

May 2009

25.5

−22.2

39.2

−11

−35.3

September 2009

39.4

22.6

33.2

−21.6

December 2009

56.3

35.1

49.1

−38.4

May 2010

51.2

73.6

162.2

−50.1

September 2010

109.6

108.6

172.7

−3.7

December 2010

131.2

180

259

−69.2

June 2011

129.5

219.6

448.1

−70.5

October 2011

143.8

168.8

298.7

−96

December 2011

130.8

191.4

529.6

−102

February 2012

133

238.6

575.8

−102.6

August 2012

165.2

233.6

535

−111.1

November 2012

207.7

237.7

616.1

−119

June 2013

211.9

223.8

430

−120.8

September 2013

228.8

273.9

577.9

−123.1

November 2013

190.3

245.1

404.1

−146.5

5 Conclusion The nearshore environment of Chilika inlet(s) is studied. The study includes longterm observation (2008–2013) on wave characteristics derived from ECMWF reanalysis, shoreline of the three spits(south, middle, and north) near the inlet(s), beach profiles of south and north spits and impact analysis of some specific cyclonic disturbances on beach morphology near Chilika inlet. The study reveals that frequency

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Case-1

Case-2

Case-2

Case-3

Fig. 7 Impact of cyclonic disturbances (Table 2) on beach morphology (Case-1: Impact of Cyclone Bijli and Aila during April and May 2009, Case-2: Impact of depression during September 2011 and Case-3: Impact of Phailin during October 2013) Table 2 Cyclonic disturbances along northwest Bay of Bengal during 2009–2013 Year

Period

Type of disturbances

Location

2009

April 14–17

Cyclone (Bijli)

Formed in the southeast Bay of Bengal and Andaman sea and moved parallel to Odisha coast in northwesterly direction and landfall at Bangladesh coast

May 23–26

Severe cyclonic storm (Aila)

Formed in the east-central of Bay of Bengal and move northerly direction and crossed West Bengal

June 16–23

Deep depression

A low-pressure area formed over the northwest Bay of Bengal and crossed West Bengal–Bangladesh coasts

September 22–23

Depression

A well-marked low-pressure area over the northwest Bay of Bengal and adjoining West Bengal–Orissa coasts resulted in heavy rains and caused floods in Orissa and Bihar

October 8–14

VSCS (Phailin)

Crossed Odisha and north Andhra Pradesh coast close to Gopalpur on October 12, 2013

October 20–26

Low pressure

Caused heavy rainfall over coastal Andhra Pradesh and Odisha

2011

2013

of Hs with range 1–2 m is highest (81%) followed by Hs in the range 0–1 m (77%). Highest waves are experienced near inlet during south-west monsoon compared to pre- and northeast monsoon. Wave periods of 5–10 s have a maximum frequency

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followed by wave period of 10–15 s. The direction of wave approach near inlet is from SW to SSE with predominant direction from SW round the year. Shoreline change near the inlet of Chilika depicts significant spatiotemporal variability. The north and middle spits show an erosional cycle while the south spit undergoes a continuous depositional process. As a result, the beach near south spit is stable while the beach near north spit undergoes very first geomorphological changes leading to opening/closing of inlet(s) mostly in the northward direction. The beach profile analysis (beach width and volume changes) further confirms depositional and stable environment at south spit and erosional and unstable environment at north spit. Shoreline information also reveals that it is progressive towards the seaside near south spit while retreating towards inner shelf of the lagoon near north spit. Impact of extreme weather events on beach morphology indicates that northern spit(s) is highly responsive compared to southern spit. The magnitude of erosion due to these episodic events is quite high compared to seasonal or interannual variability in beach morphology. The investigation warrants urgent attention on conservation/stability of north spits for maintaining inlet stability, which, in turn, would be helpful for sustainable management of Chilika lagoon. Acknowledgements The authors are very much thankful to the Chief Executive, Chilika Development Authority, Bhubaneswar for encouragement and rendering all support to carry out this research work, and to the authorities of Berhampur University for extending laboratory facilities at the Department of Marine Sciences.

References 1. Mwakumanya MA, Bdo O (2007) Beach morphological dynamics: a case study of Nyali and Bamburi Beaches in Mombasa. Kenya J Coast Res 232:374–379. https://doi.org/10.2112/040354.1 2. Nienhuis JH, Ashton AD (2016) Mechanics and rates of tidal inlet migration: modeling and application to natural examples. J Geophys Res Earth Surf 121:2118–2139. https://doi.org/10. 1002/2015JF003777 3. Hayes MO (1980) General morphology and sediment patterns in tidal inlets. Sediment Geol 26:139–156. https://doi.org/10.1016/0037-0738(80)90009-3 4. Pradhan S, Mishra SK, Baral R, Samal RN, Mohanty PK (2017) Alongshore sediment transport near tidal inlets of Chilika Lagoon; east coast of India. Mar Geod 40:187–203. https://doi.org/ 10.1080/01490419.2017.1299059 5. Huang J, Jackson DWT, Cooper JAG (2002) Morphological monitoring of a high energy beach system using GPS and total station techniques, Runkerry, Co. Antrim, Northern Ireland. J Coast Res 398:390–398 6. Mohanty PK, Patra SK, Bramha S, Seth B, Pradhan U, Behera B, Mishra P, Panda US (2012) Impact of groins on beach morphology: a case study near Gopalpur Port, east coast of India. J Coast Res 279:132–142. https://doi.org/10.2112/JCOASTRES-D-10-00045.1 7. Pradhan U, Mishra P, Mohanty PK, Behera B (2015) Formation, growth and variability of sand spit at Rushikulya River Mouth, South Odisha Coast, India. Procedia Eng 116:963–970. https://doi.org/10.1016/j.proeng.2015.08.387 8. Jayakumar S, Raju NSN, Gowthaman R (2004) Beach dynamics of an open coast on the west coast of India. In: 3rd Indian national conference on harbour and ocean engineering, NIO, Goa, pp 9–16

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9. Venkatarathnam K (1970) Formation of the Barrier Spit and other sand ridges near Chilka Lake on the east coast of India. Mar Geol 9:101–116. https://doi.org/10.1016/0025-3227(70)90063-0 10. Gopikrishna B, Sinha J, Kudale MD (2014) Impact on salinity of Chilika Lake due to changes in the inlet system. Indian J Mar Sci 43(7) 11. Chandramohan P, Kumar VS, Nayak BU (1993) Coastal processes along the shorefront of Chilka Lake, east coast of India. Indian J Mar Sci 22:268–272

Study of Bamboo Bandalling Structures in the Tidal River for River Bank Erosion Md. Lutfor Rahman

Abstract In this case, the V-shape bamboo bandalling structures are constructed with 45° angle with the flow direction. The experimental setup is facilitated with both the flood and ebb tide from upstream to downstream and vice versa. There is an arrangement at the upstream for flow entry and flow out and also the same arrangement in the downstream to ensure the flood and ebb tide. For this reason, riverbank as well as riverbank sedimentation which is demonstrated in the real Rupsha River near the city of the Khulna, Bangladesh. Keywords Tidal river · Bamboo bandalling structures · Velocity · Sedimentation

1 Introduction Bangladesh is a riverine country. One-third of the rivers are tidal in nature. There is a lot of erosion in the tidal rivers. Both the ways water flow is to be guided by the V-shape bamboo bandals. Bandal is used to prevent riverbank from erosion. V-shaped bandal is effective against both spring tide and neap tide. Bank protection and river training works are one of the prime necessities for poverty alleviation and national growth. The issue is the safety of lives, land, and sustainability of the infrastructure against the forces acting in the rivers. Untrained alluvial rivers of Bangladesh are big problems to the socioeconomic and environmental sector of the country. A number of earthen embankments were constructed along the major rivers for the protection of rural people and agricultural lands from flooding. Since then the embankments were retired several times due to riverbank erosion and bank protection are often required during the monsoon and post-monsoon season. Groins and revetments are applied as a method of bank protection as a conventional method.

Md. L. Rahman (B) Hydraulic Research Directorate, River Research Institute, Faridpur, Bangladesh e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_5

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The bank protection structures and the recurrent measures have been monitored for several years. FAP 21 produced some progress in process-based modeling of two mechanisms by which the mere presence of bank protection structures increases the loads: (i) the deeper bend scour due to stopping of bank migration [1]; and (ii) the attraction of channels and associated flow attack toward scour holes [2]. The stopping of bank erosion is assumed to produce deeper bend scour through: (i) prevention of bank sediment supply, (ii) channel narrowing due to retarded point bar growth, (iii) bend deformation due to the local prevention of channel migration and (iv) vortices generated by flow impingement. A method was developed by Klaassen et al. [3], based on empirical laws derived from a large set of satellite images [4]. Jagers implemented the prediction method in a computer model and tested it against observations [5, 6]. He also constructed and tested an artificial neural network for the prediction of low-water planform changes in the Brahmaputra–Jamuna.

2 Methodology To meet the above objectives of the study, a laboratory experimental setup was used as shown in Fig. 1. The data is collected for water depth and velocity from the laboratory experimental setup. Length of left bank is 14.15 m and right bank is 15.43 m and that of channel width is 1.0 m. Area of two fixed beds is 4.9 m2 and area of mobile bed is 29.4 m2 and both of the two banks were constructed by bricks. Volume of sand in the mobile bed is 6.76 m3 . The d50 and specific gravity of the sand are 0.225 mm and 2.65, respectively. Twelve number of V-type bandals were installed in the flume bed. The distance from one bandal to another is 1.35 m. Length of each bandal is 0.70 m. Four bandals were installed along the left bank. First of these bandals is 1.0 m apart from the upstream fixed bed. Another set of four bandals was installed along the left bank in the downstream. In the middle portion of the longitudinal section, another set of four bandals was installed. With the aid of this experimental setup, there are the working principles of bandals as shown in Fig. 2. In this working principle, it is seen that bed load and suspended load is transported [7]. In details, it is noted that the surface current is diverted toward the main channel. The sediment in water is pushed down through the bandals and deposited behind the bandals with the low velocity of water.

3 Objectives of the Study The main objectives of this study to investigate the flow field around the bamboo bandalling structures. The specific research objectives are as follows: (1) to know the navigational channel development due to the effect of bamboo bandalling structures constructed near both the laboratory flume.

Study of Bamboo Bandalling Structures in the Tidal River …

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Fig. 1 Experimental setup

(2) to understand the application of bamboo bandalling structures when placed both in laboratory and field. (3) to get an idea about the performance of the bamboo bandalling structures.

4 Data Collected for Analysis Data collected from the experimental setup of Fig. 1 is presented in Table 1. Data collected was the distance from the left bank of the channel, water depth and measured

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Table 1 Collected velocity at a different location of the experimental setup Section no. Distance from Depth, d (cm) Velocity (m/s) LB (cm) 0.2d 0.6d 1

2

3

4

5

6

30 60 90 120 150 180 30 60 90 120 150 180 30 60 90 120 150 180 30 60 90 120 150 180 30 60 90 120 150 180 30 60 90 120 150 180

24 24 27 32 30 26 23.5 25 27.5 33 29 22.5 24 25 25.5 27 28 28 25 27 26 28 29 29 31 35 29 30 28.5 27 25 26 30 31.5 34 30.5

0.110 0.264 0.397 0.511 0.418 0.233 0.031 0.161 0.253 0.439 0.500 0.449 0.031 0.031 0.264 0.428 0.480 0.521 0.061 0.295 0.346 0.439 0.367 0.356 0.031 0.150 0.356 0.387 0.367 0.377 0.031 0.212 0.367 0.356 0.356 0.377

0.150 0.305 0.418 0.490 0.418 0.253 0.031 0.212 0.325 0.480 0.521 0.511 0.031 0.130 0.264 0.439 0.531 0.449 0.031 0.336 0.397 0.408 0.367 0.346 0.031 0.181 0.387 0.377 0.336 0.346 0.031 0.212 0.346 0.356 0.356 0.356

0.8d 0.150 0.243 0.408 0.459 0.408 0.356 0.041 0.192 0.336 0.500 0.480 0.511 0.031 0.031 0.233 0.387 0.511 0.459 0.161 0.284 0.367 0.356 0.305 0.336 0.031 0.150 0.336 0.315 0.315 0.284 0.181 0.264 0.325 0.336 0.346 0.325

Study of Bamboo Bandalling Structures in the Tidal River …

53

Fig. 2 Working principle of the bamboo bandalling structures

Fig. 3 Velocity plot from left bank (LB) toward right bank versus water depth

Fig. 4 Velocity plot from left bank (LB) toward right bank versus water depth

velocity in 0.2, 0.6, and 0.8 times the water depth. This three-point velocity is plotted in Figs. 3, 4, 5, 6, 7, and 8.

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Fig. 5 Velocity plot from left bank (LB) toward right bank versus water depth

Fig. 6 Velocity plot from left bank (LB) toward right bank versus water depth

Some photographs have been taken to observe the sedimentation phenomena near the riverbank, which is demonstrated in the real Rupsha River near the city of the Khulna, Bangladesh as shown in Fig. 9.

5 Result and Discussion It is referred to all the figures and Table 1 to observe the performance of the bamboo bandalling structures applied in the tidal river in Bangladesh. It is evident from the plot of the section-1 through section-6 that there is maximum velocity at the center of the channel, where the flow is concentrated due to the effect of the bamboo bandals. Velocity is less near the bamboo bandals area both in the laboratory experiment as

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Fig. 7 Velocity plot from left bank (LB) toward right bank versus water depth

Fig. 8 Velocity plot from left bank (LB) toward right bank versus water depth

Fig. 9 The river bank of Rupsha River is protected by using bamboo bandalling structures at Khulna, Bangladesh

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well as in the real river of the Rupsha. In the area within the bamboo bandals, the velocity is reduced where siltation is encouraging.

6 Conclusion and Recommendation In conclusion, it can be stated that the performance of the bandals is acceptable in the tidal river. There is sediment deposition as in Fig. 10 and that of as in Fig. 11 of the bamboo bandals used for the river bank erosion protection. Due to the effect of the bamboo bandalling, deposition occurred near the bandals. The bamboo bandals will be the sustainable solution. Further study will be required to make the test result more fruitful.

Fig. 10 Photographs shows the sediment deposited near the eroded bank within the bamboo bandals field

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Fig. 11 River before the construction of bamboo bandals in the left and that of after the flood in the right of the photographs

References 1. Mosselman E, Shishikura T, Klaassen GJ (2000) Effect of bank stablization on bend scour in anabranches of braided rivers. Phys Chem Earth Part B 26(7–8):699–704 2. Mosselman E, Sloff CJ (2002) Effect of local scour holes on macroscale river morphology. In: Bousmar D, Zech Y (eds) River flow 2002: proceeding of the international conference on fluvial hydraulics, vol 2, Louvain la Neuve, Belgium, 4–6 September 2002, pp 767–772, Balkema, Lisse 3. Klaassen GJ, Mosselman E, Brühl H (1993) On the prediction of planform changes in braided sand bed rivers. In: Wang SSY (ed) Advances in hydro science and engineering. University of Mississippi, University, Mississippi, pp 134–146 4. Klassen GJ, Masselink G (1992) Planform changes of a braided river with fine sand as bed and bed and bank material. In: Proceedings of the fifth international symposium on river, sedimentation, 6–10 April 1992, Karlsruhe, pp 459–471 5. Jagers HRA (2001) A comparison of prediction methods for medium-term planform changes in braided rivers. In: Proceeding IAHR symposium on River Coastal and Estuarine Morph dynamics, Genova, 10–14 September 2001, Obihiro, Japan, pp 713–722 6. Jagers HRA (2003) Modelling planform changes of braided rivers. PhD theses, University of Twente. ISBN 90-9016879-6 7. Rahman MM, Nakagawa H, Ishigaki T, Khaleduzzaman ATM (2003) Channel stabilization using bandalling. Annuals of Disaster Prevention Research Institute, Kyoto University, no 46 B, pp 613–618

Development of Predictive Tool for Coastal Erosion in Arctic—A Review Mohammad Saud Afzal and Raed Lubbad

Abstract Arctic permafrost constitutes one-third of the world’s coastline that is characterized by the presence of ice and cohesive sediments. Erosion of Arctic coastline has adverse impacts on social life and economy of the communities living in the area. There are two main processes of coastal erosion in the Arctic regions: thermodenudation and thermoabrasion. Studies suggest that erosion along the Arctic coastline is considerable and increasing. With increasing global warming, sea-ice is disappearing at an accelerated rate and wave growth in Arctic has increased to an alarming level. The situation is worsened by the fact that most of the existing knowledge regarding coastal erosion pertains to temperate areas and for non-cohesive sediments. A brief review of existing numerical models used for Arctic coastal erosion is presented, which shows that there exist some knowledge gaps which need to be closed first. The study recommends that an ideal solution is to develop a predictive tool consisting of four different models coupled with each other; (1) Earth system model to provide boundary conditions to other models, (2) Hydrodynamic module to calculate flow, sediment transport, and wave propagation in ice, (3) Thermal permafrost model to provide permafrost temperature field, ice content, bulk density, ice content, and sediment type to (4) The Arctic Coastal erosion model (thermoabrasion and thermodenudation). The coupled model will introduce more physical processes but a fully coupled model shall be complex and computationally expensive. Nevertheless, it shall produce the best possible predictions in local areas where site conditions are available. The model should also be validated against field observations and experimental data. Keywords Coastal erosion · Arctic · Thermoabrasion · Thermodenudation Permafrost M. S. Afzal (B) · R. Lubbad Department of Civil and Environmental Engineering, Norwegian University of Science and Technology, 7491 Trondheim, Norway e-mail: [email protected]; [email protected] M. S. Afzal Department of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, West Bengal, India © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_6

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1 Introduction Arctic permafrost constitutes one-third of the world’s coastline [1]. These coastlines are characterized by the presence of ice and cohesive sediments. Coastline erosion in Arctic negatively impacts the communities residing near these coasts due to increase in flooding, destruction of residential and commercial buildings and sites of scientific and archaeological importance. Despite this large share of coastline and a possible threat to communities living along the Arctic coast, the understanding of the phenomena responsible for erosion in Arctic is still relatively poor. The need to understand these phenomena is underscored by many studies that demonstrate rapid coastal erosion in the Arctic. In addition, the tools to address coastal erosion, in general, are limited to temperate areas and non-cohesive sediments. There are two main processes of coastal erosion in the Arctic regions; thermodenudation and thermoabrasion. Thermodenudation is defined as the gradual thawing of permafrost bluffs due to solar radiation, warmer air temperature and snow-melt [2]. The thawed sediment gets unstable and fails, depositing scree at the base of the slope. This scree is then eroded and finally removed by waves and currents. Usually, thermodenudation takes place at coastlines with fine sediment and a high ice content. This process is characterized by lower and consistent erosion rates and occurs mostly during calm conditions. Thermodenudation is more a thermal-dominated process, since the sea water has no or only little contact with the frozen bluff and is just responsible for the removal of the deposited material at its toe. However, the deposited material can protect the bluff and slow down its erosion, when there are higher water levels or waves [3, 4]. Thermoabrasion on the other hand occurs during storms and high water levels, where deposited material at the toe of the slope is removed and the frozen bluff is directly exposed to the influence of the warm seawater [2]. It then thaws quickly due to convective heat transport, whereby the melted sediment is transported offshore and out of the littoral zone by waves and currents. This thawing process can lead to the formation of horizontal niches, whose depth increases during several storms and years. When the overhanging material becomes too heavy and cannot be held by the shear or bending strength of the soil, it collapses as a block usually along an ice wedge. Typically, the block, consisting of frozen and unfrozen sediment, gradually vanishes due to the effects of warm water and wave forces. If the block stays in front of the bluff, it protects the bluff from further erosion. Arctic coastline is majorly divided into 4 different regions [5]: Alaskan, Canadian mainland, Siberian, and others (including Svallbard, Zemlya, Franz Joseph Land, Novaya, and Greenland). One of the areas where highest erosion rates in Arctic are found, is located along the Alaskan coastline [6]. The Alaskan coastline along Kotzebue Sound includes bluffs, shallow slumps, and mudflows with long-term average erosion rate of 0.1 m/year [7]. Along the north slope of Alaska from Icy Cape to Demarcation Bay, coastal erosion studies (e.g., [7, 8]) indicate long-term average erosion rate of 1.4 m/year with a maximum rate of 18.6 m/year. Mainland coastline of Canada is unlithified coast with high rates of erosion. It is mainly comprised of unconsolidated sediments. It exhibited a retreat rate of 0–6 m/year within the

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timespan of 1970s and 1980s [9]. Among the Siberian coastlines, Laptev Sea coast consists of bluffs of unconsolidated material. The failure mode of these bluffs is thermal–mechanical undermining with weighted mean coastal erosion rate of 0.7 m/year [1]. A study [10] from 1965 to 2011 revealed that most recent 2-year erosion rates (5.3 m/year) are roughly 2 times faster than the 42-year average (2.2 m/year). All Siberian yedoma ice complex coastlines show a mean erosion of 1.9 m/year which goes as high as 25 m/year [11]. The observations discussed above indicate that there is an increase in the rates of Arctic coastal erosion in past decades, which is further intensified due to increasing global warming. Increase in global warming leads to disappearing of sea-ice in Arctic. Sea-ice is melting earlier (1.5 day/year) in the spring and is developing later in the fall (2 day/year) [12]. Since 1979, the sea-ice extents have decreased by approximately half, leading to the Arctic Death Spiral [13]. Due to global warming the perennial ice is being rapidly replaced by thinner first-year ice, leading to significant changes in the thickness of the ice cover [14]. Traditionally, the Arctic Ocean has had little to no waves to characterize since the large swath of perennial sea-ice severely limits the fetch length for wave development. However, as the perennial sea-ice is melting and the duration of open water is increasing, ocean waves are now increasingly developing in the Arctic Ocean. As more open surface is exposed, larger amplitude and longer wavelength waves can be generated. Study by Thomson and Erick Roger [15] has shown that in the Arctic Ocean there is now enough open water that wind-seas are able to evolve into swell-seas. With increasing wave growth in Arctic the threat of erosion increases. One of the other important phenomenon due to the melting of seaice is increased insolation of the ocean since the reflectivity of ocean is decreased. Also due to increased wave growth in Arctic, mixing of heat from ocean surface to ocean bottom increases resulting in increased basal melting of sea-ice. This delivery of heat to ice-rich permafrost regions results in accelerated and devastating erosion rates (with average rates up to 17.3 m/year [16]).

2 Existing Models Relevant to Arctic Coastal Erosion Numerical models are extensively used to predict state of permafrost coast. Although widely used, the current models of permafrost bluff erosion are not universally applicable, capable of predicting only on narrow range of parameters and prone to sitespecific conceptual model. Figure 1 presents an overview of existing modeling tools applicable to Arctic. A brief review of existing models is discussed in the following subsections. Frederick et al. [5] has more detailed overview of the numerical models that are currently being used to predict coastal erosion in Arctic. Here slightly different way of classification is presented, wherein modeling approach for Arctic coastal erosion can be classified into two major classes depending upon the area in consideration; Large and Local scale models.

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Fig. 1 Overview of existing modeling tools applicable to Arctic

2.1 Large Scale Classification in large scale takes into account both regional- and global-scale models. Prominent modeling that features in this classification are large-scale hydrodynamic modeling (further classified as flow and wave models) and permafrost thermal models (two classes of permafrost thermal models; regional scale and global scale). On a larger scale (regional/global scale) software like DELFT3D- FLOW is used for modeling the flow of water and transport of ice in Arctic. Delft3D, developed at Technical University, Delft, Netherlands is an open-source software. Delft3DFLOW is modular suite based on Navier–Stokes equation of motion to perform 2D and 3D hydrodynamic and sediment transport simulations. There is an ongoing integration of an ice modeling module called DELFT3D-ICE used for the estimation of ice flow movements, coverage extent, and thickness; the module can be linked to other models to investigate long-term movements, growth, and potential effect on a study area [17, 18]. Ocean-ice wave models are regional models that focus on short-term weather forecasting. These models include the phenomena that initiate the wave action along with propagation characteristics; thus, require large spatial and time domain. Currently, WAVEWATCH III [19] is being used as operational regional-scale ocean-ice model for short-term weather forecasting. WAVEWATCH III is a third-generation spectral wave model which is most widely used software for modeling the generation and propagation of waves in Arctic. Ice modeling on a global scale focuses on coupling atmospheric forcing with ice pack velocities and heat flux changes over years to understand gross effects of sea-ice on climate. Sea-Ice Earth models are based on momentum equation that calculate ice motion forced by drags of wind and water, Coriolis, etc. This model considers ice as linear viscous fluid when strain is small and treats ice as viscoplastic material under common stress condition. However, in sea-ice models, ice is typically considered as isotropic rather than anisotropic. CICE (Los Alamos National Laboratory sea-ice model) is a widely successful global-scale sea-ice model where ice is treated as isotropic material and can be coupled with various climate modeling (for example, Hybrid Coordinate Ocean Model, HYCOM).

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Regional-scale permafrost thermal models are subsurface heat and mass transfer models which are used to simulate physical process of freeze-thaw based on mathematical equation like energy equation, Darcy’s law, etc. They couple the phase change with fluid flow and are hence called thermal-hydro models. They are limited to small domains due to the complexity of the model. The predictions, therefore, are of high quality in comparison to local observations. One of the most prominent studies is the InterFROST Project which is a numerical model inter-comparison study that benchmarks several thermo-hydro coupled codes [20]. To date, a total of fourteen codes (and their development teams) have participated in this study. Global-scale permafrost models are earth system model that use large grid and calculate within greater area. In global- scale models, the physical equations are typically parametrized and focused on lower boundary for atmospheric transfer schemes [21] and are expected to be less accurate in comparison to local observations. The Coupled Model Intercomparison Project phase 5 (CMIP5) described in [22] provides another excellent review of the existing global-scale permafrost thermal models.

2.2 Local Scale Classification in local scale takes into account smaller modeling domains. Prominent modeling that features in this classification are small-scale hydrodynamic modeling and coastal erosion models in Arctic which models the processes of Thermodenudation and Thermoabrasion. Flow modeling on a local scale can be handled using CFD programs where the calculations are on a finer scale with higher accuracy. This type of modeling is computationally expensive. Examples of CFD program that has been tested for Arctic coastal erosion include OPENFOAM and REEF3D. Wave model on a local scale deal with the interaction of waves with ice (wave–ice interaction models). They capture the ice geometry dependent scattering and dissipation due to propagation of waves. Wave–ice interaction models can be further categorized into four class [23] (a) viscous, (b) viscoelastic, (c) scattering, and (d) turbulence. Viscous models treat ice as composed on small ice flows in a liquid suspension of effective viscosity much greater than water. Viscoelastic models also treat ice similarly but add elasticity of ice. Scattering models systematize individual collision events of ice floes in suspension whereas turbulence models are based on attenuation of waves by ice covers due to turbulence. Thermodenudation is usually modeled using THM (Thermo-hydro-mechanical) models. Nishimura et al. [24] developed a coupled THM finite element analysis for frozen soil. The models consider freezing and thawing in water-saturated soils and can be applied to analyze frost heave, foundation stability, or mass movements in cold regions. Later, [25] developed a coupled THM model for porous materials under frost action. A further improvement was THM model by [26], wherein special effort was paid to the description of the porosity and implementation of a thermal model with phase change. Amiri et al. [27] developed a constitutive THM model for saturated

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frozen soils, which were assumed to be a combination of solid grains, unfrozen water, and ice. The part of the stress carried by the solid grains was considered to be responsible for any deformation due to mechanical loading. Besides the solid phase stress, a cryogenic suction was implemented in the model. Amiri et al. [28] then developed a constitutive model for frozen and unfrozen soil, which expressed the behavior of the frozen soil as a function of the temperature. It is a critical-state elastoplastic time-independent mechanical soil model, which follows a similar approach as the soil model developed earlier by [27]. Recently, [29] developed a stabilized thermo-hydro-mechanical finite element model to simulate the freezing and thawing of porous media, in the finite deformation range. Whereas, earlier models often neglect the flow of unfrozen water, energy dissipation due to phase transition and geometry nonlinearity this model takes all these mechanisms into account. Thermoabrasion processes are usually simulated with block failure models, which describe the development of niches, the block failure, and the block erosion after the failure of the bluff. Hoque and Pollard [30] developed an analytical bluff erosion model, which can be used to analyze the block failure mechanisms for varying cliff heights, long-term strength, and ice-wedge locations of permafrost coasts. Ravens Thomas et al. [31] developed a coastal/shoreline erosion model for the Beaufort Sea. The niche growth was modeled according to [32]. Later, [12] developed a model, which captures the submarine and subaerial erosion, notch formation and force balance on the bluff and the failure tracks of the bluff. The model is quite similar to that of [31] with some improvements like shorter time steps, consideration of fieldand time-lapse imaginary observation and inclusion of other approaches besides the Kobayashi formula to describe the erosion rate. Recently, [33] developed a model to assess the influences of ice wedges and horizontal niche on the coastal erosion, which is based on their earlier model. As an improvement over the earlier model of [30], this model takes the influence of pore water pressure in the active layer into account. Commercially, COSMOS is a coastal profile model that has been used extensively to model coastal and sediment erosion in temperate and tropical climate. The thermo-erosion module was successfully developed and used to predict bluff erosion at coastlines of the Canadian Beaufort Sea and it was also used to simulate thermo-mechanical erosion at a coastline in Russia [34].

3 Conceptual Integrated Arctic Coastal Erosion Predictive Tool One of the most important steps before conceptualizing an integrated Arctic coastal erosion predictive tool is to identify existing knowledge gaps. The primary shortcoming of all ice–wave interaction models developed so far is that they either assume that the energy is conserved or they impose an arbitrary dissipation based on a nonmeasurable parameter. It is, therefore, important to determine the process or processes by which energy is dissipated as it propagates through a field of broken ice.

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Arctic coastal erosion models developed so far do not take into consideration timedependent ocean temperature. Present Arctic coastal erosion models do not account for detailed bathymetry in wave generation calculations for storm surge and simply use local spatial scale for wave propagation. These models assume a single static ground temperature rather than using time-dependent, two-dimensional permafrost temperature field and also do not use temperature and ice content dependent geotechnical permafrost strength properties. Apart from the knowledge gaps, previous sections also highlight the importance of conducting more research on Arctic and its urgency is underscored by the rapid changes in Arctic coastline due to oceanographic and geomorphic perturbations associated with climate change. It is also important to note that processes of Arctic coastal erosion is influenced greatly by processes such as storm surge, wave propagation, correct permafrost temperature, and changing sediment properties. Models that predict these processes exist individually, but coupling them is required. This is a challenging task since it requires feedback between different models which is both computationally expensive and requires coupling between modules having mismatch of spatial and temporal scales. However, with the growth of computational powers, it is expected that such a predictive tool shall exist within the next decade. The proposed predictive tool is shown in Fig. 2 along with different model components (modules) and required coupling between those modules. It shall consist of 4 main components; Earth system model, hydrodynamic model, permafrost thermal model, and coastal erosion model. Other than these modules, accurate site conditions are important for good results. Current proposal of predictive tool is inspired by coupled Arctic coastal erosion model proposed in [5]. Earth system model is by definition global-scale model that provides boundary conditions to the rest of the modules (on the level of regional scale) in the predictive tool. It provides parameters like sea level rise, wind spectra, atmospheric temperature as a function of time and space, time-dependent ocean surface temperature, solar and evaporation fluxes to hydrodynamic model. Atmospheric temperature and snowfall as a function of time and space is passed to thermal permafrost model. Hydrodynamic model consists of two submodules; wave module and flow circulation module. Wave module focuses on interaction of waves and ice resulting in the three-dimensional wave energy spectra and the wave propagation in presence of sea-ice. This information is then passed onto the circulation module, which uses them to calculate region-specific oceanographic conditions like wave height, surge height, ocean temperature, and salinity. Less is known about the wave–ice interaction but more ongoing experimental research throughout the world will definitely make it more robust. Apart from three-dimensional wave energy spectra, wave module passes radiation stress, wave-induced current and orbital velocities to the flow circulation module and currents from hydrodynamic models is passed back to the wave models forming a feedback system. The hydrodynamic module also makes use of site conditions like bathymetry of the region, sediment grain size and strength, salinity and tidal variation. The oceanographic conditions from hydrodynamic module is passed as boundary conditions onto permafrost thermal model which, along with site conditions like heat

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Fig. 2 Conceptual Integrated Arctic Coastal Erosion Predictive tool. Adopted and modified with credits to original idea by [5]

flux, porosity, and permafrost sediment type, calculates the dynamic ice content and unsteady temperature field of the coastal permafrost. The outputs from permafrost thermal model includes permafrost temperature field in space and time, ice content, bulk density, ice content, and sediment type. The Arctic coastal erosion model shall model thermodenudation and thermoabrasion in one module. The output from permafrost thermal model is used as boundary conditions in the coastal erosion model. This module shall calculate the failure strength of the permafrost coast as a function of the temperature of the permafrost. After the failure, the bluff geometry is changed and the module calculates the eroded sediment volume and mass which is transferred back to ocean circulation module which later updates the local site conditions like updated coastline, sediment transport and water quality data. After failure, the new permafrost bluff geometry is passed on to permafrost thermal model so as to update the latest locations of the boundaries. The coupled model will introduce more physical processes, but a fully coupled model shall be complex and computationally expensive. Nevertheless, it shall produce best possible predictions in local areas where site conditions are available. The model should also be validated against field and experimental data.

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4 Conclusions and Future Directions Current study focusses on the review of existing numerical modeling tools to predict Arctic coastal erosion and proposing a conceptual integrated Arctic coastal erosion predictive tool. The study highlights that the rate of Arctic coastal erosion is already at an alarming level, which is expected to get worse due to climate changes. The review of existing models to study the process of erosion in Arctic shows that there exists some knowledge gaps in understanding of the phenomena which needs to be closed. An ideal solution is to develop a predictive tool consisting of four different models coupled with each other; (1) Earth system model to provide boundary conditions to other models, (2) Hydrodynamic module to calculate flow, sediment transport and wave propagation in ice, (3) Thermal permafrost model to provide permafrost temperature field, ice content, bulk density, ice content, and sediment type to (4) The Arctic coastal erosion model. The coupled model will be complex and computationally expensive that can produce best possible predictions in local areas where site conditions are available. Validation of the model against field and experimental data shall be required. Presently, efforts are underway at NTNU to close the existing knowledge gaps and develop such a predictive tool. Acknowledgements This work was carried out as part of a Center for Research-based Innovation called Sustainable Arctic Marine and Coastal Technology (SAMCoT) at Norwegian University of Science and Technology Trondheim, Norway, funded by the Norwegian Research Council and industrial partners. The authors would also like to acknowledge the efforts done my M.Sc. students, Agnes Katharina Schneider and Nauman Raza, for helping with parts of the text and graphics used in the paper.

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Evaluation of Hydrodynamic Performance of Quarter Circular Breakwater Using Soft Computing Techniques N. Ramesh, A. V. Hegde and Subba Rao

Abstract Breakwaters are massive structures constructed to provide the required tranquility within the ports. They are also used for safeguarding the beaches from eroding due to the severe action of waves, especially during inclement weather. In recent years, innovative structures such as Semi-circular and Quarter-circular Breakwaters (QBW) are being evolved to fulfill the ever-increasing demand from the coastal sector. QBW is a caisson with quarter circular surface towards incident waves, with horizontal bottom and a vertical wall on its rear side placed on a rubble mound foundation. In this paper, the experimental data collected at National Institute of Technology, Surathkal is used. The data collected is analysed by plotting the non-dimensional graphs of reflection coefficient, reflected wave height and incident wave height for various values of wave steepness. The values are used for prediction of QBW adopting Multi-Layer Perceptron (MLP) and Radial Basis Function (RBF) networks. Goodness-of-Fit (GoF) test using Kolmogorov–Smirnov (KS) test statistic is applied for checking the adequacy of MLP and RBF networks to the experimental data. The performance of these networks is evaluated by using Model Performance Indicators (MPIs), viz. correlation coefficient, mean absolute error and model efficiency. The GoF test results and values of MPIs indicated the MLP is better suited amongst two networks adopted for evaluation of hydrodynamic performance of QBW. Keywords Correlation coefficient · Kolmogorov–Smirnov test Mean absolute error · Model efficiency · Multi-layer perceptron Quarter-circular breakwater · Radial basis function

N. Ramesh (B) · A. V. Hegde · S. Rao National Institute of Technology Karnataka, Surathkal, Mangalore 575025, Karnataka, India e-mail: [email protected]; [email protected] S. Rao e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_7

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1 Introduction Breakwater is a structure generally, used in coastal protection works and also for creating tranquility in basin in harbors. Over the years, breakwater was of rubble mound weighing in tons. In the latter part of nineteenth-century innovative structures like tetrapods, tripods and other interlocking blocks are also evolved. Considering the huge quantity of rock material required, at the beginning of twenty-first century caisson type of breakwater were thought off. One such breakwater is Quarter-circular Break Water (QBW), a new-type breakwater first proposed by Xie et al. [15] on the basis of Semi-circular Break Water (SBW). The QBW is usually placed on rubble mound foundation and its superstructure consists of a quarter circular surface facing sea sides, a horizontal bottom and a rear vertical wall. The QBW structure is hollow, hence, the weight and materials required are less and it is more suitable where the foundation is relatively weak. The QBW is a prefabricated caisson, which can be properly designed for handling stresses and can be transported and placed with more precision at the desired location. Depending upon the purpose the Quarter-circle breakwater may be fabricated as emerged or submerged type structure, with and without perforation to dissipate the incident wave energy.

2 Literature Review Jiang et al. [9] studied the performance of QBW by comparing the hydraulic performances of SBW and QBW under similar hydraulic conditions. They conducted 2-Dimensional (2D) vertical wave numerical model and physical model studies, and found that wave reflection of both QBW and SBW are closer to each other. They stated that the wave reflection coefficient (Kr ) remains almost same with values less than 1.0 even when freeboard (hc ) value becomes 2–3 times incident wave height (Hi ) for both types of breakwaters. During wave overtopping in submerged condition, they found high flow velocity and vortexes near the rear walls of QBW, which may be due to the top sharp corner and sudden expansion of flow around QBW. They described that the flow fields in front of both QBW and SBW are similar in both in submerged as well as emerged conditions and this explains the closeness of reflection coefficient values for both breakwaters. Shi et al. [13] studied the hydrodynamic performance of QBW under both regular and irregular wave conditions. Regular waves were generated by reciprocating wave paddle at a constant speed, whereas irregular waves were generated by frequency spectrum simulation with target spectrum of JONSWAP type. For analyzing the wave reflection, two types of wave reflection coefficients were described by Shao [12], viz. (i) Kr that describes the whole effect of wave reflection by breakwater and (ii) Circular-surface reflection coefficient (Krc ) that describes the reflective effect by circular surface on the adjacent flow field in front of the breakwater. The study revealed that at the same relative freeboard height (hc /Hi ), the value of Kr was higher

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than Krc that indicates the entire reflective effect of QBW is stronger than that by the circular surface on the adjacent flow field. To estimate the energy dissipation as the wave passes over the breakwater wave energy loss parameter (KEloss ) was described. KEloss is the ratio of dissipated wave energy to the original gross wave energy within the process of wave structure interaction. Based on the results obtained from the study, it was found that the loss of wave energy for emerged breakwater is larger than that for submerged breakwater. Hegde and Ravikiran [8] conducted experiments on the physical model of QBW in 2D wave flumes to evaluate the reflection characteristics of QBW of different radii in different submergence conditions. The models were made of galvanized iron sheets and coated with a cement slurry to simulate concrete surface. For finding the variation of Kr different graphs were plotted with the incident wave steepness (Hi /gT2 ) (where, g is the gravitation and T is the wave period) for various submergence ratios (d/hc ) and different ranges of (R/Hi ) (where, d is the depth of water and R is the breakwater radius). For all values of d/hc and R/Hi , they found that Kr increases logarithmically (best-fit) as incident wave steepness increases. The study revealed that whatever may be the depth, caisson radius, height of structure crest (from seabed) steeper the waves the more will be the reflection from breakwater. Hafeeda et al. [7] conducted experiments in a 2D monochromatic wave flume on a seaside perforated QBW model. They analyzed the experimental data by plotting the non-dimensional graphs of Kr (i.e., Hr /Hi ) (where Hr is the reflected wave height) for various values of R/Hi . They observed that the value of Kr increased with increase in wave steepness and when the freeboard (hc ) increased then the value of Kr also increased. They found that when the height of the structure (hs ) increases, a smaller height of the QBW portion of the caisson is exposed to waves, which is the effect of the curvature is less pronounced that tend to lesser dissipation and more reflection. Binumol et al. [3] conducted physical model studies of QBW with three different radii and S/D (spacing to the diameter of perforations) ratio. Dimensional analysis was carried out to find the non-dimensional parameters such as incident wave steepness, depth parameter (d/gT2 ), height of structure, depth of water, wave run up (Ru /Hi ), wave rundown (Rd /Hi ), etc., using Buckingham’s π-theorem. The experimental data collected was analyzed by plotting the graph of dimensionless wave run up and dimensionless wave rundown for various values of wave steepness and different heights of structure to the depth of water. They observed that the value of Ru /Hi increases with an increase in wave steepness for all values of hs /d and d/gT2 . This was because as wave height increases there is an increase in wave energy and hence run up increases with an increase in wave steepness. For all values of hs /d and d/gT2 , the dimensionless wave rundown was found to decrease with increase in wave steepness for all values of hs /d and d/gT2 because as wave height increases there is an increase in wave energy resulting in more run up and hence less rundown. Rd /Hi was also found to increase with the increase in the depth parameter (d/gT2 ), because at higher water depths the effect of curvature is more pronounced resulting in lower run up and hence more wave rundown. Balakrishna and Hegde [2] investigated reflection coefficient (Kr ) and dissipation (or loss) coefficient (KL ) for physical models of quarter circle caisson breakwater for different radii with constant S/D ratio. They

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observed that reflection coefficient was found to increase with wave steepness, which was similar to all earlier studies. Dissipation coefficient decreased with the increase in wave steepness. The study revealed that as wave period decreases the value of loss coefficient decreases. The study also revealed that as hs /d increases, dissipation increases which is a reverse trend in the case of reflection, this trend is found to be true for all values of d/gT2 values. Generally, computational intelligence techniques, viz., Artificial Neural Network (ANN), Adaptive Neuro-Fuzzy Interface System (ANFIS), Support Vector Machine (SVM) regression, genetic algorithm, etc., have been efficaciously proposed as an efficient tool for modelling and predictions in coastal engineering problems [1]. Karthik and Rao [11] reviewed the study on the application of soft computing techniques include ANN-based Multi-Layer Perceptron (MLP) and Radial Basis Function (RBF) networks, ANFIS, SVM and Fuzzy Logic in breakwater studies. In the present study, MLP and RBF networks are used for prediction of the variables considered for evaluation of the hydrodynamic performance of QBW. Goodness-of-Fit (GoF) test using Kolmogorov–Smirnov (KS) test statistic is applied for checking the adequacy of MLP and RBF networks to the experimental (or observed) data. The performance of these networks is evaluated by using Model Performance Indicators (MPIs), viz., Correlation Coefficient (CC), Mean Absolute Error (MAE), and Model Efficiency (MEF). This paper presents the procedures adopted in evaluating the hydrodynamic performance of QBW using MLP and RBF networks with an illustrative example.

3 Methodology Artificial Neural Network (ANN) modeling procedures adapt to the complexity of input–output patterns and accuracy goes on increasing as more and more data become available. Figure 1 shows the architecture of ANN that consists of an input layer, hidden layer, and output layer [14]. From ANN structure, it can be easily understood that input units receive data from external sources to the network and send them to the hidden units, in turn, the hidden units send and receive data only from other units in the network, and output units receive and produce data generated by the network, which goes out of the system. In this process, a typical problem is to estimate the output as a function of the input. This unknown function may be approximated by a superposition of certain activation functions such as tangent, sigmoid, polynomial, and sinusoid in ANN. A common threshold function used in ANN is the sigmoid function (f(S)) expressed by Eq. (1), which provides an output in the range of 0 ≤ f(S) ≤ 1. N  −1  and Si  Ii Wij + Oi , j  1, 2, 3, . . . , M f(S)  1 + exp(−Si ) i1

(1)

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Fig. 1 Architecture of ANN

where Si is the characteristic function of ith layer, Ii is the input (I) unit of ith layer, Oi is the output (O) unit of ith layer, Wij is the synaptic weights between input (i) and hidden (j) layers, N is the number of observations and M is the number of neurons (or units) of hidden layer [10].

3.1 Theoretical Description of MLP Network MLP network [6] is based on an architecture with a single hidden layer as shown in Fig. 2. Gradient descent is the most commonly used training algorithm in MLP in which each input unit of the training dataset is passed through the network from the input layer to the output layer. The network output is compared with the target output and output error (E) is computed using Eq. (2). 2 1  Xi − X∗i 2 i1 N

E

(2)

where Xi is the observed value of ith sample and X∗i is the predicted value for ith sample. Wij (M)  −ε

∂E + α Wij (M − 1) ∂Wij

(3)

where Wij (M) is the weight increments between ith and jth layers during M neurons (units) and Wij (M − 1) is the weight increments between ith and jth layers during

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Fig. 2 Structure of MLP network

M − 1 neurons. In MLP, momentum factor (α) is used to speed up training in the very flat region of the error surface to prevent oscillation in the weight and learning rate (ε) is used to increase the chance of avoiding the training process being trapped in local minima instead of global minima.

3.2 Theoretical Description of RBF Network RBF network is supervised and three-layered feedforward neural network and presented in Fig. 3. The hidden layer of RBF network consists of a number of nodes and a parameter vector called a “centre”, which can be considered the weight vector. In RBF, the standard Euclidean distance is used to measure the distance of an input vector from the center. The design of neural networks is a curve-fitting problem in a high dimensional space in RBF [10]. Training the RBF network implies finding the set of basis nodes and weights. Therefore, the learning process is to find the best fit to the training data. The transfer function of the nodes is governed by nonlinear functions that are assumed to be an approximation of the influence that data points have at the center. The transfer function of an RBF is mostly built up of Gaussian rather than sigmoid. The Gaussian function decrease with distance from the center. The transfer function of the nodes is governed by nonlinear functions that is assumed to be an approximation of the

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Fig. 3 Structure of RBF network

influence that data points have at the center. The Euclidean length is represented by rj that measures the radial distance between the datum vector X(X1 , X2 , . . . , XM ) and the radial center X(j)  (W1j , W2j , . . . , WMj ) can be written as: M 1/2    2 (j) rj  X − X   Xi − Wij

(4)

i1

where rj   is the Euclidean norm and ( ) is the activation  function.  A suitable transfer function is then applied to rj to give (rj )  X − X(k) . Finally, the output layer (k − 1) receives a weighted linear combination of (rj ). X(k)  W0 +

N 

c(k) j (rj )  W0 +

j1

N 

  (j)   c(k) j  X−X

(5)

j1

where, cj is the center of the neuron in the hidden layer and (rj ) is the response of the jth hidden unit and W0 is the bias term [11].

3.3 Goodness-of-Fit Test GoF test [5] involving, viz., Kolmogorov–Smirnov (KS) test statistic is applied for checking the adequacy of applying MLP and RBF networks to the series of experimental data. Theoretical description of the KS test statistic is as follows: N

KSC  Max(Fe (Xi ) − FD (Xi )) i1

(6)

where Fe (Xi )  (i − 0.35)/N is the Empirical Cumulative Distribution Function (CDF) of Xi and FD (Xi ) is the computed CDF of Xi by MLP and RBF.

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3.4 Model Performance Analysis The performance of MLP and RBF networks used in prediction of the variables (KL , Kr, and Kt ) is evaluated by Model Performance Indicators (MPIs), viz., Correlation Coefficient (CC), Mean Absolute Error (MAE) and Model Efficiency (MEF), and is given as follows:  ∗

N  ∗ X − X X − X i i i1 CC     2  2 N  ∗ N ∗ X − X − X X i i i1 i1 

 N  1   ∗ Xi − Xi ∗ 100 MAE(%)  N i1 ⎛  ⎞

N  ∗ 2 X − X i i MEF(%)  ⎝1 − i1  2 ⎠ ∗ 100 N X − X i i1

(7)

where X is the average value of observed data and X∗ is the average value of predicted data [4]. The network with high CC, less MAE, and better MEF is considered as best suited amongst MLP and RBF networks adopted in the prediction of the variables used for evaluation of the hydrodynamic performance of QBW.

4 Application In this paper, a study on the comparison of the hydrodynamic performance of QBW was carried out. The experimental data, viz., depth of water (d), wave period (T), incident wave height (Hi ), transmitted wave height (Ht ), reflected wave height (Hr ), transmission coefficient (Kt ), loss coefficient (KL ), wavelength (L), reflection coefficient (Kr ), incident wave steepness (Hi /gT2 ), relative freeboard (hc /Hi ) and relative wave height (Hi /d) collected at National Institute of Technology, Surathkal, is analysed by plotting the non-dimensional graphs of reflection coefficient, reflected wave height and incident wave height for various values of wave steepness. The values were used for prediction of QBW adopting ANN-based MLP and RBF networks.

4.1 Description of Experimental Setup The study was conducted in the regular wave flume available in the marine structures laboratory of the Department of Applied Mechanics and Hydraulics, National Institute of Technology Karnataka, Surathkal. The experiments were performed in

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a wave flume with dimensions of 50 m long, 0.74 m wide and 1.1 m deep. Out of 50.0 m, 42 m length has a smooth concrete bed. It has a 6.3 m long, 1.5 m wide and 1.4 m deep chamber at one end, where wave flap is hinged at the bottom generates waves. The flap is controlled by an induction motor of 11 kw, 1450 rpm and is regulated by an inverter drive, 0–50 Hz rotating with a speed range of 0–1550 rpm. This facility is able to generate regular waves of 0.08–0.24 m of periods 0.8–4 s. A series of vertical asbestos sheets are spaced at about 10 cm distance from each other and kept parallel to the length of the flume to dissipate the generated waves by damping the disturbance caused by successive reflection and to smoothen them. The QBW model is placed in the flume 28 m away from the wave flap, above the rubble mound foundation (Fig. 4). The slope used for the rubble foundation is 1:2. Three capacitance-type wave probes were used for measuring the incident and reflected wave heights. The wave probes were placed at a distance of 4 m from the center of the model. In the present study, 75% of data was used for training (TRG) and 25% of data for testing (TES). Table 1 presents the descriptive statistics (i.e., Average, Standard Deviation (SD), Coefficient of Variation (CV), Coefficient of Skewness (CS ), and Coefficient of Kurtosis (CK )) of the observed data of the variables that are considered for prediction for evaluation of the hydrodynamic performance of QBW.

Fig. 4 A schematic diagram of experimental setup Table 1 Descriptive statistics of the observed data Descriptive KL Kr statistics Data points Data points Data points (1–27) (28–36) (1–27)

Kt Data points (28–36)

Data points (1–27)

Data points (28–36)

Average

0.519

0.609

0.154

0.079

0.823

0.772

SD CV (%)

0.134 25.8

0.128 21.0

0.070 45.3

0.046 57.9

0.076 9.3

0.089 11.5

CS

−0.205

−0.789

−0.110

0.537

−0.329

0.602

CK

−1.139

−1.112

0.049

−0.430

−1.249

−1.238

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5 Results and Discussions Statistical software, namely, SPSS (Statistical Package for the Social Sciences) is used to predict the hydrodynamic characteristics of QBW such as refraction coefficient, reflection coefficient, and loss coefficient using MLP and RBF. The experimental data was trained with MLP and RBF networks, which are used to determine the optimum network architecture for the variables, viz., KL , Kr, and Kt . The determined Optimum Network Architecture (ONA) with model parameters obtained from MLP and RBF developed through REG was used for prediction of QBW.

5.1 Prediction of KL , Kr, and Kt Using MLP The momentum factor (α) and learning rate (ε) were fixed as 0.65 and 0.08, while optimizing the network architecture of MLP for KL , Kr, and Kt . The network data was trained with ONA (i.e., 12-15-1) with one input layer with 12 units, one hidden layer with 15 hidden units and one output layer with 1 unit. The network was tested with model parameters for the prediction of the variables (KL , Kr, and Kt ) to evaluate the hydrodynamic performance of QBW.

5.2 Prediction of KL , Kr, and Kt Using RBF By using the procedures of RBF, as described in Sect. 3.2, the experimental data was trained with model parameters to determine the ONAs of KL , Kr, and Kt . The ONAs were determined as 12-7-1 for KL whereas 12-10-1 for Kr and 12-4-1 for Kt . The ONAs were used to test the network data of the variables considered in the study. The time series plots of predicted values of the variables (KL , Kr and Kt ) using MLP and RBF networks together with observed data are presented in Figs. 5, 6 and 7. The scatter plots of observed and predicted variables with the model fit and R2 (Coefficient of determination) values are presented in Figs. 8, 9 and 10. From Figs. 5, 6 and 7, it can be seen that the predicted values of the variables (KL , Kr and Kt ) using MLP network gives better performance than RBF during the testing period. From Figs. 8, 9 and 10, it can be seen that the R2 values obtained from fitted model using MLP for KL , Kr and Kt variables are 0.970, 0.926 and 0.980, which indicates that there is a perfect fit between the observed and predicted variables.

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Fig. 5 Time series plots of observed and predicted values of KL (using MLP and RBF)

Fig. 6 Time series plots of observed and predicted values of Kr (using MLP and RBF)

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Fig. 7 Time series plots of observed and predicted values of Kt (using MLP and RBF)

Fig. 8 Scatter plots of observed and predicted values of KL (using MLP and RBF)

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Fig. 9 Scatter plots of observed and predicted values of Kr (using MLP and RBF)

Fig. 10 Scatter plots of observed and predicted values of Kt (using MLP and RBF)

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5.3 Analysis Based on GoF Test The KS test statistic values of MLP and RBF networks for the variables KL , Kr and Kt were computed and found to be varied between 0.125 and 0.210. These values were noted to be less than of its theoretical value of 0.221 at 5% level, and at this level, both MLP and RBF are found to be acceptable for prediction of the variables (KL , Kr and Kt ). The predicted variables were used for evaluation of the hydrodynamic performance of QBW.

5.4 Performance Analysis Based on MPIs The model performance of MLP and RBF networks used in predication of the variables was evaluated by MPIs and the results are presented in Table 2. From Table 2, it may be noted that the MEF obtained from MLP network is higher than the corresponding values of RBF. The CC values obtained from MLP for the predicted variables vary from 0.950 to 0.998. Also, from Table 2, it may be noted that the percentages of MAE obtained from MLP for the predicted variables (KL , Kr and Kt ) during TRG and TET periods are less than the corresponding values of RBF. From GoF test results using KS test statistic and model performance analysis using MPIs values, it was found that the MLP network is better suited amongst two networks adopted for prediction of the variables for evaluation of hydrodynamic performance of QBW.

5.5 Analysis Based on Descriptive Statistics In addition to MPIs, the overall performance of MLP and RBF networks used in prediction of the variables (KL , Kr, and Kt ) was analyzed through the descriptive statistics (i.e., Average, Standard Deviation (SD), Coefficient of Variation (CV), Coefficient of Skewness (CS ) and Coefficient of Kurtosis (CK )), and the results are presented in Table 3. From the values of descriptive statistics of the variables, as given in Tables 1 and 3, the percentage of deviation on the average predicted value of KL using MLP network with reference to the average observed value was computed as 0.6% and 0.2% for training and testing periods. Similarly, for Kr , the values were computed as 1.9% (for training) and 1.3% (for testing). For Kt , the values were computed as 0.2% (for training) and 0.1% (for testing).

MEF (%)

CC MAE (%)

MPIs

96.3

0.981 1.6

98.8

0.994 1.2

TES

58.8

0.769 6.8 89.9

0.956 3.5

TES

90.9

0.950 1.6

Kr MLP TRG

MLP TRG

RBF TRG

KL

97.7

0.968 0.9

TES

Table 2 Values of MPIs for KL , Kr , and Kt given by MLP and RBF networks

71.7

0.836 3.0

RBF TRG

78.7

0.677 2.7

TES

Kt

97.3

0.986 0.9

MLP TRG

99.5

0.998 0.5

TES

66.7

0.825 3.7

RBF TRG

86.2

0.959 2.7

TES

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0.135 22.2

−0.651

−1.501

0.129 25.0

−0.033

−1.386

CS

CK

0.608

0.516

SD CV (%)

−1.108

−0.113

0.119 23.0

0.515

−1.714

−0.852

0.095 15.5

0.611

TES

−0.297

0.491

0.066 43.7

0.151

MLP TRG

RBF TRG

MLP TRG

TES

Kr

KL

Average

Descriptive statistics

0.693

0.666

0.045 57.7

0.078

TES

−0.104

0.535

0.054 34.9

0.154

RBF TRG

Table 3 Descriptive statistics of the predicated variables (KL , Kr and Kt ) using MLP and RBF

2.177

1.166

0.023 28.4

0.081

TES

−1.154

−0.287

0.076 9.3

0.821

MLP TRG

Kt

−0.949

0.635

0.085 11.0

0.770

TES

−1.663

0.100

0.070 8.6

0.814

RBF TRG

−1.836

0.649

0.060 7.8

0.767

TES

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6 Conclusions The paper described the procedures involved in the prediction of the variables, viz., KL , Kr, and Kt adopting MLP and RBF networks. The performance of these networks was evaluated by GoF test using KS test statistic and model performance analysis using MPIs. From the results of data analysis, the following conclusions were drawn from the study: (i) Optimum MLP network architecture, viz., 12-15-1 was used for training the network. (ii) KS test results supported the use of both MLP and RBF networks in evaluating the hydrodynamic characteristics parameters. (iii) Qualitative assessment through time series and scatter plots indicated that the fitted curves using MLP is closer to the fitted curves of the experimental data. (iv) Model performance analysis indicated the MLP is better suited amongst two networks adopted for prediction of KL , Kr and Kt . (v) For KL , the values of CC, MAE, and MEF given by MLP were found to be 0.994, 1.2% and 98.8% respectively during the testing period. Similarly, the values of CC, MAE, and MEF were computed as 0.968, 0.9%, and 97.7%, respectively, for Kr . For Kt , the values of CC, MAE, and MEF were computed as 0.998, 0.5%, and 99.5%. (vi) The study suggested that the predicted variable of KL , Kr and Kt by MLP network could be considered for evaluation of the hydrodynamic performance of QBW. Acknowledgements The authors are grateful to Dr. (Mrs.) V. V. Bhosekar, Additional Director and Director In-charge, Central Water and Power Research Station, Pune, for providing research facilities to carry out the study. The authors are thankful to National Institute of Technology, Surathkal, for the supply of experimental data used in the study.

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8. Hegde AV, Ravikiran L (2013) Wave structure interaction for submerged quarter circle breakwaters of different radii-reflection characteristics. World Acad Sci Eng Technol 7(7):1367–1371 9. Jiang XL, Gu HB, Li YB (2008) Numerical simulation on hydraulic performances of quarter circular breakwater. China Ocean Eng 22(4):585–594 10. Kaltech M (2008) Rainfall-runoff modelling using artificial neural networks: modelling and understanding. J Environ Sci 6(1):53–58 11. Karthik S, Rao S (2017) Application of soft computing in breakwater studies—a review. Int J Innov Res Sci Eng Technol 6(5):8355–8359 12. Shao LM (2003) Separation of incident waves and reflected waves and study of reflection coefficient. Dalian University of Technology Press, Dalian (in Chinese) 13. Shi YJ, Wu Mi-Ling, Xue-Lian Jiang, Yan-bao Li (2011) Experimental research on reflection and transmitting performance of quarter circle breakwater under regular and irregular waves. China Ocean Eng 25(3):469–478 14. Tokar S, Markus M (2000) Precipitation runoff modelling using artificial neural network and conceptual models. J Hydrol Eng 5(2):156–161 15. Xie SL, Li YB, Wu YQ, Gu HB (2006) Preliminary research on wave forces on quarter circular breakwater. Ocean Eng 24(1):14–18

Statistical Analysis of Coastal Currents from HF Radar Along the North-Western Bay of Bengal Samiran Mandal, Saikat Pramanik, Subrota Halder and Sourav Sil

Abstract Highly accurate ocean current measurements are very much important in the field of ocean engineering. Over the past decades, the High-Frequency (HF) Radars are known to be one of the important marine instruments for oceanographic studies. The present work focuses mainly on statistical analysis of HF radar-measured ocean surface current along the Odisha coast, north-western Bay of Bengal during 2015. The observations indicate that northward propagating Western Boundary Current (WBC) and southward propagating East India Coastal Current (EICC) can reach up to 1.8 m/s and 1.0 m/s, respectively. The zonal (meridional) components vary in the range −0.8 to 0.8 (−0.6 to 0.7) m/s along with standard deviation of 0.25 m/s for both the components with 99% significance level. The boxplot analysis shows the extreme values of both the zonal and meridional currents along with the negative medians; however, certain outliers are observed only for zonal currents. The 25th percentile is less than −0.20 m/s for the meridional currents, whereas opposite result for zonal currents. The zonal and meridional currents follow normal distribution, whereas the current magnitude and kinetic energy follow Weibull distribution. The Weibull shape parameter (β) varies for both the parameters: current magnitude (β > 1) and kinetic energy (0 < β < 1) due to the variations in moments, which indicates that in case of kinetic energy (current magnitude), the failure rate decreases (increases) over time. This circulation variability can be attributed predominantly to the winds and the coastal dynamics. Keywords Bay of Bengal · HF radar · Ocean currents · Statistics and tides

S. Mandal (B) · S. Pramanik · S. Halder · S. Sil School of Earth, Ocean and Climate Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar, India e-mail: [email protected] S. Halder Indian Institute of Tropical Meteorology, Pune, India © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_8

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1 Introduction Over the past two decades, the High-Frequency (HF) radars are known to be one of the important marine instruments for oceanographic studies and thereby have proved to be the most efficient instrument for measuring ocean surface currents along the coast. The high-frequency datasets provide us the opportunity for multi-scale analysis of ocean surface currents along the coastal regions. The Bay of Bengal (BoB), covering the north-eastern part of the Indian Ocean (76°–100°E, 4°–24°N), is a semienclosed tropical ocean basin. The current system on the western boundary in the BoB is well known for its unique circulation pattern with high complexity as compared to the rest of the basin. The space–time current variability, northward during spring and southward during autumn, has been studied from various hydrographic datasets [1], satellite altimetry datasets [2–4] and numerical simulations [5–7] in the past few decades. Earlier circulation studies were mostly basin scale and from ocean models and satellites. The observational data are limited along the Indian coast of the BoB, till Earth System Science Organization—National Institute of Ocean Technology (ESSO-NIOT), Indian National Centre for Ocean Information Services (ESSOINCOIS) have installed five pairs of the long-range SeaSonde HF Radar systems along the Indian coastline, operating continuously since 2009, in order to remotely sense the ocean surface currents covering the coastal regions of India [8]. Specifically, we focus on the HF radar datasets (4.8 MHz) installed along the Odisha coast (from Puri and Gopalpur stations) that is available (courtesy: INCOIS) hourly on a 6-km grid (albeit with spatial and temporal gaps) over a limited region (18–20 N, 85–87 E) (Fig. 1). The current observations from HF radar and their statistical distribution are the new findings of this study. The HF Radars can be used for real-time ocean monitoring and ocean state forecasting purposes through the numerical simulations. Among the implications, one of the major implications is the efficient management of coastal hazards. Also, the HF Radar-derived surface currents maps enable to improve the navigation for safety purposes in the restricted areas (ports and harbours). The finer temporal variability of the surface currents enables Lagrangian tracking of small parcels of surface water, which enables hazard mitigation in managing suspended sediments in dredging, in emergency situations where flotsam and other drifting items need to be found, and in pollution control. Nowadays, the real-time tsunami monitoring is also provided by the HF Radars. Inspired by all these, the present study focuses primarily on the statistical analysis of the coastal currents in 2015 along the north-western BoB. The structure of the paper is as follows; a brief description of Weibull distribution is given in Sect. 2. The data and methodology are discussed in Sect. 3, the results and discussions are described in Sect. 4, and finally, the conclusions are reported in Sect. 5 followed by acknowledgements and a list of references.

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Fig. 1 The data coverage (shaded) during 2015 in percentage (%). The location at nearshore ‘N’ is indicated by the triangle symbol. Black contours denote the isobaths of −50, −200, −500, −1000, −1500 and −2500 m. The red dots are the HF Radar stations along Odisha coast

2 Weibull Distribution The Weibull probability density function (PDF) is defined only for all positive values, x > 0, as f (x; k, λ) 

β  x β−1 −(x/λ)β e λ λ

where λ and β are the two positive parameters. The term λ is the scale parameter of the distribution, and β is the shape parameter. Many studies have indicated that the distribution of wind speed can be represented by the Weibull distribution [9]. Depending on the values of the parameters, the Weibull distribution can be used to model weather forecasting. In this study, we will examine how the values of the shape parameter, β, and the scale parameter, λ, affect such distribution characteristics, like, the shape of the curve, the reliability, and the failure rate. Note that in the rest of this paper, the general form of Weibull distribution (2 parameters) has been assumed.

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3 Data and Methodology The measurements of high radar frequency echoes backscattered from the sea surface can be used to deduce information on both waves and surface currents. These radars are of direction finding type, consisting of one receiving and one transmitting antennae at each of the locations. The two radars at the Odisha coast which are located at Gopalpur (84.96°E, 19.30°N) and the other at Puri (85.86°E, 19.80°N) covers a region of ~200 km from the coast [8], the locations are shown in Fig. 1. The high resolution (~6 km) and high-frequency (hourly) surface current from HF Radar during 2011 (source: INCOIS, India) along the Odisha coast is initially used for this analysis. The daily winds derived from ASCAT are used with 25 km × 25 km spatial resolution, provided by IFREMER, France due the concurrent period of HF Radar data availability. The current time series at the location with maximum data availability is chosen for the analysis. The basic statistics (standard deviation, median, probability distribution function) have been derived with the help of box plots, frequency distribution curves, via, kernel distribution estimation. In addition, the surface current variability has also been analysed along the north-western BoB.

4 Results and Discussions A thorough statistical analysis has been carried out at location N (with maximum data availability). The statistical metrics include the standard measures of centre (mean, mode and median) and dispersion (range and standard deviation), student’s t-test, kernel distribution estimation. In addition, both the higher frequency variability as well as daily variability has also been analysed. This section is divided into two parts with focuses statistical analysis and daily variability of the currents.

4.1 Variability of Coastal Currents The HF Radar datasets are important to explain the higher resolution sub-mesoscale features which are not even resolved by the models. So, the main focus of this section is the ability of the radars to capture the oceanic and associated coastal processes. The validation of the surface currents on daily scale has already been carried out using OSCAR (satellite-derived currents) and HYCOM (model-simulated currents) currents, as no other in situ observations are available in this domain [10]. The southward flow is usually observed during the months of January, but in 2015 the southward flow persisted till mid of February. However, the reversal phase is observed from February end, which indicates the formation of the northward Western Boundary Current (WBC). Northward currents are strong with an amplitude of

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Fig. 2 a The current direction and magnitudes in m/s (sticks) for HF radar (upper panel) at location N for the year 2015. The lower panel shows the rose plots for b winds and c HF radar currents

1.8 m/s (Fig. 2a). However, the reversal of currents is again observed during July and the intensified southward propagating EICC is observed during October–November 2015 (Fig. 2a). The current magnitude of 1.2 m/s is observed during this period, as compared to the springtime WBC. This reversal is caused mainly due to the reversal of the winds. In addition, the present year is rich with eddy variability and propagated along the coastline (Fig. 2a), which may be due to interaction with the coastal topography (Fig. 1). It is surprising to note that the WBC in its intensified stage is observed very nearby the coastline. The rose plot for the surface currents (Fig. 2b) and the winds (Fig. 2c) indicate that the north-eastward and south-westward circulation patterns are generally forced by the winds, whereas the other variability observed in the circulation pattern is expected to be due to the local coast and continental shelf dynamics. The detailed analysis will be carried out in the nearby future.

4.2 Statistical Analysis of Coastal Currents Since the main focus of the work is the statistical analysis of the HF radar-derived surface currents, so the following statistical results have been derived. The zonal

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Fig. 3 The boxplots for a zonal and b meridional currents at the location N. The red plus marks are the whiskers. The red line in the middle of the box in the median. The upper (lower) end of the box indicates the third (first) quartile

component and meridional components vary in the range −0.8 to 0.8 m/s and −0.6 to 0.7 m/s, respectively (Fig. 3). The mean current is negative for the entire year, however, the sometimes currents are clearly positive, specifically during the following three periods: mid-February to May, August and December. Very low standard deviation of 0.25 m/s is observed for both the components. The boxplot analysis shows extreme values of both the zonal and meridional currents along with the negative medians; however, certain outliers are observed only for zonal currents (Fig. 3). The 25th percentile is less than −0.2 m/s for the meridional currents, whereas opposite result for zonal currents. The interquartile range is observed more for meridional component indicating more variability. However, the variability will be observed more in case of the box analysis is done on the monthly basis. Also, student’s t-test shows that the null hypothesis is rejected and that the mean of the data is significantly different from zero, with 99% significance level. Finally, both the velocities components (zonal and meridional), current magnitude and kinetic energy are analysed through the kernel distribution estimation, i.e. the probability distribution functions are determined. The zonal and meridional currents follow a normal distribution (Fig. 4a, b) whereas, the current magnitude and kinetic energy follow Weibull distribution (Fig. 4c, d). In case of ocean surface currents derived from HF Radars, the shape parameter (β) varies for both the quantities:

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Fig. 4 The probability density functions of the time series at location N for a zonal currents (m/s) b meridional currents (m/s) c kinetic energy (m2 /s2 ) and d current magnitude (m/s)

the value is 1.74 for current magnitude (i.e. β > 1) and 0.87 for kinetic energy (i.e. 0 < β < 1) due to the variations in moments (Fig. 4c, d). On the other hand, the scale parameter (λ) varies for both the quantities as, 0.3 and 0.12 for current magnitude and kinetic energy, respectively (Fig. 4c, d). For a value of 0 < β < 1, the failure rate decreases over time. This happens if there is significant ‘infant mortality’, or abstract values are detected early and the failure rate decreases over time as the abstract values are discarded of the population. For a value of β > 1, the failure rate increases with time. This happens if there is an ‘aging’ process, or parts that are more likely to fail as time goes on. So, shape parameter (β) analysis indicates that in the case of kinetic energy the failure rate decreases over time, whereas in the case of current magnitude, the failure rate increases over time. The main driving force of surface currents seems to be the wind forcing in the open ocean whereas, nearby the coastline it is driven both by the winds and coastal

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Fig. 5 The probability density functions of the time series at location N for a kinetic energy (m2 /s2 ) and b wind magnitude (m/s) of winds from ASCAT

dynamics. To obtain the relationship with the wind, similar distribution analysis has been carried out with winds at the same location. The shape parameter (β) varies for both the quantities: the value is 1.86 for wind magnitude and 0.93 for kinetic energy due to the variations in moments (Fig. 5a, b). On the other hand, the scale parameter (λ) varies for both the quantities as, 5.71 and 32.65 for wind magnitude and kinetic energy, respectively (Fig. 5a, b). The results from the analysis of the winds are consistent with those of the surface currents (Fig. 2b, c). So, the variability in the circulation pattern can be attributed to the variability in the wind pattern. The presence of lots of gap in the current datasets for the year 2015 restricts our study to daily scale, so high-frequency variability will be checked once the gap filling is done. The tidal analysis with carried out in future to aid the knowledge of the tidal driven current in this region via, ADCPs [11] and tide gauge datasets [12].

5 Conclusions The study indicated the usability of the statistics derived from the HF radar datasets in this domain, via, their statistical analysis. The northward propagating WBC and southward propagating EICC can reach up to 1.8 m/s and 1.0 m/s, respectively during 2015. The zonal component and meridional components vary in the range −0.8 to 0.8 m/s and −0.6 to 0.7 m/s, respectively. The mean current is negative for the entire year, however, the currents are clearly positive, during pre-monsoon (May) and post-monsoon (August) period, with a low standard deviation of 0.25 m/s for both components of currents. The analysis shows the extreme values of both the zonal and meridional currents along with the negative medians; however, certain outliers are observed only for zonal currents. The 25th quartile is less than −0.2 m/s

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for the meridional currents, whereas the opposite result for zonal currents. Also, student’s t-test shows that the null hypothesis is rejected and that the mean of the data is significantly different from zero, with a 99% significance level. The current/wind magnitude as well as the kinetic energy (for both current and wind) follows a Weibull distribution, which indicates that in case of kinetic energy the failure rate decreases over time, whereas in case of the current magnitude, the failure rate increases over the time. Hence the variability in the circulation pattern is attributed to the variability of the winds. This statistical study will be helpful for engineering purposes as well as ocean state forecasting purposes through numerical simulations. The study also gives an insight of the coastal circulation on the Odisha coast, as it captured the basin scale as well the mesoscale oceanic processes. Acknowledgements We acknowledge the financial support given by the ESSO-INCOIS, Ministry of Earth Sciences (MoES), and Science and Engineering Research Board (SERB) of Department of Science and Technology (DST), Government of India. Also, we sincerely thank Coastal and Environmental Engineering Group, NIOT, Chennai for constant monitoring of the HF Radars and making the data availability efficient. We also acknowledge IITBBS for providing the research facility.

References 1. Babu MT, Sarma YVB, Murty VSN, Vethamony P (2003) On the circulation in the Bay of Bengal during northern spring inter-monsoon (March–April 1987). Deep Sea Res Part II 5:855–865 2. Somayajulu YK, Murty VSN, Sarma YVB (2003) Seasonal and inter-annual variability of surface circulation in the Bay of Bengal from TOPEX/Poseidon altimetry. Deep-Sea Res I 50:867–880 3. Durand F, Shankar D, Birol F, Shenoi SSC (2009) Spatio-temporal structure of the East India Coastal Current from satellite altimetry. J Geophys Res 114:C02013 4. Gangopadhyay A, Bharat Raj GN, Chaudhuri AH, Babu MT, Sengupta D (2009) On the nature of meandering of the springtime western boundary current in the Bay of Bengal. Geophys Res Lett 40:2188–2193 5. Shankar D, McCreary JP, Han W, Shetye SR (1996) Dynamics of the East India Coastal Current: 1. Analytic solutions forced by interior Ekman pumping and local alongshore winds. J Geophys Res 101(C6):13975–13991 6. Vinayachandran PN, Kagimoto T, Masumoto Y, Chauhan P, Nayak SR, Yamagata T (2005) Bifurcation of the East India Coastal Current east of Sri Lanka. Geophys Res Lett 32:L15606 7. Sil S, Chakraborty A, Ravichandran M (2011) Numerical simulation of surface circulation features over the Bay of Bengal using regional ocean modeling system. Adv GeoSci 24:117–130 8. John M, Jena BK, Sivakholundu KM (2015) Surface current and wave measurement during cyclone Phailin by high frequency radars along the Indian coast. Curr Sci 108(3):405–409 9. Monahan AH (2006) The probability distribution of sea surface wind speeds. Part I: Theory and SeaWinds observations. J Clim 19:497–520 10. Mandal S, Sil S (2017) Coastal currents from HF radars along Odisha Coast. Ocean Dig Q Newsl Ocean Soc India 4:112 11. Jithin AK, Unnikrishnan AS, Fernando V, Subeesh MP, Fernandes R, Khalap S, Narayan S, Agarvadekar Y, Gaonkar M, Tari P, Kankonkar A, Verneka S (2017) Observed tidal currents on the continental shelf off the east coast of India. Cont Shelf Res 141:51–67 12. Murty TS, Henry RF (1983) Tidal harmonics in the Bay of Bengal. J Geophys Res 88(C10):6069–6076

Numerical Modelling and Experimental Investigation on the Effect of Wave Attenuation Due to Coastal Vegetation S. Hemavathi , R. Manjula

and N. Ponmani

Abstract Coastal areas are prone to natural disasters like tsunami and earthquake. The losses occuring due to these disasters are voluminous, since high population densities are generally located along the coastal region. The massive velocity and salinity of waves causes soil erosion and affect the structures present along the coastal belt. Coastal vegetation such as seagrass canopies acts as a natural barrier to soil erosion and to the wave impact. Seagrass is the most abundantly found marine species along the Indian coast. It is located at an ideal depth to dissipate the waves before reaching the shore. The use of seagrass as a buffer zone is gaining momentum in the field of coastal engineering as it also helps in conserving the ecosystem. This paper presents the wave attenuation due to seagrass by numerical modelling and experimental investigation. The Cymodocea Serrulata species (CSS) was selected for the study which is found in coastal regions of India like Palk Bay and Gulf of Mannar. Wave attenuation by the CSS vegetation for different wave heights and wave periods was studied. The numerical model for wave attenuation was created using Flow 3D software and artificial vegetation (silicon rubber tubes) was used for the experimental investigation carried out at wave flume in National Institute of Technology, Tiruchirappalli (NITT). Multiple waves were created from the numerical simulation by varying the wave heights, wave periods and transmitted wave heights at different meadow widths were recorded and analysed. The results of numerical modelling were compared with the experimental investigation. The submergence ratio increases from 0.47 to 0.53. The wave attenuation increases from 60 to 54% of that of original wave height. The model exhibits increased efficiency (the relative plant height (h/d)) in wave height reduction. S. Hemavathi (B) · R. Manjula · N. Ponmani Department of Civil Engineering, National Institute of Technology Tiruchirappalli, Tiruchirappalli 620015, Tamil Nadu, India e-mail: [email protected]; [email protected] R. Manjula e-mail: [email protected] N. Ponmani e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_9

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Keywords Wave attenuation · Submergence ratio · Wave–vegetation interaction

1 Introduction For centuries, the coastal areas have been an inviting habitat for civilizations as they provide plenteous marine resources, fertile farmland and opportunities for trade and transport. At present, about 39% of the world’s population (2.7 billion) lives within 100 km of the coastal areas worldwide, and this number is expected to increase to 3.2 billion (38%) by the 2030s [1]. On the downside, coastal areas are also prone to many natural hazards such as flooding, storms and sea level rise etc., thereby disrupting the sensitive ecosystems and subsequently human livelihood. Another major coastal hazard is erosion. High-velocity and salinity of waves savagely attack coastlines, affect the structures present along the coastal belt causing devastating property damage. Governments have taken measures to control the velocity of waves that hit the shoreline by constructing barrier structures such as breakwater, which helps in attenuating the wave velocity. Coastal vegetation such as seagrasses and reefs forms an integral part of the coastal region. Their natural form enables the attenuation and/or dissipation of waves and acts as a natural barrier to erosion caused by wind and also the impact of waves. Since the man-made breakwater structures require a lot of funding, technical assistance and also, create a new set of environmental danger, the use of coastal vegetation, a natural resource to prevent soil erosion, therefore, can be ecologically and economically feasible. Therefore, fundamental understanding of the effect of wave–vegetation interaction has become of major interest for coastal engineers and researchers for wave attenuation and for coastal restoration purposes. Cymodocea serrulata species (CSS), is one of the species of seagrass found from Chabjuwardoo bay in mid-Western Australia extending across the Timor Sea, the south coast of Indonesia, and throughout the Andaman Sea in the Indian Ocean. This species, which has a cuboidal form with minimum thickness is fast growing and can recolonize after disturbance [2]. In India, it is found from the Coromandel Coast to the Malabar coast and in the Lakshadweep island. The objective of the project carried out is to study the wave–vegetation interaction in a laboratory scale by using an artificial equivalent of the CSS plants. A numerical model for generating regular two-way wave using FLOW-3D is developed and an experimental setup is made to compare the attenuation of waves empirically. Also, the effect of wave attenuation for different submergence ratios, wave period and wave height for numerical and experimental investigation are also studied.

1.1 Empirical Studies In the past, numerous field studies have been documented and quantified [3, 4] for wave–vegetation interactions by considering that the vegetation in open channels is to be an added bed resistance to the flow. These field studies mainly focused on bed

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roughness in low-energy environments. However, large variations in wave attenuation were recorded in the studies, due to the difference in the physical characteristics of the plant species, coverage, and wave conditions. Several attempts have also been done to investigate wave attenuation under controlled conditions in a laboratory flume. Both natural vegetation [5, 6] and artificial vegetation [7, 8] were used for simulation. These flume experiments generally adopt “varying one parameter of interest at a time” principle by isolating the influence of a single plant species or wave property on wave dissipation while holding the rest of parameters constant. Parametric analyses of wave–vegetation interaction on wave attenuation have been reported by researchers exhibits mixed results, however, an increase in wave attenuation with larger incident wave height was generally observed [9].

1.2 Modelling Wave Attenuation From the literature, a number of analytical models and model extensions have been proposed for wave–vegetation interactions. Most of the models employed an empirical drag coefficient to measure the plant stem-oriented drag force induced by the wave. However, models also approximate vegetation with higher base friction factors [5] with many of them devised an empirical drag coefficient for the estimation of the wave-induced drag forces along the plant stem [10, 11]. one of the most widely used hydrodynamic models based on empirical estimates of the fluid drag forces on wave–vegetation interactions has been the ratio between the damping of incident wave height (H o ) and the local wave height (H). This form of the model is being formulated with different dissipation by several researchers. From the literature, it has been generally concluded that careful examination of the physical conditions of the vegetation, based on the biomechanics of the plant species, is essential for the application of the proposed models. Therefore, numerical implementations are introduced in order to combine the effect of wave propagation and plant-induced damping. Initially, numerical studies were focussed on the application of potential flow theory for estimating the vegetation-induced drag on waves [10]. However, numerical models were mainly proposed on wave height evolution, wave–vegetation interactions under irregular wave conditions and for the analysis of the consequences of wave transformations, etc. [12].

2 Methodology The methodology from which the present results were derived is similar to that used in the previously published literature [13]. To prevent duplication of the description of details just a brief account of the physical, numerical modelling, instrumentation and procedures is shown in a flowchart (Fig. 1) and the details are following.

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Identification and collection of Species

Evaluation of species parameters and wave parameters

Physical modelling

Numerical modelling

Wave generation in flume set up and use artificial sea grass

Model of wave flume using FLOW 3D, create sea grass meadow set up using AUTOCAD

Obtaining results for different heights and time periods

Simulation of model (with and without vegetation), for different heights and time periods

Comparison of empirical and numerical results Fig. 1 Flowchart for the procedure

2.1 Physical Model Setup The experiments were performed in a wave flume of Hydraulics Engineering Laboratory of the Department of civil engineering, National Institute of technology (NITT), Tiruchirappalli, India. The wave flume measures 10 m long, 0.6 m deep and 0.26 m wide and is equipped with an electro-hydraulic piston wave generator. A sandy slope wave absorber of 1:7 was installed at the end of the flume for eliminating wave reflection. A 6 m long flat, horizontal area was made in the middle portion of the flume and a patch of 1 m long artificial CSS was placed above, as shown in Fig. 2. The vegetation field started approximately 3 m from the wave paddle.

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Water level Vegetation field (CSS)

2

0

3

4

6

8 (m)

Fig. 2 Details of the experimental setup

2.2 Idealized Vegetation CSS is one of the common and widespread seagrass species thought to be stable although it has been threatened by pollution, localized coastal development, siltation, dredging and destructive fishing methods. It has nearly flat leaves 2–4 mm wide with semi-circular, smooth leaf tip and plain rhizome. Figure 3a, b shows the structure of natural CSS plants and the leaf part. To construct the idealized vegetation, the artificial vegetation must reproduce not only the physical properties of the natural seagrass species it represents but also it must closely follow the flow resistance of the plant canopy itself. After a series of wave forcing tests, silicon tubes were selected to represent the natural CSS as its Young’s modulus is closer to that of the seagrass species. The silicone tubes were discretely designed such that it reproduced the flexibility and buoyancy properties typical of the natural CSS plants. It was bought and cut into pieces with the length (0.18–0.22 m) similar to the natural CSS. These were arranged with a density of 300–400 shoots per sq. m into the concrete block of 1 m length and 0.24 m width

Fig. 3 a Cymodocea Serrulata species (CSS); b leaf part of CSS (Source Algaebase.org)

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Table 1 Measured physical properties of natural and artificial vegetation at laboratory, NITT Parameters Natural seagrass (CSS) Artificial sea grass Modulus of elasticity (MPa) Density

(kg/m3 )

0.97

1

600

1000

Thickness of leaf (mm)

0.2–1

0.5–1

Width of leaf (mm)

10–15

10–15

Length of leaf (m)

0.2–0.25

0.18–0.22

Fig. 4 a Tensometer apparatus at Laboratory, NITT; b stress–strain curve of CSS

for support. The concrete is set for drying for a couple of days until it is ready for the experiment (Table 1 and Fig. 4).

2.3 Test Conditions and Instrumentation The flume was filled up with water up to a height of 10 cm and the test model is then placed in the flume at the distance of 3–4 m from the wave paddle. A scale attached to the flume at different intervals of the flume for recording the values of the wave heights. The wavemaker is entered with the required wave height and thus the regular waves are generated throughout the flume interacting with vegetation. The wave heights at different points of the flume, i.e. just before the wave interacts with vegetation (Ho), at the 50% of the meadow width (H50%), at the 100% of the meadow width (H100%) is found out. It is found out by video recording the movement of the wave at a particular and taking the average of the wave height values in a time period of 2 min. Similarly, the wave heights at different percentages of meadow width are found out.

2.4 Numerical Modelling Using Flow 3D In the present work, numerical modelling was carried out to test the wave attenuation using FLOW-3D software. FLOW-3D is a commercial software package based on

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the volume of fluid (VOF) methodology, developed by Flow Science, Inc. A computerized three-dimensional model of the physical experiment was constructed and imported into FLOW-3D as a stereolithography (stl) file. Once in FLOW-3D, the 3D model was discretized into about multitude of square cells, and wall boundaries were used for enveloping a computational domain. For the present analysis, a set of three-dimensional, partial differential equations were considered as governing equations. For an incompressible Newtonian fluid (water), this set of equations consists the following: (1) the continuity equation; (2) the momentum equations (conservation of momentum per unit mass) in each of the three dimensions; the equation for energy conservation; and, the equations for a turbulence model using turbulent kinetic energy (k), and the turbulent dissipation rate (ε) equation (k-ε) [10, 12]. The governing equations for k-ε are generally derived from the Navier–Stokes equations. Also, the higher order correlations of turbulence fluctuations in k-ε equations are replaced by closure conditions. The k-ε equation, in that case, takes into account the effect of vegetation (see Eqs. 3 and 4). ∂ VF VF ∂ρ 1 + ∇ · (ρ · u¯ · A f )  − ρ ∂t ρ ∂t   − 1 ∂ u¯ 1 → + (u¯ · A f · ∇ u) ¯  − ∇ P + ∇ · (τ A f ) + G ∂t VF ρ

(1) (2)

where V F is the volume fraction open to flow, ρ is the fluid density, u is the velocity component, P is the pressure, Af is the area fraction, τ is the viscous stress tensor and G is the body acceleration. The equations of motion for the fluid velocity components (u, v, w) in the three space directions are the Navier–Stokes equations given as follows: ∂u ∂t ∂v + ∂t ∂w ∂t

1 1 ∂p ∂u ∂u ∂u + v · Ay R + w Az }  − + G x + fx {u · A x VF ∂x ∂y ∂z ρ ∂x   1 1 ∂p ∂v ∂v ∂v + v · Ay R + w Az }  − R + G y + fy {u · A x VF ∂x ∂y ∂z ρ ∂y 1 1 ∂p ∂w ∂w ∂w + + v · Ay R + w Az }− + G z + fz {u · A x VF ∂x ∂y ∂z ρ ∂z +

(3) (4) (5)

In these equations: (Gx , Gy , Gz ) are body accelerations and (f x , f y , f z ) are viscous accelerations. The exact formulation of these differential equations that describe the model is not given here as they shall be found elsewhere [14, 15]. The model domain was created to measure the wave attenuation due to artificial seagrass vegetation for the experimental conditions are given as follows. A flat domain that consists of a flume of dimension 7 m in length, 0.6 m in depth and 0.26 m in width and artificial seagrass bed of 0.26 m in width and 1 m in length. The experiments were carried out for two different submergence ratios of 0.47(h  21 cm and d  45 cm) and 0.53(h  21 cm and d  40 cm) respectively for two different wave periods were set for 1.8 s and 2 s. The initial wave height at the beginning of the flume and the transmitted wave heights at different widths (0, 50, and 100%) along the meadow of vegetation were recorded.

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The steps carried out are: Initially a model diagram was annotated of the problem and a modelling approach is selected which is considered to be ideal. Since air and water are present in the model, an interface of the two liquids was generated and the units for dimensions were mentioned accordingly. Required physical mechanisms such as viscosity and turbulence of the fluid and gravity were provided as input. The body of the flume was meshed with a cell size of 0.1 m and the vegetation with cells of size 0.01 m. The boundary conditions were defined for the flume and initial conditions for fluid elevation is defined. Regular waves with different wave amplitudes and wave periods are created. The basis for output is chosen and the simulation is run and the results are obtained. The flume setup with vegetation that was made in the laboratory was simulated at similar environmental conditions using this software and the results are analysed.

2.5 Results and Discussion The study of the wave–vegetation interactions generally depends on the careful analysis of the collective effects between the flow induced by waves and the plant blades of the meadow covering. Therefore, it is useful in such cases, to measure and analyse the wave characteristics such as the change in velocity profile generated by the wave and the wave damping due to meadow covers. The tests performed have been characterized by a multiple local wave heights H, wave periods t and incident wave heights Ho. The wave heights were measured by two probes one at the beginning of the meadow and the other at its end. The relative wave damping, the ratio between the local wave height (H) to the incident wave height (Ho) was correlated with the percentage of meadow width. For the present study, the tests were carried out using artificial vegetation for different local wave heights of 10, 10.5 and 12 cm and wave period t of 2.6 s. To evaluate the submerged vegetation on wave propagation, the variation of wave heights along the meadow was measured for different wave conditions experimentally. The numerical model was simulated for the similar experimental conditions and the results for H/Ho versus percentage of Meadow width for different wave heights are graphically plotted in Figs. 5, 6 and 7 as follows. The results clearly indicated that there are significant interactions taken place between wave-induced flow and the vegetation. The wave height damping increases indicated by H/Ho, the ratio between the local wave height to the incident wave height when meadow width increases from the entry of the wave until the exit. The wave height reduction is consistent in all the three different testing conditions as shown in Figs. 5, 6 and 7. The wave height damping with the decreasing of the H/Ho ratio can be explained corresponds to a more penetration of wave motion within the water column, which causes a more interaction between the wave-induced flow and the plants. Also, the resulting increase of wave height dumping, when the incident wave height (Ho) increases (Fig. 7), indicates nonlinearity of dumping along the meadow.

Numerical Modelling and Experimental Investigation … Fig. 5 H/Ho versus percentage of meadow width for 2.6 s, h  10 cm

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1.00

Experimental Numerical

0.95

H/Ho

0.90 0.85 0.80 0.75 0.70 0.65 0

20

40

60

80

100

Meadow width percentage Fig. 6 H/Ho versus percentage of meadow width for 2.6 s, h  10.5 cm

1.00

Experimental Numerical

0.95

H/Ho

0.90 0.85 0.80 0.75 0.70 0

20

40

60

80

100

Meadow width percentage

From Fig. 7, it can be seen that in experimental setup the wave height at the end of meadow width is 66% as that of the wave height at the entry point. According to numerical modelling, the wave height has shown an exponential decrease along the meadow width. The wave height is 72% as that of the wave height at the entry point. Figure 8 shows the combined experimental and numerical model results such that the wave height damping phenomena is clearly indicated as a percentage of meadow width with wave heights. Wave height reduced exponentially when it propagates through CSS meadows. The error between the numerical and experimental model of wave attenuation using literature found to be around 8.25% [13]. Similarly, for

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Fig. 7 H/Ho versus percentage of meadow width, for 2.6 s, h  12 cm

1.00

Experimental Numerical

0.95

H/Ho

0.90 0.85 0.80 0.75 0.70 0

20

40

60

80

100

Meadow width percentage Fig. 8 H/Ho versus percentage of meadow width

1.00

Experimental Numerical

0.95

H/Ho

0.90 0.85 0.80 0.75 0.70 0.65 0

20

40

60

80

100

Meadow width percentage

the experiments carried out at flume, NIT-Trichy and numerical model developed at similar testing conditions, the error percentage was found to be 8.33%. The results obtained from the present study are in good agreement qualitatively with the outcomes of [13], although there are some variations found in the waves height reduction. Such differences can be attributed to the difference in testing conditions such as the physical and mechanical properties (Young’s modulus and flexural strength) of the silicon tubes used, the plant blades submergence, the general shape and configuration of the plant mimics.

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2.6 Summary and Conclusions For hydraulic engineers, prediction of flow characteristics for coastal vegetation is a major concern due to plant induced drag during wave–vegetation interaction. Numerical models, therefore, can be used as a reliable, cost-effective multidimensional tool to understand the flow interaction in vegetated floodplains. Simulations of different well-documented laboratory experiments yielded encouraging results. Based on comparisons of H/Ho versus percentage of Meadow width for different wave heights, the FLOW-3D-based model produced good agreement with measured experimental data. • Wave height and velocity reduces exponentially as the wave propagates through the vegetation. The loss of energy as a result of interference of the vegetation with the wave propagation causes a reduction in wave heights. • For Wave height of 0.10 m the attenuation was found to be around 0.7 (70% of original wave height), 0.105 m attenuation of around 0.75 (75% of original wave height) was recorded and for wave height of 0.12 m attenuation of around 0.8 was observed (80% of original wave height). • The important parameters affecting it are submergence ratio, wave amplitude, plant morphology. • Different species of seagrass can be selected and used in the protection of coastal area shorelines, Coastal Ecological Sensitive Areas (ESA), which act as protective shields during natural calamities like tsunami and cyclones. Acknowledgements The authors acknowledge the National Institute of Technology, Tiruchirappalli (NITT) for the financial support and for allowing the use of FLOW-3D software.

References 1. Kummu M, de Moel H, Salvucci G, Viviroli D, Ward PJ, Waris O (2016) Over the hills and further away from coast: global geospatial patterns of human and environment over the 20th–21st centuries. Environ Res Lett 2. The IUCN redlist of threatened species. http://www.iucnredlist.org 3. Quartel S, Kroon A, Augustinus P-F, Van Santen P, Tri N-H (2007) Wave attenuation in coastal mangroves in the Red River Delta, Vietnam. J Asian Earth Sci 29(4):576–584 4. Lövstedt C-B, Larson M (2010) Wave damping in reed: field measurements and mathematical modelling. J Hydraul Eng 136(4):222–233 5. Möller I, Spencer T, French JR, Leggett DJ, Dixon M (1999) Wave transformation over salt marshes: a field and numerical modelling study from North Norfolk, England. Estuar Coast Shelf Sci 49(3):411–426 6. Stratigaki V, Manca E, Prinos P, Losada I-J, Lara J-L, Sclavo M, Amos C-L, Caceres I, SanchezArcilla A (2011) Large scale experiments on wave propagation over Posidonia Oceanica. J Hydraul Res IAHR 49(Suppl 1):31–43 7. Fischer-Antze T, Stoesser T, Bates P, Olsen N-B (2001) 3D numerical modelling of openchannel flow with submerged vegetation. J Hydraul Res 39(3):303–310. https://doi.org/10. 1080/00221680109499833

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8. Luhar M, Coutu S, Infantes E, Fox S, Nepf H (2010) Wave-induced velocities inside a model seagrass bed. J Geophys Res 115:C12005 9. Bradley K, Houser C (2009) Relative velocity of seagrass blades: implications for wave attenuation in low energy environments. J Geophys Res 114:F01004 10. Mendez F-J, Losada I-J (1999) Hydrodynamics induced by wind waves in a vegetation field. J Geophys Res 104(C8):83–96 11. Mullarney J-C, Henderson S-M (2010) Wave-forced motion of submerged single-stem vegetation. J Geophys Res 115:C12061 12. Luhar M, Coutu S, Infantes E, Fox S, Nepf H (2010) Wave-induced velocities inside a model seagrass bed. J Geophys Res 115:C12005 13. Beena MJ, Shirlal KG, Rai S, Rajasekaran C (2015) Effect of artificial sea grass on wave attenuation and wave run-up. Int J Mod Eng Res 14. Fischer-Antze T, Stoesser T, Bates P, Olsen N-B (2001) 3D numerical modelling of openchannel flow with submerged vegetation. J Hydraul Res 39(3):303–310. https://doi.org/10. 1080/00221680109499833 15. Babaali H, Shamsai A, Vosoughifar H (2014) Computational modeling of the hydraulic jump in the stilling basin with convergence walls using CFD codes. Arab J Sci Eng. https://doi.org/ 10.1007/s13369-014-1466-z

Studies on the Morphological Changes by Numerical Modeling Along Kakinada Coasts N. Sharmila, R. Venkatachalapathy and M. Mugilarasan

Abstract Prediction of morphological changes has immense application for development of coastal infrastructure. More relevantly, various sectors are facing the coastal erosion problem, which needs to develop the model for the concern coasts. Even though there are a number of free softwares available to model and validate the coast, commercially available softwares such as MIKE 21 were used in the present study. Hence, this chapter investigates the hydrodynamics, spectral waves and sediment transport modeling by dynamic coupling of waves and currents using MIKE 21 Flexible Mesh coupled model at Kakinada coast. For this study, waves, tides and current data were collected during July and December 2009 (NE and SW seasons). Further, the simulation was done by preparing the model, evaluating the critical factor and providing the sensitivity analysis to evaluate the sediment transport pattern at Kakinada coast. Finally, the model performs various statistical measures and were compared with observed data for calibration during SW and NE monsoons. This calibration shows that the observed data has good agreement with model data. Hence, the overall simulation shows that the transport of sediment is strongly controlled by tidal currents and wave ordination, which significantly enhances bed shear stress that results in increases of sediment remobilization. Keywords MIKE 21 · Tidal currents · Sediment transport · Morphological Hydrodynamics · Spectral waves

N. Sharmila (B) International Maritime Academy, Jamin Kottur, Puduchatram, Chennai 600124, Tamil Nadu, India e-mail: [email protected] R. Venkatachalapathy Faculty of Marine Sciences, Centre of Advanced Study in Marine Biology, Annamalai University, Parangipettai 608502, Tamil Nadu, India M. Mugilarasan NCSCM, Anna University, Chennai, Tamil Nadu, India © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_10

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1 Introduction Coastal morphodynamics provide a key role in understanding the interaction of forces and topography that give rise to the distinctive characters of the world’s shoreline. Morphological models are based on the empirical field and laboratory studies, supplemented by computer simulations which helps to generate a greater understanding of coastal regions [1]. Computer simulation can be based on the pattern of change inferred over long timescales and consistent with a process known to operate over shorter timescales. The coastal morphodynamics is concerned primarily with physical features and environmental in the coastal regions, which occurs over a broad range of time and length scale. Sambasiva Rao and Vaidyanadhan [2, 3], Sastry et al. [4], Rengamannar and Pradhan [5] had made deliberate morphological changes around the Godavari delta region. Later, Ramkumar [6, 7] had made an attempt to study morphological evolution off Kakinada bay. Several researchers had studied about sediment characteristics [8–11] using transport along shore flow pattern [12] and multi-data satellite sensor data [13, 14] with GIS technique [15–18]. Guru Prasad and Gaddem [19] had presented about the global warming effects on Uppada coast, a fishing village of Andhra Pradesh. Nageswara Rao et al. [20, 21] had studied the Holocene evolution and coastal morphodynamics of Godavari estuary. Satyaprasad [22] studied about the morphodynamics of the beaches and sand spit, Kakinada Bay. Recently, Jain et al. [23] studied on Morphodynamics of Godavari Tidal Inlets and Kakinada spit using time series multi-sensor satellite data for the period of 1987–2004. No such systematic approach had been made to study the Kakinada coast using modeling software. The primary aim of this chapter is to simulate hydrodynamic, spectral wave, and sediment transport modeling using dynamic coupling of waves and currents. The objectives are to understand the hydrodynamic and sediment transport of the study area; prepare a model to represent the hydrodynamic conditions at the locations using MIKE 21 FM coupled model and evaluating the sediment transport pattern in that location; identify the critical factor in hydrodynamic, spectral and sediment transport modeling in the study area and provide a sensitivity analysis for the parameter governing sediment transport and finally assess the performance of the model using statistical tools and techniques have been made by comparing the model-derived parameters against the corresponding observed data.

2 Study Area Kakinada (long. 82° 14 –82° 22 E and lat. 16° 5 –17° 05 ) is situated on the east coast of India, about 160 km southwest of Visakhapatnam. It has an average elevation of 2 m (6 ft) from mean sea level. It is the main receptacle for the river run into the Godavari estuarine system. The total area of the bay is 132 km2 , which contribute two major distributors of the river Godavari which are Coringa and Gaderu opening into the

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Kakinada bay. River Godavari transports a considerable quantity of sediments to the sea, which nourishes the sandy beaches in the vicinity. The Seafloor up to a distance of 3 km is sand, from 3 to 20 km it is covered with clay, and up to 20–30 km, it is covered with shells the outermost zone consisting of clay, fine sand, and shell fragments [8]. The geomorphology of the Kakinada coast consists of mudflats, mangrove swamps, sandy beach, and sandy Island. On the western side of Kakinada coast is the mainland of Kakinada which was formed by deltaic and flood plains. The coastal strip north of Kakinada consists of windblown sand and sand dunes which are succeeded landward by laterites, sandstones and Khondalities. The lowest part of the delta is made of a series of sand ridges interpreted to be ancient beach ridge forms, due to high waves and detrital materials brought by the river from its drainage basin. On the eastern side of the bay, there is a long narrow sandbar continuous with the eastern tip of the Hope Island separating the bay from the sea. Due to the presence of the sandbar, the Kakinada bay forms a semi-enclosed body of water where the water movements are unique. An industrial belt, running north–south the length of the city, separates the eastern part of the coast. Uppada beach is primarily considered as Kakinada beach which has one of the longest coastlines in Indian beaches.

3 Methodology 3.1 Field Investigation The bathymetry survey was carried out in the Kakinada coast from north of Godavari to Uppada including bay region, during July 2009 using single beam echo-sounder (ODOM Hydrotrac) interfaced to a differential global positioning system (DGPSTrimble) and laptop computer in a water-resistant case mounted on a fishing trawler boat along with heave sensor (HS-50, Heave sensor). Wave and tide parameters were measured using the MIDAS Wave Recorder (Valeport tide gauges—Valeport Limited, U.K.) and current data was measured using Recording Current Meters (Aanderaa RCM9) for two monsoons (northeast (NE) and southwest (SW) monsoon) from 14 to 28 July and 14 to 30 December during 2009 at Kakinada coast, respectively (Table 1).

3.2 Numerical Model In this chapter MIKE 21/3 Coupled FM module (integration of Mike 21 HD, SW and ST modules) developed by DHI by combined wave/current/sediment transport for the study area. The reason for selection of MIKE 21/3 Coupled FM models is that they suit for the condition of flexible mesh, which enables more accurate representation and easy user interface to handle the problems with better real-time scenario. The flexible mesh also allows reducing the grid size locally at areas of special interest.

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Table 1 Deployment locations for Kakinada coast Location Location Latitude Longitude no. name (°N) (°E)

Deployment Instrument depth (m) name

Tide measuring interval (min) 12

1

Offshore

17° 02.154

82° 24.181

19.5

2

Mouth of bay

17° 05.589

82° 25.698

8.1

3

Near Godavari

16° 49.885

82° 24.111

8.1

Valeport 730D and AanderaaRCM9 Valeport 730D and AanderaaRCM9 Valeport 730D and AanderaaRCM9

12

12

Coupled FM model simulates three models in parallel while interchanging the input of one model to simulate the output of another model. Wave radiation stress obtained as the SW model output is fed input to the hydrodynamic model. Water level flow and current variation from HD model provides input to the ST model.

3.3 Model Setup 3.3.1

Bathymetry

Setting up a mesh includes appropriate selection of the area to be modeled, adequate resolution of the bathymetry, flow, wind and wave fields under consideration and definition of codes for open and land boundaries. The model is set up as a UTM-44 projection using depth data from nearshore surveyed bathymetry data. The model computational domain (520 km2 ) has 20 × 26 km in x and y directions, respectively. A nested approach is used to create the mesh for minimizing the errors in calculation of results. The large and small mesh was created, for which larger domain a resolution of 7 km is used progressively reducing to 12 km for Kakinada coast. The total number of elements used in this mesh is 6232 with 3600 nodes. To run the model, stability used here as The Courant–Friedrichs–Lewy (CFL) number which is chosen as 0.9.

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Hydrodynamic Model

The hydrodynamic module is based on the numerical solution of the two-dimensional shallow water equation the depth-integrated incompressible Reynolds averaged Naviers–Stokes equation. Thus, the model consists of continuity, momentum, temperature, salinity, and density equations. The following equations are used to obtain the conservation of mass and momentum integrated over the vertical flow and water-level variation. ∂d ∂ζ ∂ p ∂q + +  ∂t ∂ x ∂ y ∂t    ∂  pq  ∂ζ gp p 2 + q 2 1 ∂ ∂ + + gh − ) + ) + (hτ (hτ xx xy ∂y h ∂x c2 · h 2 ρw ∂ y ∂y h ∂ ( pa )  0 − Ωq − f V Vx + ρw ∂x

∂p ∂ + ∂t ∂ x



p2 h



     ∂q ∂ q2 ∂  pq  ∂ζ gp p 2 + q 2 1 ∂ ∂ + + + gh + (hτ (hτ − ) + ) yy xy ∂t ∂ y h ∂x h ∂y c2 · h 2 ρw ∂ y ∂x h ∂ ( pa )  0 − Ω p − f V Vy + ρw ∂x y Various sensitivity tests were carried out to analyze the effect of variations of different parameters on the hydrodynamic model results. Flooding depth was set at 0.05 m, and drying depth was set at 0.15 m to capture the intertidal area appropriately in the model domain. Bed resistance was calculated using the roughness heights as Chezy number of 72 m3 /s. Horizontal eddy viscosity coefficient defines as the turbulent mixing in the water in which Smagorinsky eddy viscosity with the coefficient of 0.5 was adopted for the simulation. The wind shear stress was simply assumed to be proportional to square of wind velocity through using the wind drag coefficient. The drag coefficient depends on the wind speed and increased with the increase of wind speed. Comparing the outputs with measurements, the drag coefficient of 0.001255 (for wind speed of 7 m/s) and 0.0026 (for wind speed of 15 m/s and higher) was chosen. The numerical simulations were carried out by imposing two open boundaries, viz., north and south of Kakinada port and the offshore boundary was considered to be zero cross flow. The model was driven by temporal variations in water level specified along the open boundaries and wind, to obtain realistic water elevation and flow patterns.

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Spectral Wave Model

The discretization in geographical and spectral space is modeled using a cell-centered finite volume method. In the geographical domain, an unstructured mesh is used as base model. The integration time is based on a fractional step approach [24]. In Cartesian coordinates, the conservation for the wave action can be written as s ∂N + ∇.( vN)  ∂t σ where N ( x , σ, θ, t) is the action density, t is the time, x  (x, y) is the Cartesian coordinates, v  (C x , C y , Cσ , Cθ ) is the propagation velocity of the wave group in the four-dimensional phase space x, y, σ, and θ, and S is the source term for the energy balance equation ∇ is the four-dimensional differential operator in the x, y, σ, θ-space. The sensitivity analysis for the present study, the optimum values of wave breaking parameter (γ  0.8), bottom friction (Nikuradse roughness) (Kn  0.04 m), and white capping coefficients (Cdis  4.5) was used in the fully spectral experiment. The wave spectrum was represented by 16 discrete directions and 25 discrete frequency bins logarithmically spaced from 0.055 to 0.6 Hz. In this formulation dissipation coefficient depended on wave hydrodynamic conditions. This dissipation coefficient also was used as a tuning parameter in which white capping dissipation source function included two free parameters; Cdis and DELTAdis [25]. In this present model, Cdis coefficient was given as 4.5 and DELTAdis as 0.5. The model was given as a cold start and spun up. The initial conditions were calculated by the model from the first time step of the wind field, using JONSWAP fetch growth expressions. These wave parameters were input at the offshore boundary, on the north and south boundary the MIKE 21 option “lateral boundary” was used whereby the basic equations were calculated along the boundary line by taking the offshore end and reducing to zero at the inshore end.

3.3.4

Sediment Transport

In the near shore region, the analysis of the erosion–accretion plays an vital importance for the development of a harbor and construction of coastal structures. MIKE 21/3 Coupled Flow Model—ST describes erosion, transport, and deposition of sand under the action of pure current or under wave and currents [26]. The sediment transport rates are calculated using two different model types; “Pure Currents” and “Combined Currents and Waves”. For “Pure Currents”, the rates are calculated directly on the actual conditions. For “Combined Currents and Waves,” the rates are found by linear interpolation of transport in sediment transport table. In the present study, sediment transport rates are simulated using Combined Waves and Current model, in which sediment transport model (STPQ3D) is prepared. Sediment transport also depends upon the nature of seabed and its grain size distribution. For which, the

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sediment properties like porosity and grain diameter were taken from the reference values reported by Narasiman et al. [27] (porosity as 0.4, grain diameter as 0.2 mm and grading coefficient is selected as 1.1). Before commencing the modeling, a sediment transport table is needed to be generated with the help of MIKE 21 toolbox. Bank erosion effect is included as 30° for the ST simulating model. The forcing parameters (waves, water flow, and current variation) are incorporated from hydrodynamics and spectral wave model in ST model for creating a sediment transport model which includes the dynamic of both waves and currents. For ST simulation boundary conditions, “Zero sediment flux gradient for outflow, zero bed change for inflow” was selected for all three boundaries (offshore boundary, north boundary, south boundary).

3.3.5

Validation of Data

Calibration and validation of the model are the most important requirement for any numerical model study. This can be achieved by the level of confidence in the prediction of models and best possible accuracy after calibration for properly optimized. First approach the performance of the models can be evaluated by calculating the statistical parameters like a correlation coefficient, RMAE, and Index of agreement from the model simulation [28]. Further, quantifying the validation process, three skill tools, i.e., the correlation coefficient (γ), relative mean absolute error (RMAE), and index of agreement (IoAd) are applied for the entire simulation period as per equation mentioned below, respectively. The equation for the correlation is (Q m − Q m )(Q c − Q c ) γ  (Q m − Q m )2 (Q c − Q c )2 where Qm and Qc are the measured value and computed value, respectively, and Q m and Q c are the measured mean value and computed mean value. RMAE is very vital for comparison of time series data on water level elevation and current velocities since it accounts for both the magnitude and direction of the flow. The RMAE has been used by several authors [29, 30] to evaluate the numerical model result and is defined by Walstra et al. [31] as R M AE 

(|Q m − Q c |) (|Q m |)

Though the experience with RMAE parameter is limited (Table 2). The IoAd, another important tool for quantifying the performance of the model [32, 33], is given by n (Q m − Q c )2    I o AD  1 − n  i1    2 i1 ( Q c − Q m + Q m − Q m )

118 Table 2 Classification of error ranges for RMAE

N. Sharmila et al. Classification

RMAE

Excellent Good Reasonable/Fair Poor Bad

1.0

The results are best when IoAd is close to 1 and worst when IoAd is close to 0.

4 Result and Discussion 4.1 Bathymetry In order to manage the marine environment or to mitigate hazards such as tsunamis or the consequences of climate change, bathymetry plays an important role for the administrations of coastal states. Including bay region, Kakinada coast, ranges in depth from 1.5 to 23.36 m, with the mean depth of 5.79 m are shown in Fig. 2. Kakinada coastline covers a 29 km and its morphology includes a Kakinada bay, Coringa mangrove forest, Hope Island, fishing harbor, deep water port and Kakinada canal (Fig. 1). Like many other bays, near the mouth it is shallow water. The southern half is too shallow and depths never exceed 2 m even in spring tides, while its northern half is 5–13 m deep. This result indicates extensive low-lying areas of Coringa mangrove due to continuous sediment deposition from Godavari channels.

4.2 Hydrodynamic Model Hydrodynamic modeling is a prerequisite to the spectral wave modeling as it influences the sediment erosion and deposition processes in the coastal region. The present modeling study was carried out to understand the tidal currents and the effect of winds on the current system for the study area. The tidal range of Kakinada coast with a maximum of 2.48 m, which normally occurs at mouth bay in December (NE monsoon), and the minimum level 0.16 m occurs on July 2009. The observed surface elevation is 1.81 m and 2.48 m during SW and NE monsoon respectively (Table 3). Further, the tidal signals are analyzed for major tidal constituents using the IOS method as described by Godin [34] and Foreman [35]. The largest amplitude is observed in M2 constituent in the order of 0.48 and 0.52, which is followed by S2 with 0.18 and 0.21, respectively for SW and NE monsoon. The Greenwich phase of the tidal constituents is 65°–85° for M2 , 106°–340° for S2 , 255°–330° for K1 and 230°–320° for O1 during

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Fig. 1 Study area and sampling locations for Kakinada coast

both seasons. The determined constituents amplitude and phase are given in Tables 4 and 5. The importance of semidiurnal constituent depends on geographical positions which can be calculated by form number. The form number is the ratio of the sums of amplitudes of the two major diurnal (K1 and O1 ) and semidiurnal (M2 and S2 ) constituents [36]. The obtained form numbers are 0.25 and 0.23 during SW and NE monsoon, indicating the study area is dominated by semidiurnal tidal constituents throughout the year. Tidal currents are very prominent towards the coastal region. Tidal current has been resolved into U components (east–west) and V components (north–south) to get the dominant flow for the coastal environment, which is responsible for sediment transport along or across the coast. Hence, the east of India experiences 0.20–0.25 m/s for coastal current patterns with seasonal changes in direction. Analysis of the current

Near Godavari Offshore Mouth of bay

Near Godavari

Monsoon

Monsoon

NE

Offshore Mouth of bay

SW

Location name

0.16

0.18 0.19

1.52 2.48

1.65

0.19

0.17 0.23

1.68

1.81 1.75

0.87

0.86 0.87

0.87

0.86 0.86

0.23

0.19 0.21

0.27

0.10 0.12

Max

–0.27

–0.07 –0.12

–0.29

–0.08 –0.13

Min

U Velocity (m/s) Mean

Max

Min

Tide (m)

Table 3 Hydrodynamic parameter during North-east and Southwest monsoon

–0.006

0.03 –0.13

–0.012

0.005 –0.015

Mean

0.15

0.22 0.12

0.30

0.23 0.13

Max

–0.05

–0.10 –0.01

–0.15

–0.22 –0.12

Min

V Velocity (m/s)

0.03

0.03 0.05

0.06

0.013 0.018

Mean

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Fig. 2 Mesh with interpolated bathymetry and contour map off Kakinada coast Table 4 Amplitude of major tidal constituents at various locations Constituent M2 , Amplitude S2 , Amplitude K1 , Amplitude (m) (m) (m) Locations 1 2 3

Jul-09 0.48 0.49 0.48

Dec-09 0.5 0.52 0.51

Jul-09 0.18 0.18 0.19

Dec-09 0.2 0.21 0.21

Jul-09 0.12 0.13 0.12

Dec-09 0.13 0.12 0.13

O1 , Amplitude (m) Jul-09 0.04 0.04 0.04

Dec-09 0.05 0.05 0.05

speed and direction at measured locations during SW and NE monsoon are given in Table 6. The maximum current speed varied with an average of 0.85 m/s, as 0.88 m/s near Godavari estuary during the NE monsoon. The magnitudes of current speed during the SW monsoon are observed to be higher compared to NE monsoon. Sastry et al. [4] has revealed that tidal range is less near Godavari estuarine region, and supply of tidal current from the south is strong with relatively larger barrier systems. The flood current reaches maximum velocity and flows in a southerly direction near Kakinada entrance channel and ebb current reaches maximum velocity at

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Table 5 Phase of major tidal constituents at various locations Constituent M2 , Phase S2 , Phase (Deg) K1 , Phase (Deg) (Deg) Locations 1 2 3

Jul-09 65 66 79

Dec-09 71 82 85

Jul-09 119 127 138

Dec-09 111 120 106

Jul-09 256 257 262

Dec-09 328 297 319

O1 , Phase (Deg) Jul-09 234 243 250

Table 6 Observed current magnitude and direction at measured locations Location SW monsoon NE monsoon Average Maximum Direction Average Maximum (m/s) (m/s) (Deg) (m/s) (m/s) 1 2 3

0.21 0.13 0.26

0.5 0.72 0.88

NNE NNE NNE

0.12 0.21 0.27

0.51 0.54 0.85

Dec-09 228 257 320

Direction (Deg) SSW SSW SSW

Godavari point in northern direction that flows along the sand spit (Fig. 3). Since tidal currents were weak and therefore an eroded material tends to be deposited at the mouth entrance and strong ebb current removes materials and has caused deepening of bay. The water level data are predicted using harmonic constituents, which indicate that these oscillations are associated with the semidiurnal pattern. The measured results are compared with modeled U–V components (Fig. 4), which shows that the current in the upper layer increases significantly under the influence of monsoonal winds [37].

4.3 Spectral Wave Model In coastal engineering, wave hindcast and prediction are important studies for coastal infrastructure development and management. For almost all marine-related activities, knowledge of coastal parameters is very essential. Wave measurement has been carried out from 14th to 29th July and 15th to 30th December 2009, which is considered as southwest (SW) and northeast (NE) monsoon as shown in Table 7. During the study period, the measured wave directions are predominantly from southeast to south for SW and northeast to southeast for NE (Fig. 5a, b). For wave generation, a wind plays a crucial role by varying in heights and periods while moving in different directions. During this period the wind direction is in the range 117° (SW) and 39° (NE) true north (Fig. 6a, b) and maximum wind speeds up to approximately 6.1 m/s (SW) and 4.4 m/s (NE). For estimating the nearshore wave parameter, the use of numerical models would be helpful to understand the wave effects along coastal regions by testing different wave conditions. The model results are given from the study carried out at Kakinada

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(a)

(b)

(c)

(d)

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Fig. 3 A flow of current during flood tide and Ebb tide for NE monsoon (a and b) and SW monsoon (c and d)

Coast during northeast and southwest monsoon. The study area is typical in its complex bathymetry, where the offshore waves penetrate around the offshore island (Hope Island) in which wave diffraction and refraction effects are considerable. Model calculation reveals that wave height for the offshore region varies as 1.02 m for SW and 1.04 m for NE monsoon as shown in Fig. 7. While the waves reach the Hope Island, the waves get diffracted, refracted and enter into the bay region. The waves reach up to 2 km from the mouth with reduction in wave height of 0.2 m. At a particular time step, the waves approaching the coast has the average value of wave heights 0.75 m with a peak period of 9.24 s. These waves are short in nature and mainly wind-generated waves. Figure 8 shows the comparison between the simulated and observed time series wave parameters. For generation of these currents, the principle mechanisms are the momentum flux gradients (radiation stress [38]) and it is owed to the decay of the incident waves. Further, simulation results show that the wave radiation stresses reach a maximum of 0.87 m3 /s2 (SW) and 0.52 m3 /s2 (NE) along the coast, while 0.62 m3 /s2 (SW) and

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Fig. 4 Comparison of surface elevation U velocity and V velocity between modeled and measured for southwest and northeast monsoon at north-near the bay mouth Table 7 Wind and wave parameter for north-east and southwest monsoon Parameter SW monsoon NE monsoon Min Max Mean Min Max

Mean

Significant wave 0.34 height (Hs) (m)

1.19

0.67

0.31

0.89

0.54

Mean period (Tm) (s)

6.9

12.6

9.5

4.8

9.4

7

Peak period (Tp) (s)

6.7

18.2

11.3

4.7

14.2

8.1

Zero up crossing 6.31 period (Tz) (s)

12.06

8.99

4.46

8.79

6.72

Mean direction (Deg)

92

232

151

67

224

118

Wind speed (U) (m/s)

0.4

6.1

2.61

0.1

4.4

1.53

Wind direction (Deg)

98

145

117.1

0.2

117.5

39.79

0.52 m3 /s2 (NE) are perpendiculars to the coast. Shear radiation stresses are quite less as the waves approach the coast almost perpendicularly with an average value of Sxy as 0.06 (0.08) m3 /s2 for southwest (northeast) monsoon. Along Andhra coast, the waves approach from a southerly to southeasterly direction during March to September and northeasterly to east–southeasterly direction for the remaining period [4]. An examination of the wave model shows that the waves

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(b)

Fig. 5 Wave rose plots for significant wave height at offshore boundary during a SW and b NE monsoon

(a)

(b)

Fig. 6 Wind rose plots for wind speed during a SW and b NE monsoon

Fig. 7 Simulation of significant wave height with wave direction during SW and NE monsoon

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Fig. 8 Comparison between modeled and measured significant wave height, mean wave period and mean wave direction at south near Godavari estuary(c) during SW and NE monsoon

approaching this part of the coastline from South to Southeast and East to Southeast during SW and NE monsoon. The calculated wave parameters are characterized by mean wave period (Tm) with an average of 9.5 (7.0) and significant wave heights (Hs) below 1.2 (0.9) m for SW (NE) monsoon. The relatively higher values of the wave period and significant wave height are related with the relatively stronger winds blowing over a longer fetch distance [39]. The inner portion of Kakinada bay forms a wave, shadow zone from waves coming from the NE and SW monsoon. The overall result indicates that near the mouth of Kakinada bay and north of Godavari estuary are wave converging points, while at the interior of the bay region, waves get diverged. Because of the convergence of wave energy near the entrance of the bay, removal of sediments especially lighter materials takes place. This coincides with the presence of sandy materials up to 2 km from the mouth. In the most interior part of the bay, wave rays are diverged indicating the reduction of wave activity and consequent deposition of clay and silt materials. These results agree well with the observations of Gujar et al. [40], Chevalier et al. [41]. It can also be seen that the occurrence of deviation is more in SW monsoon than NE monsoon season. This might be the reason for changes in wind sea dominant during the SW monsoon [42]. A change in the momentum flux (Radiation stress) is caused by the waves that affect the mean motion of water and its level. Radiation stresses are responsible for the setup and set down of longshore current in the nearshore region. Cross-shore currents are created due to the normal radiation stress (Sxx and Syy ) and longshore currents

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are created due to the shear radiation stress (Sxy and Syx ) in the water column. In the nearshore region, the total shear stress depends upon the three parameters such as currents, waves, and water level modulation. Particularly, wave shear stress is stronger near the coast (5 km), reaches 1 N m−2 as the reference wave, but there is a rapidly decreases of its intensity with bathymetry and vanishes 20 km offshore [41]. The total shear stress varies with time as current and wave action on the bottom along with the tidal cycle. The wave shear stress enhances at low tide for smaller depth and while current shear stress evolves with minimal currents, i.e., maximum at ebb tide due to combination of tidal currents. Therefore, at the entrance of the bay total shear stress is maximum at low tide and minimum of flood tide. Moreover, the incidence angle of wave affects directly the convergence and divergence of wave around the coastal area; as a result, erosion and deposition are certainly modulated by ordination of wave [41].

4.4 Validation of Model For all modeler opinions, simulations depend on data availability, characteristics of the water body, model calibration, and validation process [43]. Comparison of the models computed with measured data provides the gross confidence in the performance. To perform the model validation, the model is run during two monsoons in which various tunning parameters are changed. These above model validations have been compared to all three stations with the time series data collected at SW and NE monsoon, respectively. The three skills tests are performed to quantify the model performance with observed data for both monsoons separately. The values of the correlation coefficient, RMAE and IoAd are shown in Tables 8 and 9. It provides a good confidence in model validation for all the wave and current parameters.

4.5 Sediment Transport Knowledge on the process of sediment transport remains as a large gap for continuous development and well-validated practical modeling system. Hence analyses on longshore sediment transport were carried along the Kakinada coast for SW and NE monsoon. With the information on waves available over the two-dimensional model, the hydrodynamic model calculates the wave forcing corresponding to the simulated coastal current. Finally, waves and current information are passed to sediment transport module to calculate the sediment dynamics for both SW and NE monsoon. Along the east coast of India, especially in the Kakinada bay circulations are controlled by the coastal current. The coastal current changes its direction seasonally, being northerly from January to July and southerly from August to December. The direction of current during this period is between southeast and southwest. These

0.93

0.80

0.78

0.85

0.60

0.82

Current V component

Significant wave height

Mean wave period

Mean wave direction

0.90

0.79

0.91

0.90

0.93

0.86

Surface elevation Current U component

Location

SW monsoon Correlation coefficient 1 2

Parameters

0.87

0.84

0.73

0.92

0.76

0.89

3

0.09

0.08

0.10

0.33

0.25

0.05

RMAE 1

0.20

0.10

0.80

0.23

0.19

0.08

2

0.08

0.08

0.10

0.19

0.20

0.02

3

0.90

0.78

0.93

0.90

0.91

0.90

IoAd 1

0.88

0.6

0.97

0.91

0.90

0.96

2

Table 8 Correlation coefficient, RMAE, and IoAd at Kakinada coast obtained from measured and modeled parameter for SW monsoon

3

0.83

0.74

0.84

0.96

0.95

0.94

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0.75

0.94

0.91

0.81

0.84

0.82

Current V component

Significant wave height

Mean wave period

Mean wave direction

0.71

0.75

0.76

0.64

0.78

0.84

Surface elevation Current U component

Location

NE monsoon Correlation coefficient 1 2

Parameters

0.89

0.71

0.92

0.90

0.92

0.93

3

0.04

0.20

0.10

0.33

0.24

0.12

RMAE 1

0.1

0.20

0.20

0.26

0.35

0.15

2

0.04

0.20

0.10

0.30

0.21

0.03

3

0.95

0.52

0.92

0.85

0.91

0.92

IoAd 1

0.61

0.65

0.86

0.81

0.84

0.86

2

Table 9 Correlation coefficient, RMAE, and IoAd at Kakinada coast obtained from measured and modeled parameter for NE monsoon

3

0.96

0.45

0.96

0.85

0.89

0.81

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currents do not seem to be influenced much by the tides [4]. Wave refraction studied by Sastry [44] indicates that when the direction of wave is southeast, the associated littoral current is directed toward upcoast while it is directed toward downcoast for the waves approaching in a northeasterly direction. During the study period, the longshore current is predominantly directed to the north for SW and NE monsoon. This is due to the wave heights and littoral current of southwest monsoon season are higher and stronger than those of the northeast monsoon season which results in a net northerly drift all along the Kakinada coast. It is observed that for waves approaching the coast from southeast, the longshore current is toward the north. This result suggests that the sediments in the nearshore region get transported from south of the Kakinada spit to toward; the north of the Hope Island deflects toward the Uppada region and tends to erode in this region. The coupled model computes hydrodynamic parameters as well as rates of sediment direction and finally calculated the bed-level change within the model. The erosion and deposition rates refer only to the changes of initial bed level which are predicted by the model. On observation, the bed level change rates would be much smaller as the initial bed level change and decreases quickly due to resultant change in the bathymetry [45]. The faster bed change is associated with the smaller morphological time steps and vice versa [46]. The absolute value of the rate of bed-level change is calculated for the whole domain which concludes that the change in bed level is prominent over the entrance of the bay during the SW monsoon than NE monsoon which is due to nearshore dynamics. Thus, bed-level change is used to update the nearshore topography which in turn simulates the realistic factors affecting coastal morphology. This study shows that for both SW and NE monsoon the northern part of Godavari estuary is getting eroded while deposition is occurring near the mouth of Kakinada bay region. However, the rate of bed level change is lesser in NE monsoon than the SW monsoon near the mouth of Kakinada bay. Therefore, throughout the study period, bed-level changes show higher rate during the SW monsoon along the Kakinada coast (Fig. 9). In the inner portion of nearshore or surf zone, the longshore sediment transport is essential due to waves action [47]. In this chapter, simulation shows that the longshore transport is toward the northern direction for waves from the SSE and S, while toward southern direction for waves from NE and ENE direction. This result shows a significant area of deposition along the mouth of the Kakinada bay and around Hope Island. The waves from the southern direction carry sediment along the shoreline from the south (north of Godavari estuary), which is deflected by offshore waves and refracted by the morphological features of Hope Island and deposits in the mouth region of Kakinada bay. The longshore current which is generated by broken waves approaches the coast at different angles. The strength and direction of currents vary with the orientation of local coastline. For improving the navigation, the prediction of wave-induced longshore currents and the sediment transport in the vicinity of ports is important. Longshore sediment transport shows the direction of south to north during SW monsoon and reverse during the NE monsoon (Figs. 10 and 11). Vector shows total load transport over a tidal cycle with the magnitude indicating

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Fig. 9 Initial bed level changes during a SW and b NE monsoon

(a)

(b)

Fig. 10 Simulation of sediment transport with current direction for a ebb flow and b flood flow during SW monsoon

the amount of sediment transport. This can be attributed to the current direction in this region and confirms with the earlier studies [12]. The coastal engineering Manual [48] states that over the longest possible time period sediment transport rates must be determined. Despite the lack of wave data for our study area, the results are expanded to make rough estimates of annual sedi-

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(a)

(b)

Fig. 11 Simulation of sediment transport with current direction for a ebb flow and b flood flow during NE monsoon

ment movement, which falls within one order of the current magnitude. In this study, characteristics of sediment transport have been calculated using a 2D model (sediment transport model). The surf zone of Kakinada coast has enormous quantities of sand stir along the shore due to the wave’s action with northerly direction for SW and NE monsoon. Chandramohan et al. [49] suggests that along the Andhra coast the predominant direction of sediment transport is toward the northeast from March to October and toward SW during the rest of the year. Sastry et al. [4] has shown that the net transport of sediment along Kakinada coast is toward north, sufficient quantity moves offshore and results in the formation of offshore bars, islands or sand spits. The rate of sediment transport is very large during the southwest monsoon owing to the prevalence of the high wave climate in the Bay of Bengal. The field measurement of net sediment transport study for Kakinada Coast estimates 0.4 × 103 m3 /year for SW monsoon and 1.2 × 103 m3 /year for NE monsoon which was low due to some error field data. In this paper, the transport is taken from modeled data, which estimates 3.2 × 103 m3 /year for SW monsoon and 7.7 × 103 m3 /year for NE monsoon. The above results nearly coincide with previous research which is estimated as 2.62 × 103 m3 /year along southern longshore sediment transport from October to February and 9.60 × 103 m3 /year along northern transport from March to September with a net drift toward the north [50, 51]. The study on the net sediment transport rate using the energy flux method has northern direction for Indian Coast reported as 0.52 million m3 /year for Visakhapatnam coast [52]. Sarma and Reddy (1988) estimated the net littoral drift of 0.54 million m3 /year toward the northern part of Visakhapatnam. Recently, the report from NSDRC, 2003, shows a transport rate for the Visakhapatnam coast has 0.31 million m3 /year (Southerly) and 0.84 million m3 /year (Northerly). Also, Parchure, 1978 estimates that the net northward littoral

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drifts at the Visakhapatnam port as 0.7 million m3 /year. Panigarhi et al. [47] has conceded a theoretical estimation and he reported that the gross sediment transport varied between 1.12 and 1.64 million m3 /year and the net sediment transport varied between 0.5 and 0.7 million m3 /year. From the above study, the quantity of longshore sediment transport rate increases from Godavari estuary up to the mouth of Kakinada bay and then gradually decrease in Uppada region indicating maximum sediment transport within the mouth region.

5 Summary and Conclusion Prediction of morphological changes has immense application for development of coastal infrastructure. More relevantly, coastal erosion has major problems faced by several sectors which needs to develop the model for the concern coasts. An investigation is done on numerical modeling of morphological changes by dynamic coupling of waves and currents using MIKE 21 Flexible mesh coupled model. The main objective of the research is to simulate hydrodynamic, spectral and sediment transport model and are compared with corresponding observed data for which field data collected for SW and NE monsoon 2009 and processed. From the processed data, the tide ranges with a maximum of 2.48 m normally occurred at mouth bay in December (NE monsoon), and the minimum level of 0.16 m occurred in July. The observed surface elevation was 1.81 and 2.48 m and obtained form number was 0.25 and 0.23 during SW and NE monsoon. This indicates that Kakinada coast has dominance of semidiurnal tidal constituents throughout the year. The highest current speed was about 0.88 (0.85) m/s at north of Godavari estuary (location 3), which was followed by the mouth of Kakinada bay about 0.72 (0.54) m/s during SW (NE) monsoon. The measured wave directions were predominantly from southeast to south for SW monsoon and north to northeast for NE monsoon. The model calculation reveals that the wave height of the offshore region varied as 1.04 m for NE and 1.02 m for SW monsoon. At a particular time step, the waves approaching the coast the average value of wave heights is 0.75 m with a peak period of 9.24 s. The overall results indicated the flood current reached maximum in southern direction near the entrance channel and ebb current reached maximum at Godavari point, flows in northern direction along the sand spit. Near the mouth of Kakinada bay and north of Godavari estuary, the waves had converging points, while at the interior of the bay region the waves got diverged. Due to convergence of wave energy near the entrance bay, there was removal of sediments especially lighter sediments. This was coincides with the presence of sandy materials up to 2 km from the mouth of bay. In the most interior part of the bay, the wave rays diverge with reduction in wave activities and consequently deposition of clay and silt materials occurs. It could also be seen that the occurrence of deviation was more in SW than in NE monsoon. This might be the reason for changes in dominant of wind sea during SW monsoon and the current in the upper layer increased significantly under the influence of monsoonal winds.

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Further, simulation results show that the wave radiation stresses reach a maximum of 0.87 m3 /s2 (SW) and 0.52 m3 /s2 (NE) along the coast, while 0.62 m3 /s2 (SW) and 0.52 m3 /s2 (NE) are perpendiculars to the coast. Therefore, in this model, the domination of wave shear stress occurs near the entrance of the bay and current domination toward offshore. At the entrance of the bay, total shear stress is maximum at low tide and minimum of flood tide. Moreover, the incidence angle of wave affects directly the convergence and divergence of wave around the coastal area; as a result, erosion and deposition are certainly modulated by ordination of wave. The calibration was made against three stations at Kakinada coast during southeast and northwest monsoon. In the calibration process scattering index was reduced to obtain best results, it was made through several runs by changing various tuning parameters. Overall comparisons and validation between modeled data with measured data showed that the models were in good correlation with similar quantities of the measured data. Initial bed change plays a vital role in prediction of erosion and deposition. Simulated bed level change rate showed that the area north of Godavari estuary was getting eroded while near the mouth of Kakinada bay was getting deposited for both SW and NE monsoon. However, the rate of bed level change was lesser near the mouth of Kakinada bay in NE monsoon than the SW monsoon. Therefore, throughout the study period, change in bed level showed higher rate during the SW monsoon along the Kakinada coast. Simulation shows that the longshore transport is toward northern direction for waves from the SSE and S, while toward southern direction for waves from NE and ENE direction This result showed a significant area of deposition was noticed along the mouth of the Kakinada bay and around Hope Island. The waves from the southern direction carried sediment along the shoreline from the south (north of Godavari estuary), deflected by offshore waves and refracted by Hope Island and deposits in the mouth region of Kakinada bay. This result suggested that the nearshore sediments were transported from south of Kakinada spit toward the north of the Hope Island and deflected toward the Uppada region where erosion tends to occur. The net sediment transport was estimated as 3.2 × 103 m3 /year for SW monsoon and 7.7 × 103 m3 /year for NE monsoon, both were present at mouth of Kakinada bay and north of Godavari estuary, respectively. It was understood that the quantity of transport rate was increased from Godavari estuary up to mouth of Kakinada bay, and then gradually decreased to Uppada region, indicating maximum sediment transport occurs within the mouth region. Based on the hydrodynamic data, the modeling of sediment transport results had shown that sediment transport was strongly influenced by wave direction, which significantly enhanced bed shear stress, results in increasing of sediment remobilization. From the above simulation, a large quantity of sediment was carried by rivers and deposited along the mouth of estuary which was piled up into barrier features by the influence of waves. These barrier features are development to form spits along the shoreline, due to the strong longshore drift. The present study shows that instantaneous response in morphological changes by hydrodynamic processes which requires the redistribution of sediment. There is a lag in the morphological response to hydrodynamic forcing which is considered as

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a time-dependent coupling mechanism, this is due to time management of sediment from one region to another. Hence morphodynamic processes disclose the positive and negative feedbacks toward shoreline region of Kakinada coast which results in the designing, constructing and maintaining of coastal and maritime projects.

6 Future Recommendation The present study has been very useful to understand the dynamics of coastal landforms such as beaches, shorelines, and sand spits, etc. Even though it helps in elucidating the information on landform features and the related coastal processes, the study could lead to further research and development in the following aspects. For accurate prediction of coastal zone management along Kakinada coast, it is required to collect the in situ continuous hydrodynamic data like wave, tide and current for at least one complete year. Further to validate the modeled data, the sediment trap measurements are to be carried out. The change in coastal landform features will be monitored by undertaking RTK–GPS survey of the coast along with shallow water bathymetry one can estimate the level of erosion and accretion of sediments, in turn, forms sand spits along the Kakinada coast. The above studies further enhance the understanding of coastal land reforms and is useful for coastal infrastructure development and management. Acknowledgements This study was carried at framework of the MoES research project entitled “Oil Spill Modelling” (Project no: MoES/8-PC/2(2)/2007-PC-IV Dated 27.03.2008) New Delhi. The authors wish to thank Dr. K. Kathirasan, Director and Dean, Faculty of Marine Sciences, Annamalai University, Parangipettai, and Dr. B. R. Subramanian, ICMAM-Project Directorate for his constant encouragement, support and providing all necessary facilities for carrying out this work. Authors also wish to thank all those in the “Oil Spill team” for their valuable support during the field campaign.

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27. Narasimham KA, Selvaraj GSD, Lalitlia Devi S (1984) The Molluscan resources and ecology of Kakinada Bay. Marine Fisheries Information Services, Technical & Extension Series 59:1–16 28. Kankara RS, Mohan R, Venkatachalapathy R (2011) Hydrodynamic modelling of Chennai coast from a coastal zone management perspective. J Coast Res 29(2):347–357 29. Fernandes EHL, Dyer KR, Niencheski LFH (2001) TELEMAC-2D calibration and validation to the hydrodynamics of the Patos Lagoon (Brazil). J Coast Res 34:470–488 30. Sousa MC, Dias JM (2007) Hydrodynamic model calibration for a mesotidal lagoon: the case of Ria de Aveiro (Portugal). J Coast Res (Special Issue 50). In: Proceedings of 9th international coastal symposium, pp 1075–1080, Gold Coast, Australia 31. Walstra DJR, Van Rijn LC, Blogg H, Van Ormondt M, (2001) Evaluation of a hydrodynamic area model based on the COAST3D data at Teignmouth 1999, TR121-EC MAST Project no. MAS3-CT97-0086. HR Wallingford, Oxfordshire, UK 32. Dawson CW, Abrahart RJ, See LM (2007) HydroTest: a web based toolbox of evaluation metrics for the standardised assessment of hydrological forecasts. Environ Model Softw 22:1034–1054 33. Wilmott CJ (1981) On the validation of models. Phys Geogr 2:184–194 34. Godin G (1972) The analysis of tides. University of Toronto press, Toronto 35. Foreman MG (1977) Manual for tidal height analysis and prediction. Pacific Marine Science report 77-10. Instiute of Ocean Sciences, Canada 36. Pugh DT (1987) Tides, surges and mean sea level. Wiley, Chichester, p 472 37. Vethamony P, Babu MT (2010) Physical processes in Gulf of Kuchchh: a review. Indian J Geo-mar Sci 39(4):497–503 38. Longuet Higgins MS, Stewart RW (1964) Radiation stress in water waves a physical discussion with application. Deep Sea Res 11:529–562 39. Poulos SE, Chronis G Th (2001) Coastline changes in relation to longshore sediment transport and human impact, along the shoreline of Kato Achaia (NW Peloponnese, Greece). Mediterr Mar Sci 2(1):5–13 40. Gujar AR, Angusamy N, Rajamanickam GV (2008) Wave refraction patterns and their role in sediment redistribution along South Konkan, Maharashtra, India. Geoacta Int J Earth Sci 7:69–79 41. Chevalier C, Froidefond JM, Devenon JL (2008) Numerical analysis of the combined action of littoral current, tide and waves on the suspended mud transport and on turbid plumes around French Guiana mudbanks. Cont Shelf Res 28(4–5):30, 545–560 42. Remya PG, Kumar R, Basu S, Sarkar A (2012) Wave hindcast experiments in the Indian Ocean using MIKE 21 SW model. J Earth Syst Sci 121(2):385–392 43. Hsu MH, Kuo AY, Kuo JT, Liu WC (1999) Procedure to calibrate and verify numerical models of estuarine hydrodynamics. J Hydraul Eng 125:162–182 44. Sastry JS (1958) Some aspects of shoreline processes and physical oceanography. D.Sc. thesis, Andhra University 45. Mishra P, Pradhan UK, Patra SK, Ramanamurthy MV, Seth B, Mohanthy PK (2014) Field measurements and numerical modeling of nearshore processes at an open coast port the east coast of India. Indian J Geomar Sci 43(7) 46. Saied UM, Tsanis IK (2005) ICEM: integrated coastal engineering model. J Coast Res 21(6):1257–1268 47. Panigrahi JK, Sathish Kumar V, Tripathy JK (2010) Littoral drift by alongshore flow at Visakhapatnam East Coast of India. J Hydro-Environ Res 1–11 48. CERC-Coastal Engineering Research Centre (2003) Coastal engineering manual, Publication EM 1110-2-1100, online Manual for USACE 49. Chandramohan P (1988) Longshore sediment transport model with particular reference to the Indian Coast. Unpubl. PhD thesis, IIT Madras, 210 50. Chandramohan P, Sanil Kumar V, Nayak BU (1991) Wave statistics around Indian Ocean. Indian J Geomar Sci 20:87–92

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51. Nayak BU, Chandramohan P, Sakhardande RN (1992) Seasonal distribution of wave heights off Yanam on the east coast of India. J Inst Eng 72:187–193 52. Chandramohan P, Nayak BU (1999) Longshore sediment transport along the Indian Coast. Indian J Geomar Sci 20:110–114

Dr. N. Sharmila received M.Sc., in Ocean Science and Technology from Annamalai University, Tamil Nadu, India, in 2009. Received Ph.D. in Ocean Science and Technology from Annamalai University, Tamil Nadu, India, in 2017. She has published more than four International papers in various reputed journals and also has been acting as a reviewer for various journals. She is actively involved as a member in various professional bodies. Presently working as a Professor and Head in International Maritime Academy, Department of Naval Architecture and Ship Building, Chennai, India. Her current research interest is Numerical modeling—MIKE 21 Coupled (Hydrodynamic, Spectral, Sediment transport) model.

Desk Studies and Modelling Sedimentation Pattern in Gulf of Khambhat L. R. Ranganath , A. V. Sriram

and M. Karthikeyan

Abstract Gulf of Khambhat (GOK) is a very complex region with high tidal range and varied bed material along eastern and western coastline within the Gulf. In this study, a process-based model for the GOK is constructed to study the sediment transport pattern covering the entire Gulf. The investigation at hand showed that modelling sediment transport is an important tool for the decision makers and designers when it comes to interferences on coastal water bodies. As we know Gulf is a portion of the ocean that penetrates into the land and is generally larger and more deeply intended than bays, so they often make excellent harbours. The major rivers flowing in the Gulf of Khambhat are Sabarmati, Mahi, Vishwamitri and Narmada. All these rivers carry huge sediments and are dumped in the Gulf of Khambhat. Due to rapid industrialization along the Gulf huge coastal infrastructural development has been executed and planned along the Gulf coast which has induced a change in the morphology of this region. A morphological study based on hydrodynamic model was carried out and the model was calibrated and validated with the various measured data sets available at CWPRS, Pune. Hence, the results of the morphological study were reviewed for plausibility using the hydrodynamic results. A hydrodynamic flow modelling system based on a cell-centered finite volume method on an unstructured mesh has been used to simulate sediment transport and bed morphological changes under actions of currents and waves along the GOK coast. In the horizontal plane, an unstructured grid is used. Keywords Waves · Tides · Current · Sediment transport · Gulf · Morphodynamic

L. R. Ranganath (B) · A. V. Sriram UVCE, Bangalore University, Bengaluru, India e-mail: [email protected] M. Karthikeyan Central Water and Power Research Station (CWPRS), Pune, India © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_11

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1 Introduction Gulf is a large area of sea or ocean partially enclosed by land, especially a long landlocked portion of sea opening through a strait. Coastlines in the Indian gulf region are subjected to high tidal variations with large mud flats. As a result, waves, tides and wind-driven currents are the dominant mechanisms contributing to mud/sediment transport and determining the nearshore morphology. In addition, other physical phenomenon, such as significant river discharge into the river mouth plays a major role in the dynamic behaviour of the coastal zone, especially in the Gulf region. Natural sediment mobilisation is an important process in the development and maintenance of coastal habitats, including wetlands, lagoons, estuaries, seagrass beds, coral reefs, mangroves, dunes and sand barriers. Overall, the degradation of coastal ecosystems and coral reefs from increasing or decreasing in sediment loads may lead to important losses in revenue caused by impacts on the tourism, fishing industries and on coastal infrastructure development. Historically, city development, especially large cities, was based on coasts due to the economic benefits of the ports. Coastal communities are concerned about sedimentation, sometimes linked to habitat change such as mangrove expansion or due to human intervention in nature such as coastal infrastructure and construction of dams. The bottom topography variation plays an important role in determining the distribution of residual current velocity and thereby sediment distribution [1], found that the resuspension parameters such as settling velocity, critical shear stress, and erosion rate constant were also important and they may cause up to a 40% difference in suspended sediment concentration. Gelfenbaum et al. [2], Sravanthi et al. [3] and Sanilkumar and Ashok kumar [4] said that the strong instantaneous and residual tidal currents are responsible for the transport and dispersal of fine-grained and sand-sized sediments across the delta. Samiksha et al. [5] and Sri Ram Kumar et al. [6] concluded that the sedimentation varied with monsoon, onshore current component was more pronounced, but tidal variations were masked to a great extent by the wind-driven circulation. Numerous researchers viz., Kunte and Wagle [7], Misra et al. [8], have monitored the sedimentation along Gulf of Khambhat based on remote sensing and geospatial techniques. The main objective of the present study is to assess sedimentation changes along Gulf of Khambhat coast, in a view to identify the erosion and accretion areas. Numerical Modelling with field observed data can be used as an effective tool to identify the areas that are vulnerable to coastal sedimentation within the Gulf and along the coast.

2 Study Area Gulf of Khambhat lies in the central west coast of India bordering the state of Gujarat. The Gulf of khambhat is in the shape of inverted funnel with Sabarmati, Mahi river flowing from north and northeast, respectively, and vishwamitri, Narmada rivers

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Fig. 1 Location map

flowing from east to west into the Gulf of Khambhat. The length of the Gulf is around 145 km, while its width varies between 20 and 110 km. Gulf of Khambhat covers approximately an area of 3120 km2 with a maximum depth of 35 m (Fig. 1).

3 Desk Studies and Analysis of Prototype Data The prototype data collected for the proposed Ethelene terminal of IPCL near Jageshwar in Bharuch channel have been given in two reports by M/s Elcome Surveys Pvt. Ltd., entitled—Final Report on Seabed and Oceanographic Investigation of the proposed Import/Export Terminal off Jageshwar for IPCL (June 1993) and Final Report on Float Studies, Current Measurements and Water Sampling for Jetty at Jageshwar for IPCL (October 1993). The important findings from the analysis of the prototype data from these reports which are considered important for the present studies are described in brief. The data in respect of the bathymetry of the area of 1932, 1973 and 1979, upland discharge data etc. available with CWPRS have also been analysed. The bathymetric data obtained from the Admiralty charts of 1932, 1973, 1979 have been compared. It is found that during 1932 there existed two channels in the Narmada Estuary. The dominant of the two was the Broach channel (now called Bharuch channel) which is located on the northern part of the estuary and a smaller channel existed on the southern side of the estuary. The southern channel though

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smaller in width, had a clear waterway detaching the Aliabet Island from the mainland even during the low tidal waters. There also existed large and small tidal flats in the Bharuch channel. From the Admiralty charts of 1973 and 1979, it is found that the southern channel deteriorated into a very narrow channel. It is also found that during 1970s, small Islands appeared at the location where the off-take of the southern channel existed, thus closing the waterway during low water and there was a clear waterway for Bharuch channel. It is found that most of the smaller Islands along the Bharuch channel except Kerselea bank have disappeared. The shoreline mapping of 1963, 1977 and 1984 of the Narmada Estuary available with CWPRS was analysed. It was observed that the southern channel was much wider than Bharuch channel in 1963. The Aliabet Island which was of size 9.5 km × 22.5 km in 1963, grew in size, both in length and width, mostly encroaching the southern channel. The increase in length has taken place on the riverside indicating that most of the sediment deposited has been brought by the river. There is an increase in the width of the Bharuch channel. At the sea end, the channel is 10 km wide. The channel width gradually reduces to about 5–20 km upstream and then there is an abrupt reduction in width from about 5–1.3 km within a stretch of 1 km. The comparison of the 1977 and 1984 shoreline plans show that there is further narrowing of the southern channel whereas Bharuch channel has remained fairly stable. Subsequently, M/s ELCOME Surveys Pvt. Ltd. has carried out the bathymetric surveys of the Bharuch channel in the vicinity of the proposed terminal off Jageshwar during the month of February 1991, February 1993 and October 1993. The findings from the comparison of the bathymetry of the surveyed area are described in the ELCOME report mentioned above. It is found from the survey that the Bharuch channel has many shoal patches with minimum depths varying from dry heights to 2 m in the deep channel portion. The shoal patches are found to be spread in the NE–SW direction indicating the direction of the tidal flows in the region. It is also found that the northern portion of the area shows greater depths close to the northern bank of the river Narmada. The detailed comparison of the contour lines has indicated that there has been considerable swallowing of the bed from 1973 to the present survey period. The Kerselea Bank has extended considerably in the northwestern direction and has narrowed the Bharuch channel. Comparison of the bathymetric chart of February 1991 and February 1993 shows that in the vicinity of the existing coastal infrastructure development in the Dahej region there is a tendency of accretion. The depths have increased from about 8 m in 1991 to about 12 m in 1993. River Narmada joins Gulf of Khambhat on the eastern side and is the largest river of the region. It has a very high peak discharge and picks up a large amount of sediments as it flows east to west. With the construction of various dams on the upstream, both in Madhya Pradesh and Gujarat, the reservoir storages have reduced the peak flows considerably. In the pre-dam scenario, the annual peak flow of about 80,000 cumecs was carrying an annual silt load of about 70 million m3 , which has now reduced to about 6–7 million m3 . It may also be noted that recently the completion of Sardar Sarovar Dam (Sept 2017) with full-fledged gates may as well lead to further reduced flow into the Narmada estuary. This reduction in the supply of sediments is

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probably making the river morphologically unstable and erosive. The instability in flow and sediment has led to erosion at upstream of the river, development of several sandbars in the middle of the reaches and erosion in lower parts of the river. The river is today characterised by wide mud flats and shallow areas along the right bank, which widens as it travels downstream. The river bed is in general muddy, with traces of sand found near the Gulf region. The river has a high tidal range of about 8 m, with MSL level of 5.1 m (near IPCL Jetty) relative to chart datum. The wave penetration into the river is very less due to the numerous bars, which act as attenuators. However, the high tidal range and associated high tidal currents keep the clay/silt in suspension making the estuary waters muddy. The tidal flows inside the Gulf are in a north–south direction. The tidal flow traps sediments in suspension in the estuary and the sediment moves up and down the estuary with the tide. The high TSS content of the Narmada estuary water, the strong tidal currents and river runoff makes the sediment regime unstable with shifting bars, characteristics of a region of excessive erosion and deposition. From the desk studies, it can be inferred that the study area is dynamic in nature and the morphological changes are prevalent and continuous in nature.

4 Data Sources 4.1 Bathymetry The field observed bathymetric information available at various locations in conjunction with the CMAP data of the study area was used in the preparation of the bathymetry. The depth contours show that there is a wide stretch of tidal flats and also shoals in the vicinity of the study area. As the tidal range is more than 6 m, a large area is subjected to flooding and drying. The contours towards south are spread apart indicating wide tidal flats. This depth information was used for setting up the computational model (Fig. 2).

4.2 Tides Field data collected during June and September 2016 was used for studies (Fig. 3). The tide data shows that the tidal range is of the order of 8.5 m during June and 9 m during the month of September. The tides in the region are very high which renders the Gulf highly dynamic and well-flushed.

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Fig. 2 Georeferenced bathymetry

4.3 Tidal Currents Recently observed, (September 2016) current data at two locations, i.e. one at the Mithivirdi (C1) on the western shoreline and the other at Dahej (C2) on the eastern shoreline was used in the calibration and validation of the model. The currents near Dahej were in the range of 0.02–1.44 m/s and the observed current near Mithivirdi was in the range of 0.04–1.65 m/s. The actual time history of velocities observed was used for the calibration of the model as shown in Fig. 4.

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Fig. 3 Boundary tide

4.4 Discharge Data Based on the analysis of the upland discharge data available at CWPRS over the period 1981–1990, the projected discharge during stage-1 and stage-2 development of Sardar Sarovar Project indicated that higher discharge occurs during the months of July, August, September and October. The maximum average monthly discharge before the development of Sardar Sarovar Project was about 5500 cumecs and after first stage development the maximum monthly discharge is expected to reduce to about 1200 cumecs which occurs during the month of September. After stage-2, development of the Sardar Sarovar Project the discharges are not likely to be higher than 200 cumecs throughout the year. These aspects are important from the point of view of the long-term stability of natural channels within the Gulf. The maximum discharge through the Narmada River during peak monsoon is expected to be around 10,000 cumecs. Similarly, the minimum discharge of 200 cumecs occurs during nonmonsoon period. At the river mouth, the freshwater discharge was prescribed based on available observations. The average runoff into the Gulf from Narmada River is nearly 800 cumecs [9]. The discharge considered during the model setup for the monsoon are given in Table 1.

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Fig. 4 Time history of current observation at C1 and C2 Table 1 Discharge of the rivers into Gulf of Khambhat

River

Discharge (m3 /s)

Sabarmati Mahi Narmada

400 400 800

4.5 Sediment Data The bed sediments in the Tapi estuary are reported to be sandy with low percentage of silt and clay. The bed sediments in the jetty area are at Dahej is found to be silty clay. From the field survey reported, it is observed that the water at the Dahej site is highly turbid and muddy. The concentration of suspended solids is very high

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and variable. The analysis of suspended solids observed from the year 1985–2002 available at CWPRS is considered. The survey conducted by National Institute of Oceanography (NIO) during the year 2011 and 2012 near Mithivirdhi shows that the maximum suspended solids at average mid-depth is 1960 mg/l. Evaluation of sediment characteristics and contamination based on analysis of surface sediments indicated that the sediment texture of the region varied considerably in space and time. Further field studies conducted during May 2013 indicated that the average suspended solid concentration near Reliance Jetty at Dahej is of the order of 200 mg/l during nonmonsoon season and the same was considered for the model studies. Average Values of SS (mg/l) at different zones of the study area during 1993–2014 are given in Table 2.

4.6 Dispersion Coefficient Dispersion studies were carried out in two phases during 2011–2012 by NIO to assess the longitudinal and transverse dispersion coefficients (Kx and Ky) of the study region. Because of high tidal current in this region, the dye dispersion is rapid which is observed by the rate of change of concentration within 1–2 h. It is also observed that the longitudinal dispersion coefficient Kx 6 is greater than the lateral direction Ky. The values of Kx range between 3.9 and 30.12 whereas Ky ranges between 0.19 and 0.71. Based on this observation, we have assumed the dispersion is proportional to the currents in the model studies.

4.7 Waves The Gulf of Khambhat is well protected from the waves emanating from the Arabian Sea, since the Gulf faces south, between the Saurashtra Peninsula and mainland Gujarat. The dominant direction of waves in the open sea south of the Narmada mouth is from the southwest in May/June, swinging to west in July/August and veering to the northwest for the remaining part of the year. January and February are the calm months and the waves gradually pick up from mid-March onwards. The magnitude of the wave in the Narmada estuary is not very high. The significant wave height while entering into the Gulf from the Arabian Sea is 5 m which reduces to 0.5 m significant waves at Dahej. The period of these waves lies in a short bandwidth of 5–6 s.

699

1021

Nearshore

Narmada estuary

566

Oct 1993

Offshore

Zone

SS (mg/l)

16,495

7301

11,284

Feb 1997

1585

1053

986

Feb 2006

1345

1083

979

Oct 2007

1388

822

704

Apr 2009

Table 2 Average values of suspended sediments at different zones of the study area

285.5

13,220

914

Jan 2012

2697

3205

5060

Mar 2012

2252

1782

2072

Sept 2012

160

396

241

Oct 2014

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5 Model Studies for Tidal Hydrodynamics Hydrodynamic studies include simulation of the flow field for the entire Gulf. The studies were carried out to assess changes in the hydrodynamic condition and formation of tidal circulations if any over a period of month. The model was run for two different seasons (i.e., Monsoon and Nonmonsoon Data). The Nonmonsoon field observed data was used for the calibration of the hydrodynamic model. The results of the hydrodynamic studies are the basic input for the sediment transport studies.

5.1 Computational Model The computational model considered for tidal flow and sediment simulation covered an area of 88,000 m by 140,000 m. The model limit extends from 0 to 44 m depth contour in the offshore in the south direction and 0–8 m depth in the north direction. The model area covers the entire Gulf of Khambhat and adjoining open sea as shown in Fig. 5. The complete model area has been discretised into computational mesh of maximum element area of 3,750,000 m2 with the smallest allowable angle of 30 and maximum number of nodes of 100,000. The bathymetry in the Gulf region is quite irregular and there are many shallow zones followed by deep channels on either side were reproduced satisfactorily.

5.2 Tidal Boundary Condition The Gulf has an open boundary at the seaward end connecting 71.750 E and 72.640 E at 210 N (Fig. 5). At the landward end, there are three open boundaries of the analysis area connecting Sabarmati, Mahi, and Narmada rivers. The discharge from Vishwamitri is ignored due to its low discharge. A realistic tidal boundary condition, used at the southern boundary and freshwater discharges from the three rivers, is provided at the river mouths. Initially, the model was simulated for non monsoon season with the above-mentioned boundary conditions and appropriate tidal input at the southern open boundary.

5.3 Calibration of Model with Non-monsoon Data The simulations were repeated by altering the fine-tuning parameters like bed friction coefficients until the observed and computed water levels as well as currents reached reasonable agreement with the field observed data. The currents were monitored and extracted at three locations, i.e. at Mithivirdi (C1), Dahej (C2) and at the centre of

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Fig. 5 Computational model showing monitoring points C, C1 and C2

the Gulf of Khambhat (C). The computed current is in good agreement with the field observed current and was found to vary from 0.01 to 1.68 m/s at the C1 point and it was in the range of 0.02–1.4 m/s at the C2 point. The magnitude of currents in the centre of the Gulf, i.e. at monitoring point C it varied in the range of 0.04–2.1 m/s indicating that the currents are strong in the middle region and it becomes weak as it approaches the coast due to friction factors. The comparison of observed and computed currents is shown in Fig. 6. The flow field during peak flooding and peak ebbing during nonmonsoon month is shown in Fig. 7.

5.4 Simulation of Flow Field During Monsoon The simulations were repeated for monsoon conditions by considering appropriate river discharges from Sabarmati, Mahi and Narmada rivers. Vishwamitri River discharge was ignored as its magnitude was negligible during the period of observation.

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Fig. 6 Comparison of observed and computed currents at C1 and C2

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Peak Flooding

Peak Ebbing

Fig. 7 Flow field during nonmonsoon

From the literature, it was inferred that with monsoon conditions the magnitude of currents that did not change much in the centre of the Gulf and the same trend was observed in model simulations as the currents varied in the range of 0.02–2.23 m/s and were found to be reasonable. At the river inlet and inside the estuary the magnitude of currents increased considerably due to the river discharge. The flow field during peak flooding and peak ebbing during Monsoon month are shown in Fig. 8.

6 Sedimentation Studies 6.1 Introduction For any development in Gulf, sedimentation studies are very essential as the nature of sediment movement is very dynamic due to the characteristic nature of sediments and typical flow conditions. Siltation in the approach channel and the harbour basin is a serious problem in west coast, which is being experienced by ports on the west coast of India. In this regard, flow field and sedimentation studies are an important element

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Peak Flooding

Fig. 8 Flow field during monsoon

in any port development during the design and implementation stage. Remote sensing studies [10] has been carried to map suspended sediment concentration (SSC) along the Indian Coast and it indicated that in Gulf of Khambhat (GOK) the sediments as well as pollutants under the influence of strong tidal currents are dispersed and settle within the Gulf of Khambhat. The inference from the study is that the Gulf of Khambhat is getting silted up swiftly which needs to be validated by model studies. Further studies conducted by researchers [11] indicated that the dispersion of sediment largely depends upon wind and wave patterns. Net landward transport of sediment occurs in this region which is can be understood from the presence of a number of mudflats within the estuary along with the siltation in the channels. High tidal range is the distinguishing feature of the Gulf because of this tidal currents dominate the flow. The tides are of semi-diurnal type with a large diurnal inequality and varying amplitudes, which increase from the south to north along the Gulf coast. The height of the tide increases tremendously from the mouth to the upstream end because the width of Gulf decreases towards the upstream end. Tidal currents are with two dominant directions; towards upstream during flood and downstream during ebb in all oscillatory motions. The maximum currents occur during mid-tide, which is around 2.5 m/s in the Gulf, and associated with high wave energy [12]. The Gulf is more or less homogeneous which is caused by the shallowness of the depths and medium to high tidal amplitudes associated with tidal currents and turbulence.

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Photo 1 Seabed features near in Mudflats and berthing at Dahej

The rivers draining into the Gulf of Khambhat carry an enormous amount of sediments in their discharges. Sabarmati, Mahi, and Narmada rivers drains into the Gulf. These rivers discharge a large volume of sediments as also the suspended load. The bottom consists of mainly the river-borne fine to coarse-grained sand. The western and northern parts of the Gulf consist of largely soft sediments of Quaternary rocks. With this background sedimentation studies were conducted for assessing the siltation pattern in the Gulf of Khambhat region. Photo1 shows the seabed features and wide tidal flats near Dahej. An average suspended solid concentration of 200 mg/l and 1900 mg/l is considered for the model studies during nonmonsoon and monsoon seasons, respectively. The sedimentation studies were conducted using Mike-21 MT module of DHI software.

6.2 Sediment Model Simulations and Interpretation of Results The siltation studies were carried out with the prevailing conditions in the Gulf of Khambat considering the infrastructure facilities in the vicinity of Dahej and adjoining areas. The model simulations were carried out for Monsoon and Nonmonsoon weather conditions separately for duration of 30 days each. The siltation trend during different phases of the tide was monitored. The computed sedimentation pattern observed during both the seasons can be seen in Fig. 9. In general, it is noticed that the sediments tend to deposit around the mudflats around the mainland, also in the depressions of seabed and natural channels in the vicinity of Dahej infrastructural development region during Nonmonsoon season. It is also noticed that the southern part of the Gulf experiences a tendency of sediment deposition. It may be attributed to the reduction of the flow velocities as the width of the Gulf expands. Further, during monsoon season it is noticed that the trend of sedimentation has considerably reduced. From the model results, it can be inferred that this decreasing trend may be due to the flushing action of considerable river discharges during Monsoon.

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Monsoon

Fig. 9 Sedimentation pattern in the Gulf of Khambhat

During the flood, the suspended sediment concentrations varied from 120 to 900 mg/l and it varied from 160 to 1020 mg/l during ebb in Monsoon season. As expected, the concentrations were higher during the ebb than during the flooding period. This is because of the joining of the three rivers, namely Sabarmati, Mahi and Narmada, in the Gulf.

7 Conclusions A depth-averaged numerical model with flexible mesh was used to compute the tidal circulation, sedimentation pattern and suspended sediment transport in the Gulf of Khambhat by including three rivers, namely, Sabarmati, Mahi and Narmada. Meanwhile, the computed mean suspended sediments were validated with the available observations in the Narmada estuary. Reasonable circulation pattern and suspended sediment concentrations have been simulated in the model. The observed data available at CWPRS on the eastern and western part of the Gulf was used for the simulations. However, additional data in the northern region would have been more appropriate. The sedimentation pattern in the Gulf of Khambhat has been simulated well as shown in Fig. 9. It is observed that trends of siltation are noticed during nonmonsoon season in the natural channels and depressions near Dahej, and the mudflats surrounding the mainland are prone to siltation. Further, the southern region of the

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Gulf has shown tendency of siltation and it may be due to the expansion of Gulf width which results in reduction of the flow velocities. Similarly, during monsoon season it was observed that the tendency of siltation has reduced considerably and it was inferred that it may be due to the flushing action by the monsoon discharges from all the rivers considered in the simulation. The model result implies that there is a significant deposition and resuspension processes within the estuary controlled by the varying tidal ranges. The complexity in bathymetry and the coastline plays a vital role in influencing the tidal currents and sediment distribution patterns in the Gulf region. Deep tidal scour channels in the mid Gulf are found to be devoid of high suspended sediment concentrations throughout the observations. Further, the impact on the present coastal infrastructure in GOK of proposed Kalpasar project needs to be studied. Acknowledgements The authors are thankful to Dr. (Mrs). V. V. Bhosekar, Director, CWPRS, Pune for her consistent support, encouragement and according permission to publish this paper.

References 1. Kunte PD, Zhaob C, Osawa T, Sugimori Y (2005) Sediment distribution study in the Gulf of Kachchh, India, from 3D hydrodynamic model simulation and satellite data. J Mar Syst 55(2005):139–153 2. Gelfenbaum G, Stevens A, Elias E, Warrick J (2009) Modeling sediment transport and delta morphology on the dammed Elwha River, Washington State, USA. Coastal Dynamics, Paper No. 109 3. Sravanthi N, Ramakrishnan R, Rajawat AS, Narayan AC (2015) Application of numerical model in suspended sediment transport studies along the Central Kerala, West-Coast of India. In: Proceeding of India international conference on water resources, coastal and ocean engineering, Aquatic Procedia, vol 4, pp 109–116 4. Sanilkumar V, Ashok kumar K (2010) Waves and currents in tide dominated location off Dahej, Gulf of Khambhat, India. Mar Geod 33(2):218–231 5. Samiksha SV, Sharif J, Vethamony P (2014) Coastal circulation off Ratnagiri, west coast of India during monsoon seasons: a numerical model study. Indian J Geo-Mar Sci 43(4):481–488 6. Sri Ram Kumar P, Dwarakish GS, Nujuma N, Gopinath DI (2015) Long term study of sediment dynamics along Mangalore Coast, West Coast of India using sediment trend analysis. In: Proceeding of the international conference on water resources, coastal and ocean engineering, Aquatic Procedia, vol 4, pp 1545–1552 7. Kunte PD, Wagle BG (2001) Littoral transport studies along west coast of India—a review. Indian J Mar Sci 30:57–64 8. Misra A, Mani Murli R, Sukumaran S, Vethamony P (2014) Seasonal variations of total suspended matter (TSM) in the Gulf of Khambhat, west coast of India. Indian J Mar Sci 43(7) 9. Haskoning Consulting Engineers and Architects (1996) Khambhat Gulf development project. Prefeasibility Survey, Draft Final Report, Narmada & Water Resources Department, Government of Gujarat, vol 5, Annex 12–13 10. Rajawat AS, Mukesh G, Yaswant P, Thomaskutty AV, Nayak S (2005) Coastal processes along the Indian coast—case studies on synergistic use of IRS-P4 OCM and IRS-1C/1D data. Indian J Mar Sci 34(4):459–472 11. Nayak SR, Hegde VS, Shalini R, Rajawat AS, Ali M, Venkateshwarlu B, Ramana IV (2012) Application of satellite remote sensing for investigation of suspended sediment dispersion

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pattern in the near shore region: a case study from the Central West Coast of India. J Coast Res 28(2) 399–406. https://doi.org/10.2112/jcoastres-d-10-00190.1 12. Sen Gupta R, Deshmukhe G (2000) Coastal and maritime environment of Gujarat. Gujarat Ecological Society, Vadodara, India

Wave Climate and Nearshore Sediment Transport Pattern Along the SE Coast of India V. Ranga Rao, Akhil Kolli, K. Stephen Raju and D. Kumaresan

Abstract Wave climate along five selected transects covering 580 km length of the SE coast of India was studied based on National Institute of Ocean Technology (NIOT) wave atlas. The wave height of 90% of the waves ranged from 0.5 to 0.8 m whereas for 10% of the waves the wave height varied from 1.5 to 2.0 m along the coast. The wave period usually varied between 4 and 6 s. During the NE monsoon season (January), the wave direction was predominantly ESE whereas during the SW monsoon the predominant direction was SSE. The wave climate data was utilized to estimate the sediment transport rates at 0.8, 2, 5, 10, 30 and 50 m depth contours across each of the five selected transects of the SE coast. The required wave parameters at these depths were calculated using Linear Wave Calculator of parabolic mild slope wave model of Danish Hydraulic Institute (DHI), Denmark. The calculated wave parameters at the different depth contours were given as input to simulate the sediment transport rates at the same depth contours using LITSTP model of LITPACK package of DHI. The remarkable feature identified in the present investigation is that most of the sediment transport was confined to nearshore waters within 10 m depth contour, i.e. within 5 km from the shoreline. The simulated results indicate that the sediment transport rate usually varied between a minimum value of 975 m3 /month and a maximum value of 73,967 m3 /month. The sediment transport rates along the coast is relatively higher during the NE monsoon season as compared to those during the SW monsoon. Keywords Wave climate · Nearshore sediment transport · LITSTP SE coast of India

V. Ranga Rao (B) · D. Kumaresan ICMAM-PD, NIOT Campus, Pallikaranai, Chennai 600100, India e-mail: [email protected] A. Kolli · K. Stephen Raju Department of Applied Mechanics & Hydraulics, NITK, Surathkal, Mangalore 575025, India © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_12

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1 Introduction The littoral sediment transport pattern along a particular coast usually takes place due to the action of breaking waves [1–4]. The breaking waves result in the pile-up of water along the coast which in turn leads to the generation of littoral currents and moves the sediment either in alongshore or offshore/onshore direction. The onshore/offshore and alongshore movement of sediment is usually dependent on several factors such as beach slope, wave period, current direction and bottom friction [5, 6]. Both the strength and direction of sediment movement varies with season and location [3, 7–13]. Chandramohan et al. [14] revealed that the sediment transport pattern along the east coast of India takes place northward for 8 months (March–October) and southward for the remaining four months (November–February) of the year. According to Chandramohan and Nayak [15], the net annual sediment transport along the east coast is northward whereas along the west coast it is southward except for the south Gujarat Coast. In the present study, an attempt was made to study the nearshore wave climate and associated sediment transport pattern along the SE coast of India.

2 Study Area The 580 km length of the study area (SE coast of India) starting from Kavali in Andhra Pradesh to Nagapattinam in Tamilnadu has three major ports (Ennore, Chennai, and Thoothukudi) and two medium ports (Cuddalore and Nagapattinam). Natural factors like cyclones, coastal flooding, coastal sediment deposition, tsunami, etc. and the anthropogenic factors such as domestic and industrial sewage due to urbanization and industrialization play a major role on the sediment dynamics along the coast. The material inputs from industries, aquaculture, tourism sector, petroleum products, fertilizer, pesticides, etc. enter the nearshore waters affecting the mangroves and related coastal environments [16].

3 Data and Methodology In order to study the spatial as well as temporal variations of the sediment transport along the SE coast of India, five cross-shore transects (A–E) were fixed as shown in the Fig. 1. Each transect covers the distance from shoreline to 50 m depth contour offshore and the details of the physiographic characteristics of each transect are given in Table 1. For each transect, the data on cross-shore bathymetry (from 0 to 50 m depth) was extracted by re-analysis of the bathymetry data from ICMAM database and by combining online bathymetry data, c-map and ICMAM field data. The directional wave

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Fig. 1 The study area showing the five transects (A, B, C, D and E) with cross-shore bathymetry profiles (values on each profile indicate the ‘bed slopes’ at corresponding depth contour)

data needed at the offshore depths were collected from the wave atlas (1998–2012) of the Indian Coast prepared by NIOT [17]. The offshore location at which the wave parameters of the NIOT wave atlas represents is around 24–26 m depending on the transect. The extracted data from the NIOT wave atlas was used to calculate the wave parameters at 0.8, 2, 5, 10, 30 and 50 m depth contours using Linear Wave Calculator

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Table 1 Details of the five transects along the SE coast Transect Id Transect Shoreline Mean slope origin at shore orientation along the (°N) transect

Transect length up to 10 m depth contour (km)

Transect length up to 50 m depth contour (km)

A

15.000N 80.192E

20

0.0047 (1:213)

6.1

25.8

B

14.000N 80.334E

10

0.0051 (1:196)

12.9

22.1

C

13.000N 80.357E

15

0.0038 (1:263)

2.7

15.2

D

12.000N 79.969E

25

0.0095 (1:105)

6.7

23.5

E

11.000N 79.935E

5

0.0034 (1:294)

3.3

19.8

(LWC) of DHI (2005). The calculated wave parameters at 0.8, 2, 5, 10, 20, 30 and 50 m depth contours for each of the five transects were later utilized as input for the LITSTP model of LITPACK [18]. The LITSTP is a one-dimensional model that includes the hydrodynamic processes and the intra-wave sediment transport mechanisms. The input data for the LITSTP module are the wave period (T), wave height (H), wave direction (θ), current speed and direction, shoreline angle, seabed slope and the mean sediment size. The wave direction alpha (α) is the angle between the wave orthogonal and the coast orthogonal (i.e. α is 0° if the wavefronts are parallel to the coast). The g value taken as 9.82 m2 /s and the density as 1028 kg/m3 . While simulating the model the depth and the bed slope values were specified at each calculated location. Both current speed and direction were specified at each of the simulated location and the sediment size (0.2 mm) was represented as the mean grain diameter d 50 . The uniformly graded sediment process was considered and the related fall velocity and the specific gravity were adopted as 0.022 m/s and 2.65 respectively. The model simulations to derive sediment transport rates along the SE coast were carried out for January and August months representing NE and SW monsoon wave climatic conditions respectively.

4 Results and Discussion 4.1 Wave Climate January (NE Monsoon): The percentage distribution of wave height, wave period and wave direction at an offshore location derived from the NIOT wave atlas for each of the five transects (A–E) are shown in Fig. 2. In January the transects C, D and E

Wave Climate and Nearshore Sediment Transport Pattern …

(a)

(b)

(c)

8 2.5

90% waves

90% waves

10% waves

10% waves

2

6

1.5

4

163

300

90% waves

250

10% waves

200 150

1

100

2

0.5

50 0

0

0 A

B

C

D

E

A

B

C

D

E

A

B

C

D

E

Fig. 2 Deepwater wave parameters—a wave height (m) b wave period (s) and c wave direction (deg) derived from NIOT wave atlas for the offshore region (around 22.8 and 30.4 m) for the five different transects (A–E) along the SE coast for January representing NE monsoon conditions

showed higher wave strengths of around 2.0 m whereas transects A and B showed comparatively lower strengths of around 1.5 m. Overall, the occurrence of higher strength waves in the offshore area (NIOT buoy location) comprised only 10% of the total waves and were within the range of 1.5–2.2 m. However, the lower strength waves which is a regular phenomena comprised 90% of the waves and ranged from 0.5 to 0.8 m height. The wave period of 90% of the waves (Fig. 2b) along the SE coast usually falls within the range of 4–5 s whereas the remaining 10% fall within 5–7 s. The wave direction in January (NE monsoon) at the different transects (Fig. 2c) indicates that, in general, the waves approach the coast between 75 (ENE) and 155 (SSE) direction. However, 90% of the waves approach the shore between 75 and 90 (ENE and E) and the remaining 10% of the waves from 125 and 155 (ESE and SSE). Thus, during the NE monsoon season about 10% of the waves having higher strengths approach the coast from the SE direction while 90% of the waves approach the coast from ENE direction. August (SW Monsoon): In August, the transects C and D (Fig. 3a) showed higher wave strengths of around 1.5 m whereas the transects A, B and E showed lower strengths of around 1.0 m. About 90% of the waves with strengths of 0.4–0.7 m and periods of 4–5 s (Fig. 3b) approach the coast from SE and SW direction (Fig. 3c). Overall, it is observed that there is a clear demarcation in the approach direction between higher and lower strength waves along the SE coast. The higher strength waves (1.0–1.5 m) even though they are of less percentage approach predominantly from the S and SE directions during both the seasons. The lower strength waves approach the coast from ENE in NE monsoon and S and SSE in SW monsoon. Further, the NE monsoon is characterized by higher strength waves as compared to that of during the SW monsoon season. The lower strength of waves in the SW monsoon season may be due to the shadowiness of Sri Lanka peninsula for S wave propagation originating from the equatorial Indian Ocean region.

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(a)

(b)

(c)

8

90% waves

10% waves

2

90% waves

200

2.5 90% waves

10% waves

1.5

6

150

4

1

100

2

0.5

50

0

0 A

B

C

D

E

10% waves

0 A

B

C

D

E

A

B

C

D

E

Fig. 3 Deep water wave parameters—a wave height (m), b wave period (s) and b wave direction (deg) derived from the NIOT wave atlas for the offshore region (around 22.8 and 30.4 m) for the five different transects (A–E) along the SE coast for August representing SW monsoon conditions

4.2 Wave Transformation in Shallow Water January (NE Monsoon): The calculated wave height (H), wave period (T) and wave direction (θ) at the different depth contours (0.8, 2, 5, 10, 20, 30, and 50 m) based on LWC for each of the five transects (A–E) for January representing NE monsoon conditions are shown in Table 2. At transect A, 90% of the wave heights varied from 0.6 m (in deep water areas) to 0.5 m (in shallow waters near shoreline), whereas the wave direction vary from 96° in deep water areas to 88° in shallow waters areas. However, 10% of the waves with heights vary between 1.6 m (in deep water areas) to 0.7 m (in shallow water areas close to shoreline) and the directions vary from 125° to 123° as the waves approach from deep water areas to shallow water areas. More or less similar trend of wave transformation was noticed along transect B. Along transects C–E the deep water wave heights at these three transects varied between 0.7 and 2.0 m whereas the shallow water wave heights varied between 0.7 and 0.8 m. Similarly, the directions varied between 135 and 81 in deep water areas and between 105 and 78 in shallow water areas (close to the coast). On the whole, the waves transformed from greater heights (around 0.7–2.0 m) to lower heights (0.7–0.8 m) as the waves approach the shore. This kind of wave transformation in January representing NE monsoon conditions may lead to southward sediment transport along the coast. August (SW Monsoon): The calculated wave height (H), Wave period (T) and wave direction (θ) at different depth contours (0.8, 2, 5, 10, 20, 30, and 50 m) utilizing NIOT wave atlas data based on LWC along the five transects (A–E) for the month August representing SW monsoon conditions are shown in Table 3. At transect A, 90% of wave heights varied from 0.5 m (in deep water areas) to 0.6 m (in shallow waters near shoreline), whereas the wave direction varies from 135° in deep water areas to 121° in shallow waters areas. However, 10% of waves with heights vary between 1.0 m (in deep water areas) to 0.64 m (in shallow water areas close to shoreline) and the directions vary from 158° to 121° as the waves approach from deep water areas to shallow water areas. More or less similar trend of wave transformation was noticed along transect B.

4

88

0.6

4

74

0.7

4

93

0.7

4

105

0.8

4

78

T (S)

θ (deg)

Transect B H (m)

T (S)

θ (deg)

Transect C H (m)

T (S)

θ (deg)

Transect D H (m)

T (S)

θ (deg)

Transect E H (m)

T (S)

θ (deg)

101

5

0.7

119

7

0.7

110

6

0.7

135

5

0.7

123

72

4

0.7

95

4

0.7

88

4

0.7

77

4

0.5

91

4

0.5

0.7

0.6

Transect A H (m)

5

2m

90%

10%

0.8 m

%occurrence 90%

Depth

96

5

1.6

119

7

1.6

115

6

1.6

135

5

1.5

123

7

1.6

10%

66

4

0.7

87

4

0.7

83

4

0.7

80

4

0.5

95

4

0.5

90%

5m

103

5

1.7

119

7

1.9

123

6

1.7

147

5

1.3

122

7

1.5

10%

64

4

0.8

84

4

0.7

81

4

0.7

81

4

0.6

96

4

0.6

90%

10 m

106

5

1.8

120

7

1.8

134

6

1.7

151

5

1.4

124

7

1.4

10%

64

4

0.8

84

4

0.7

81

4

0.7

81

4

0.6

96

4

0.6

90%

107

5

1.9

120

7

1.9

135

6

1.9

151

5

1.5

125

7

1.5

10%

NIOT wave atlas

64

4

0.8

84

4

0.7

81

4

0.7

81

4

0.6

96

4

0.6

90%

30 m

107

5

1.9

120

7

1.9

135

6

1.9

151

5

1.5

125

7

1.5

10%

64

4

0.8

84

4

0.7

81

4

0.7

81

4

0.6

96

4

0.6

90%

50 m

107

5

1.9

120

7

2.0

135

6

1.9

151

5

1.5

125

7

1.6

10%

Table 2 Transformed wave parameters at different depth contours covering deep water areas (50 m) to shallow water areas (0.8 m) across transects A–E in January (NE monsoon)

Wave Climate and Nearshore Sediment Transport Pattern … 165

4

121

0.6

4

120

0.7

4

133

0.7

5

127

0.4

3

116

T (S)

θ (deg)

Transect B H (m)

T (S)

θ (deg)

Transect C H (m)

T (S)

θ (deg)

Transect D H (m)

T (S)

θ (deg)

Transect E H (m)

T (S)

θ (deg)

133

5

0.7

133

6

0.7

121

6

0.7

121

7

0.7

122

137

3

0.4

136

5

0.6

132

4

0.6

126

4

0.5

126

4

0.5

0.64

0.6

Transect A H (m)

7

2m

90%

10%

0.8 m

%occurrence 90%

Depth

144

5

0.6

123

7

0.9

131

6

1.1

136

7

1.1

127

7

1.0

10%

150

3

0.4

144

4

0.6

145

4

0.6

132

4

0.5

132

4

0.5

90%

5m

162

5

0.6

143

7

1.0

155

6

1.1

138

7

0.9

137

7

0.9

10%

152

3

0.5

148

4

0.6

150

4

0.7

135

4

0.5

134

4

0.5

90%

10 m

178

5

0.8

183

7

1.1

160

6

1.2

146

7

0.9

142

7

0.9

10%

158

3

0.5

150

5

0.62

150

4

0.7

135

4

0.5

135

4

0.5

90%

188

5

1.0

173

7

1.5

173

6

1.5

157

7

1.0

158

7

1.0

10%

NIOT wave atlas

152

3

0.4

149

5

0.6

151

4

0.7

135

4

0.5

135

4

0.5

90%

30 m

189

5

1.0

173

7

1.5

176

6

1.7

157

7

1.1

158

7

1.0

10%

152

3

0.4

149

5

0.6

151

4

0.7

135

4

0.5

135

4

0.5

90%

50 m

189

5

1.0

173

7

1.5

176

6

1.7

161

7

1.1

158

7

1.0

10%

Table 3 Transformed wave parameters at different depth contours covering deep water areas (50 m) to shallow water areas (0.8 m) across transects A–E in August (SW monsoon)

166 V. Ranga Rao et al.

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167

Along transects C–E the deep water wave heights at these three transects varied between 0.4 and 1.7 m whereas the shallow water wave heights varied between 0.4 and 0.7 m. Similarly, the directions varied between 179 and 189 in deep water areas whereas in between 116 and 133 correspondingly in shallow water areas close to the coast. On the whole, the waves transformed from greater heights (around 0.5–1.5 m) to lower heights (0.4–0.7 m) as the waves approach the shore. Such wave transformation in August representing SW monsoon conditions may lead to northward sediment transport especially along the southern part of SE coast.

4.3 Nearshore Sediment Transport––LITSTP After obtaining the transformed wave parameters at the required depth from LWC, the sediment transport rate at that depth was simulated using LITSTP model for each of the five transects as described in Sect. 3. To study the nearshore sediment transport pattern along the SE coast simulations for the months of January and August representing the NE and SW monsoon conditions respectively were carried out and the results were plotted as shown in Fig. 4.

Fig. 4 Simulated sediment transport rate at different depth (0.8, 2.0, 5.0, 10.0 and 20.0 m) contours along each of the five transects (A–E) under the wave conditions of January (NE monsoon). Values on the figure represent the magnitude in m3 /month/m while the arrows indicate the direction of sediment transport

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Fig. 5 Simulated sediment transport rate at different depth (0.8, 2.0, 5.0, 10.0 and 20.0 m) contours along each of the five transects (A–E) under the wave conditions of August (SW monsoon). Values on the figure represent the magnitude in m3 /month/m while the arrows indicate the direction of sediment transport

In general, it is observed that the rate of sediment transport in January (NE Monsoon) is higher close to the coast and gradually decreased towards the offshore area up to 20 m depth contour. Sediment transport was negligible beyond 20 m depth at almost all the five transects studied. The sediment transport rate due to 90% of the waves is low (21–105 m3 /month/m) (Fig. 4a). High sediment transport rate of 192–798 m3 /month/m (Fig. 4b) occurs at 2 m depth contour due to 10% of the waves. More or less similar features were observed in August (SW monsoon) as that of January (NE monsoon) but the direction of sediment transport was predominantly northward with lower sediment transport rates. The sediment transport rate during the SW monsoon is relatively lower than that of during the NE monsoon (Fig. 5). The highest sediment transport rate of 1.3–47 m3 /month/m (Fig. 5a) was seen due to 90% of the waves while 8–22 m3 /month/m (Fig. 5b) due to 10% of the waves representing SW monsoon conditions. From the simulated sediment transport rates as mentioned under Figs. 4 and 5, the computed gross sediment transport rate along each of the five transects due to 90% wave occurrences for the months January (NE monsoon) and August (SW monsoon) is given in Table 4. It is clearly noticed that the sediment transport rate during the SW monsoon is low (975–42,251 m3 /month) when compared to that of during the NE monsoon (13,319–73,967 m3 /month) at almost all the transects. The highest

Wave Climate and Nearshore Sediment Transport Pattern …

169

Table 4 Sediment transport (ST) rate (m3 /month) due to 90% of wave occurrences along the SE coast Transect Id January (NE monsoon) August (SW monsoon) ST due to 90% waves

ST due to 90% waves

A

13,319

12,643

B

21,143

21,664

C

50,618

42,251

D

42,959

15,573

E

73,967

975

Table 5 Sediment transport (ST) rate (m3 /month) due to 10% of wave occurrences along the SE coast Transect Id January (NE monsoon) August (SW monsoon) ST due to 10% waves

ST due to 10% waves

A

67,297

5436

B

144,517

14,201

C

206,890

15,442

D

53,031

12,249

E

164,225

15,337

sediment transport rate of 73,967 m3 /month was noticed during the NE monsoon season while the lowest sediment transport rate of 975 m3 /month was noticed during the SW monsoon along the SE coast. The gross sediment transport rate along each of the five transects due to 10% wave occurrences for the month of January (NE monsoon) and August (SW monsoon) is given in Table 5. It is noticed that the sediment transport rate during the SW monsoon is low compared to that of during the NE monsoon season at almost all the transects. For validation, the simulated sediment transport rates were compared with published studies for this region [15, 19–21]. The simulated sediment transport rates reasonably matched well with the values obtained from the past studies as shown in Fig. 6.

5 Conclusion Along the SE coast of India, 90% of the waves have wave heights ranging from 0.5 to 0.8 m whereas 10% of the waves have heights of 1.5–2.0 m. The wave period usually varies between 4 and 6 s. During the NE monsoon season (January) the wave direction is predominantly ESE whereas during the SW monsoon it is SSE. A remarkable feature identified in the present study is that most of the sediment transport is confined to the nearshore waters within 10 m depth contour i.e. within

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Fig. 6 Comparison between the simulated sediment transport rates and studies reported for the study area

5 km from the shoreline. The simulated results indicated that the sediment transport rate usually varied between a minimum value of 975 m3 /month and a maximum value of 73,967 m3 /month. The sediment transport rates along the coast are relatively higher during the NE monsoon season as compared to that of the SW monsoon. The direction of the sediment transport is southward in January representing the NE monsoon wave climatic conditions whereas northward in August representing the SW monsoon wave climatic conditions. Acknowledgements The authors wish to express their sincere thanks to Dr. M. Rajeevan, Secretary, Ministry of Earth Sciences, and Dr. M. V. Ramana Murthy, Head, ICMAM, for their keen interest and encouragement. The authors (Akhil Kolli and Stephen Raju K.) express their gratitude to Dr. Subba Rao, NITK, Suratkal and Dr. P. Madeswaran, of ICMAM, Chennai for providing the necessary permissions and facility to carry out internship at ICMAM in the field of nearshore sediment dynamics. The authors are thankful to NIOT for providing the wave atlas of Indian coast for the present study.

References 1. Zheng J, Li R, Yu Y, Suo A (2014) Influence of wave and current flow on sediment-carrying capacity and sediment flux at the water—sediment. Water Sci Technol 338:1090–1099 2. Baldock TE, Manoonvoravong P, Pham KS (2010) Sediment transport and beach morphodynamics induced by free long waves, bound long waves and wave groups. Coast Eng 57:898–916

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3. Eaton RO (1950) Littoral processes on sandy coasts. In: Proceedings of the first conference of coastal engineering, pp 140–154 4. Johnson DK (1919) Shore processes and shoreline development. Wiley, p 584 5. Daily JW, Stephen SC (1951) Characteristics of solitary waves. Proc Am Soc Civil Eng 77–107 6. Munk WH (1949) Thesolitary wave theory and its application to surface problems. Ann N Y Acad Sci 51:396–424 7. Manohar M (2017) Sediment movement at south Indian ports. Coast Eng 359–405. https:// journals.tdl.org/icce/index.php/icce/article/view/1911/1170. Accessed 3 June 2017 8. Gilbert GK (1890) Lake Bonneville. Monographs of U. S. Geological Survey I: 584 9. Johnson JW (1953) Sand transport by littoral currents. In: Proceedings of the fifth hydraulic conference, vol 34, pp 89–109 10. Johnson JW (1957) Thelittoral drift problem at shoreline harbours. Proc Am Soc Civil Eng 83:1–37 11. Johnson JW (1956) Dynamics of near shore sediment movement. Bull Am Assoc Pet Geol 40:2211–32 12. Johnson JW (1953) Engineering aspects of diffraction and refraction. Trans Am Soc Civil Eng 118:617–652 13. Kuenen H (1950) Marine geology. Wiley, pp 221–251 14. Chandramohan P, Nayak BU, Raju VS (1990) Longshore-transport model for south Indian and Sri Lankan coast. J Water Way Port Coast Ocean Eng 116:408–423 15. Chandramohan P, Nayak BU (1991) Longshore sediment transport along the Indian coast. IJMS 20:110–114 16. Ramesh R, Nammalwar P, Gowri VS (2008) Database on coastal information of Tamilnadu. Environmental Information System Centre, Department of Environment, Government of Tamilnadu, Institute of Ocean Management, Anna University, Chennai 17. NIOT (2017). http://moes.gov.in/writereaddata/files/press_release_atlas_on_wave_related_ information.pdf. Accessed Aug 2017 18. DHF (2005) DHI Water & Environment, MIKE Zero, Denmark 19. Gowthaman R, Sanil Kumar V, Siddaramaish G, Shanas DR, Jena BK Jai Singh (2015) Nearshore waves and longshore sediment transport along Rameshwaram island off the east coast of India. Int J Nav Archit Ocean Eng 7:939–950 20. Rajab PM, Thiruvenkatasamy K (2016) Shoreline change studies due to construction of breakwaters at Ariyankuppam river mouth in Puducherry—a union territory of India, south India. Indian J Sci Technol 9:45 21. Saravanan S, Chandrasekar N (2010) Potential littoral sediment transport along the coast of south eastern coast of India. Earth Sci Res 14:153–160

Nondimensional Methods to Classify the Tidal Inlets Along the Karnataka Coastline, West Coast of India N. Amaranatha Reddy, Vikas Mendi, Jaya Kumar Seelam and Subba Rao

Abstract This classification of tidal inlets is essential to maintain the stability of the inlets as well as to study the changing patterns of tidal inlets in India. Tidal inlets around the world have been classified as either wave-dominated or tide-dominated or river-dominated, since the 1970s. Tidal inlet classification for 471 inlets along the coast of India was carried out by Vikas M et al., based on wave and tide information. But only 30 inlets were considered for river-based classification due to lack of discharge information. In order to consider the river-based classification, the river flood discharge was estimated using Synthetic Unit Hydrograph (SUH) methods for Karnataka coast. In this study, 29 tidal inlets along the coast of Karnataka are selected for the classification based on river discharge. The classification hasbeen Q tide versus √ f 5 and done in two aspects; without considering wave period i.e. √ gH5 gH   Qf Qtide by considering wave period i.e. g1.75 H1.25 T2.5 versus g1.75 H1.25 T2.5 where Qtide is peak tidal discharge, Qf is river discharge and H is wave height. The results obtained are validated with hydrological and geomorphological classifications and the dominant forces over the dynamics of the inlets are determined. Q

Keywords Tidal inlets · Nondimensional classification · Flood discharge

N. Amaranatha Reddy (B) · V. Mendi · S. Rao National Institute of Technology Karnataka, Surathkal, Mangalore 575025, Karnataka, India e-mail: [email protected]; [email protected] V. Mendi e-mail: [email protected] S. Rao e-mail: [email protected] N. Amaranatha Reddy Madanapalle Institute of Technology and Science, Madanapalle, India J. K. Seelam CSIR-National Institute of Oceanography, Dona Paula, Goa, India © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_13

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1 Introduction All over the world, there exists a large variety of coastal systems which vary in many aspects. Particularly, the Indian coast comprises of headlands, rocky shores, sandy spits, barrier beaches, open beaches, embankments, estuaries, inlets, bays, and marshy lands. Oscillation of the shoreline along the Indian coast is seasonal. The above said features of coastal systems are shaped over decades by various activities viz. movement of tectonic plates, sediment transport and forcing functions like tide, wave and river discharge. Among various features, the present study considered only the coastal tidal inlet systems, which is defined as an opening along the shoreline that provides a linkage between the open sea and hinterland water body. The Indian coastline is having different coastal inlet systems which are basically formed by means of three major forcing functions viz. tide, waves and river discharge. The west coast of India experiences high wave activity during the southwest monsoon with relatively calm sea conditions prevailing during the rest of the year. Based on different aspects, numerous methods have been evolved to classify the coastal inlet systems. The classification methods introduced by Burgess et al. [1] records over 25 methods covering variety of aspects to classify coastal systems in both Great Lakes and marine coastal states in the USA. Duck and Silva [4] reviewed the coastal lagoons around the world under the hydromorphological impacts of historical, contemporary and proposed engineering activities. Coastal inlets systems classified based on land–sea interface which would be more important from the perception of geologists and geomorphologists [2] (Davies 1980). Based on the shapes of tidal inlets de Vriend et al. [3] introduced the classification by taking consideration of three significant forcing functions viz. waves, tide and river flow as inlet morphology drivers. Kierfve [8] and Isla [7] applied hydromorphological conditions and geomorphological features for classification of USA coasts based on the isolation level of coastal lagoons restricted by the coastal barrier. Roy et al. [13] proposed a classification scheme by adding biological criteria to classify estuaries within New South Wales (NSW), Australia. In his studies, the estuaries have been summarized into five groups viz. (i) Bays, (ii) Tide-Dominated Estuaries (TDE), (iii) Wave-Dominated Estuaries (WDE), (iv) Intermittent Estuaries (IE) and (v) Freshwater bodies with different stages of sediment infilling as (a) youthful, (b) intermediate, (c) semi-mature and (d) mature. Unlike Roy et al. [13], Saintilan [14] classified the coastal systems giving more emphasis on geomorphological criteria than biological parameters. Heap et al. [6] proposed another method using the ratio of wave power to tide power at the estuary entrance and classified 780 coastal systems around the coast of Australia.

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Hydrodynamic classification introduced by Hayes [5] based on the only two main hydrodynamic forcing functions of waves and tide. Using hydromorphological aspects of twenty one coastal plain shorelines, Hayes [5] proposed a morphological classification based on the ratio of mean tidal range and mean annual significant wave height in form of graph distinguishing five regions of Wave-Dominated (WD), Mixed Energy-Wave-Dominated (ME-WD), Mixed Energy-Tide-Dominated (METD), Tide-Dominated- Low (TD-L) and Tide-Dominated-High (TE-H) along with a region for barrier formation. The decision of the coastal classification scheme to be followed for various coasts along worlds’ coastline depends on the needs of the researches for the betterment of society. In the present scenario, environmental sustainability is given more attention; the classification systems based on hydromorphological perspective has given prime importance [17]. In this study, dimensionless classification including three forcing functions which are obvious in the shaping of the inlet [17] are considered to classify 29 coastal tidal inlets along the Karnataka coastline by including the wave period in one case and excluding in the other.

2 Study Area Figure 1 shows the study area considered for proposed work. The coastline of Karnataka spreads over a length of 320 km along the three coastal districts viz. Dakshina Kannada, Udupi and Uttara Kannada and bounded between 11° 31 –18° 45 N and 74° 14 –78° 40 E. There are nearly about 14 rivers that drain into the Arabian Sea and most of them originate in the Western Ghats. Twenty nine tidal inlets are identified in the study region by discarding the inlets whose throat width at the entrance less than 5 m. The naming of the inlets have been done based on nearby landmarks at entrance of inlets that are observed in SoI topographic maps or high-resolution satellite images through Google Earth®. The names and locations of the inlets are given Table 1. Oceanographic climate of the study coastal region is dominated by three seasons, viz. southwest monsoon (June–September), northeast monsoon (October— January) and fair weather period (February–May). Generally, the tides along coast of Karnataka are semi-diurnal. The west coast of India experiences high wave activity during the southwest monsoon with relatively calm sea conditions prevailing during the rest of the year.

3 Methods and Methodology Tidal inlet classification is essential to demarcate the coastal inlet systems into various clusters and to study their characteristics over a period of time. Around the world, these inlets differ in various aspects viz. shape of inlet, dynamics, geology, and its functioning and hence tidal inlet classification systems gives us better knowledge to

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Fig. 1 Study area

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Table 1 Total flood discharge values (m3 /s/h) at considered inlet locations [10] Inlet no. Inlet name Inlet location Flood discharge (m3 /s/h) Longitude (E) Latitude (N) 1

Karwar

74° 09 31

14° 50 29

14080.45

13

41

14° 45 08

92.98

2

Kelaginakeri

74°

3

KantrivadaGudda

74° 15 51

14° 44 41

79.37

16

42

42

628.02

45

4

Belekeri

74°

5

Ankola

74° 17 02

14° 39 41

118.36

6

Belamber

74° 17 32

14° 38 49

66.52

7

Manjaguni

74°

21

36

8

Tadri (Tadadi Port)

28

14°

00

11053.84

74° 23 34

14° 31 11

3921.80

25

25

27

14°

95.77

9

Alvekodi 2

74°

10

Honavar

74° 28 11

14° 17 56

8441.24

11

Manki

74° 30 05

14° 11 20

38.48

12

Navayatkeri

74o

29

6

13

Alvekodi 1

74° 31 04

14° 01 36

987.99

14

Jali

74° 32 05

13° 59 05

20.23

33

58

01

162.95

16

59

14°

03

14°

65.89

15

Mavakurve

74°

16

Hadin

74° 35 08

13° 56 59

50.27

17

Gorta

74o 34 58

13° 55 26

29.48

36

55

20

255.29

25

13°

10

18

Alvegadde

74°

19

Paduvari

74° 37 27

13° 52 05

316.54

20

Koderi

74° 40 11

13° 47 38

277.62

21

Gangoli

74°

41

38

02

4344.34

22

Kundapura

74° 44 11

13° 27 00

15.54

41

43 45

13°

13° 13o

22

15

4370.94 1320.51

23

Badanidiyoor

74°

24

Malpe

74° 41 44

13° 20 50

Kaup

74°

46

01

13°

13

26

46

36

13°

06

42

87.84

25

10.76

26

Nadsal

74°

27

Hejamadi

74° 48 22

13° 04 31

1566.25

28

Gurpur and Netravathi

74° 51 49

12° 50 43”

12008.95

53

45

29

Kanwatheertha

74°

15

12°

38

164.95

understand their characteristics. Past literature show numerous tidal inlet classification systems based on various perspectives, however, it is a well-established fact that the tidal inlet systems experience three predominant forcings viz. tide, waves and discharge from river. Earlier classification methods available in the literature mainly focused on two different aspects such as hydrological and geomorphological. Recent classification by Vu [17] attempted the classification of tidal inlet systems in NSW,

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Australia, considering a hydraulic perspective. The present study considers nondimensional classification of tidal inlet systems in two aspects by taking an account for mean wave period and without mean wave period along with the main forcing parameters viz. peak tidal discharge, freshwater flow, and wave height.

3.1 Input Parameters Required for Classification The tidal range (R) is obtained by simulating the variations of tide for a duration of 15 days covering a neap and spring tide along the west coast of India using MIKE21 Flow Model (FM). The boundaries for the MIKE21 FM tidal model are taken from the global tidal constituents available through the MIKE21 tidal prediction toolbox. The significant wave heights are obtained along the Karnataka coastline for about a length of 320 km using MIKE21 Spectral Wave (SW) model simulated for a period of one year by giving global winds as input. The tidal ranges and average annual significant wave heights were extracted at 10 m water depths at corresponding tidal inlet locations. Lagoon or Bay area (Ab ) is calculated using satellite images for majority of the inlets. The resulting areas are verified with the help of MIKE21 and Google maps area calculator tool from Draft Logic. The tidal prism (P) is obtained by multiplying the basin area after deducting the volume of sandy shoals with tidal range. The peak or mean tidal discharge is calculated using the formula Q tide  Pπ/T in which P is tidal prism and T is tidal period. Flood discharge (Qf ) is the amount of surface runoff discharges into the ocean or sea from the lagoon/bay. The Water Resources Information System (India-WRIS) have installed the gauging stations to measure the river discharge. Most of the installed gauging stations are far away from the inlet locations and there is limited river discharge information along the Karnataka coastline. Hence, the flood discharge values are taken from Reddy et al. [11], where the total flood discharges values along the 29 tidal inlets of Karnataka were calculated based on traditional Synthetic Unit Hydrograph (SUH) methods like Snyder, Soil Conservation Service along with Central Water Commission SUH methods and probability distribution functions (pdfs) based SUHs like simplified two-parameter Gamma distribution method and hybrid model. Since the pdfs were satisfying the Unit Hydrograph criterion (i.e., area under is unity), for the present study flood discharge values are taken from simplified two-parameter Gamma distribution method and are given in Table 1.

3.2 Inlet Classification There are numerous methods to categorize coastal inlet systems in the literature. Keeping environmental sustainability in view, nowadays hydromorphological perspective related to ecological parameters has been given due importance in classifi-

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Table 2 Dimensionless method of coastal systems without wave period [17] No Criteria Type of dominance 1

Q tide √ < 75 5

Wave-dominated coast

2

Q tide √ > 75 5

Tide-dominated coast

3

√Q f

River-dominated coast

gH gH

gH5

≥2

cation coastal tidal inlets. The classification methods considered in the present study are explained in the following sections.

3.2.1

Nondimensional Classification Without Considering Mean Wave Period [17]

This nondimensional method of classification [17] is based on the relative strengths of the three major driving forces viz. tide, waves and discharge from river. Three terms that are considered are (i) Qf (yearly averaged river discharge in m3 /s); (ii)  5 g H (yearly averaged wave forcing in m3 /s) and (iii) Qtide (yearly averaged peak tidal discharge in m3 /s). These three parameters are compared with each other, came out with remarkable conclusion by dividing the coastal systems into three groups. They are tide-dominated coast and wave-dominated coast, and river-dominated coast. ˆ Q The dimensionless quantities √Q tide 5 and √ f 5 are presented in which tidal forcing gH

gH

is quantified with regard to peak tidal discharge and wave forcing represented with regard to sediment transport capacity. The criteria developed from her studies for classification are given in Table 2.

3.2.2

Nondimensional Classification by Considering Wave Period

The intercomparison of the waves and peak tidal discharge as inlet morphological ˆ drivers may be studied two aspects. The first one is √Q tide 5 , which compares peak gH

tidal discharge to the sediment transport capacity of the waves [9]. The second one Qˆ tide is gT taking the mean annual wave period (T) into consideration, which is crucial H2 parameter in relation to runup height [9] and the ability of waves in building of berms [15]. Vu [17] discussed the methodology of classification by including the wave period but not done the classification along the NSW, Australia. Therefore, this method is called as Modified Vu method. Modified Vu [17] method considered wave period along with the significant wave height in the nondimensional quantities ˆ √Q tide 5 and √Q f 5 by the runup scale which leads to new dimensionless quantities like gH

gH

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Table 3 Criteria for dimensionless classification method with wave period Qˆ tide

Qf

(g1.75 H 1.25 T 2.5 )

(g1.75 H 1.25 T 2.5 )

Type of dominance

0.0001 0.045

WD TD RD

Note WD (ICOLLs)—Wave-Dominated (Intermittently Closed and Opened lakes and Lagoons, WD—Wave-Dominated, TD—Tide-Dominated and RD—River-Dominated

ˆ

Q

Q tide f and g1.75 H 1.25 , respectively. The classification criteria for various T 2.5 ) (g1.75 H 1.25 T 2.5 ) ( types of dominance using Modified Vu [17] method is depicted in Table 3.

4 Results and Discussion It is observed that the nondimensional classification of tidal inlet systems introduced by Vu [17] with and without considering the mean wave period mostly matches with the geomorphological classification system. Mixed energy dominance in geomorphological classification may be because of either tide or waves. Twenty tidal inlets out of 29 fell under wave-dominated—Intermittently Closed and Opened Lakes and Lagoons (WD-ICOLLs) which are showing the same type of dominance for the geomorphological classification. These 20 inlet entrances are having seasonal closed or opened behavior at the inlet entrance since both forcings from tide and river discharge are not significant enough to maintain the inlet entrance open at all times. This opening and closure processes occur in monsoon and summer seasons. During the monsoon season, when there is an excessive river discharge from the watershed region, the seasonally closed inlet entrances will be overtopped and thereby creating an opening in the shoreline. Alternatively, in the summer season due to high wave activity or due to tidal currents which results in high coastal sediments obstructs the inlet entrance which eventually close the inlet entrances. Seven inlets namely Karwar, Manjaguni, Tadri, Honavar, Gangoli, Malpe, Gurpur and Netravathi showed the tide dominance for both nondimensional methods, whereas, the geomorphological classification indicates wave-dominated at two inlets viz. Honavar and Malpe. This may be because of the constraints or error in the estimation of the bay area which may bring changes in tidal prism values. The Hejamadi and Kundapura inlets are classified as river-dominated inlets under the consideration of wave period and as tide-dominated inlets if wave period is not taken into account. The same inlets are classified as tide-dominated inlet at Kundapura and wave-dominated inlet at Hejamadi by geomorphological classification. These discrepancies need to be further investigated through field measurements. The dimensionless classification methods used in this study show exact type of dominance in comparison with

Nondimensional Methods to Classify the Tidal Inlets …

181

Fig. 2 Classification of tidal inlets along Karnataka coastline using Vu [17] without wave period

geomorphological classification at 25 tidal inlets. From these studies, we conclude that the dimensionless methods used in the study perform well along the Karnataka coastline for the given forcings (Figs. 2, 3 and Table 4).

5 Conclusions Twenty-nine coastal tidal inlets are classified along the coastal Karnataka by consideration two nondimensional methods with and without wave period. The present study gives a better understanding of tidal inlet classification under three main forcing functions such as waves, tide, and freshwater flow. Both the methods used in the study gave sound evidence for inlets along the coastal Karnataka in comparison with geomorphological classification method (i.e. 25 out of 29 tidal inlets shown the same type of classification for all the three methods). However, further field studies are required to eliminate the discrepancies observed in the present study.

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Fig. 3 Classification of tidal inlets along Karnataka coastline using Vu [17] with wave period

Table 4 Classification of inlets based on the type of dominance Inlet no. Inlet name Geomorphological Nondimensional classification classification Without Considering wave [16] considering wave period period 1 2

Karwar Kelaginakeri

TD WD

TD WD (ICOLLs)

TD WD (ICOLLs)

3

Kantrivada Gudda

WD

WD (ICOLLs)

WD (ICOLLs)

4

Belekeri

ME

WD (ICOLLs)

WD (ICOLLs)

5

Ankola

WD

WD (ICOLLs)

WD (ICOLLs)

6

Belamber

WD

WD (ICOLLs)

WD (ICOLLs)

7

Manjaguni

TD

TD

TD

8

Tadri (Tadadi Port)

ME

TD

TD

9

Alvekodi 2

ME

WD (ICOLLs)

WD (ICOLLs)

10 11

Honavar Manki

WD ME

TD WD (ICOLLs)

TD WD (ICOLLs) (continued)

Nondimensional Methods to Classify the Tidal Inlets … Table 4 (continued) Inlet no. Inlet name

183

Geomorphological classification [16]

Nondimensional classification Without Considering wave considering wave period period

12

Navayatkeri

ME

WD (ICOLLs)

WD (ICOLLs)

13

Alvekodi 1

WD

WD (ICOLLs)

WD (ICOLLs)

14

Jali

ME

WD (ICOLLs)

WD (ICOLLs)

15

Mavakurve

WD

WD (ICOLLs)

WD (ICOLLs)

16

Hadin

WD

WD (ICOLLs)

WD (ICOLLs)

17

Gorta

ME

WD (ICOLLs)

WD (ICOLLs)

18

Alvegadde

ME

WD (ICOLLs)

WD (ICOLLs)

19

Paduvari

ME

WD (ICOLLs)

WD (ICOLLs)

20

Koderi

ME

WD (ICOLLs)

WD (ICOLLs)

21

Gangoli

TD

TD

TD

22

Kundapura

TD

TD

RD

23

Badanidiyoor

WD

WD (ICOLLs)

WD (ICOLLs)

24

Malpe

WD

TD

TD

25

Kaup

ME

WD (ICOLLs)

WD (ICOLLs)

26

Nadsal

WD

WD (ICOLLs)

WD (ICOLLs)

27

Hejamadi

WD

TD

RD

28

Gurpur and Netravathi Kanwatheertha

TD

TD

TD

WD

WD (ICOLLs)

WD (ICOLLs)

29

Note WD—Wave-Dominated, ME—Mixed Energy, TD—Tide-Dominated, WD (ICOLLs)—WaveDominated (Intermittently Closed and Opened Lakes and Lagoons), RD—River-Dominated

References 1. Burgess R et al (2004) Classification framework for coastal systems 600/R-04/061. Office of Research and Development, US EPA, p 66 2. Carter RWG (1989) Coastal environments: an introduction to the physical ecological and cultural systems of coastlines. Academic Press, London, p 617 3. de Vriend HJ, Dronkers J, Stive MJF, van Dongeren A, Wang ZB (1999) Coastal inlets and tidal basins. Lecture Notes, TU Delft, Delft 4. Duck RW, da Silva JF (2012) Coastal lagoons and their evolution: a hydromorphological perspective. Estuar Coast Shelf Sci 110:2–14 5. Hayes MO (1979) Barrier island morphology as a function of tidal and wave regime. In: Leatherman SP (ed) Barrier islands from the Gulf of St. Lawrence to the Gulf of Mexico. Academic Press, New York 6. Heap A et al (2001) Australian estuaries & coastal waterways: a geoscience perspective for improved and integrated resource management. Report to the national land and water resources audit, theme 7: ecosystem health. Australian Geological Survey Organisation, p 188 7. Isla FI (1995) Coastal lagoons. In: Periloo GME (ed) Geomorphology and sedimentology of estuaries. Elsevier, Amsterdam, pp 241–272

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8. Kjerfve B (1994) Coastal lagoon processes. Elsevier oceanography series, vol 60. Elsevier, Amsterdam, p 576 9. Nielsen P (2009) Coastal and estuarine processes. Advanced series on ocean engineering. World Scientific, p 343 10. Reddy NA, Vikas M, Jaya Kumar S, Rao S (2015) Classification of tidal inlets along the central east coast of India. In: 8th international conference on Asian and Pacific coast (APAC-2015). Department of Ocean Engineering, IIT Madras, India 11. Reddy NA, Jaya Kumar S, Rao S, Nagaraj MK (2018) Flood estimation at ungauged catchments of western catchments of Karnataka, West coast of India. ISH J Hydraul Eng 12. Roper T et al (2011) Assessing the condition of estuaries and coastal lake ecosystems in NSW. Estuaries and coastal lakes. Office of Environment and Heritage, p 270 13. Roy PS et al (2001) Structure and function of south-east Australian estuaries. Estuar Coast Shelf Sci 53:351–384 14. Saintilan N (2004) Relationships between estuarine geomorphology, wetland extent and fish landings in New South Wales estuaries. Estuar Coast Shelf Sci 61:591–601 15. Takeda I, Sunamura T (1982) Formation and height of berms. Trans Japan Geomorphol Union 3:145–157 16. Vikas M (2015) Classification of tidal inlets along the Indian coast. M.Tech thesis, Department of Applied Mechanics and Hydraulics, NITK, Karnataka, India 17. Vu TTT (2013) Aspects of inlet geometry and dynamics. PhD thesis, The University of Queensland, Australia

Study of Dynamic Changes Through Geoinformatics Technique: A Case Study of Karwar Coast, West Coast of India Arunkumar Yadav , Basavanand M. Dodamani and G. S. Dwarakish

Abstract Shoreline is one of the geo-indicators of the coastal zone. Coastal zone is subjected to threats due to change in shoreline. Shoreline change leads to modification and causes for damages of properties, infrastructure around the shoreline region. These modifications, changes of land expands too many issues of the environment under the coastal zone. The present study was carried out by employing remote sensing and GIS techniques for the coastal regime of Karwar, India. LANDSAT8 remote sensing data was integrated with the GPS data collected during the field survey. The satellite data is processed and analyzed using ERDAS IMAGINE 2014 tool and ArcGIS 10.3 tool, respectively. High Water Line (HWL) is considered for the extraction of shoreline. The visual interpretation of satellite imageries is carried out to distinguish the HWL. Net Shoreline Movement (NSM) was evaluated by adopting Digital Shoreline Analysis System (DSAS) tool. Statistical methods such as Weighted Linear Regression (WLR), Linear Regression Rate (LRR) and End Point Rate (EPR) were used to estimate the changes of shoreline. The present study reveals that shorelines of Karwar Coast, Ravindranath Taghore beach experiences an average erosion rate is −4.61 m/year (EPR), −1.49 m/year (LRR), and 0.19 (WLR) and Devbagh beach experiences an average erosion rate is −9.74 m/year (EPR), −7.53 m/year (LRR), and −11.55 m/year (WLR). Keywords Shoreline change · Beach morphology · GPS · Remote sensing · GIS

1 Introduction The border between land and sea is termed as shoreline. Due to dynamic environmental conditions, it keeps on changing its profile and position regularly. Sea-level rise, waves, tides, winds, irregular storms, and the geomorphic processes of erosion A. Yadav (B) · B. M. Dodamani · G. S. Dwarakish Department of Applied Mechanics and Hydraulics, National Institute of Technology Karnataka, Surathkal, Mangalore 575025, Karnataka, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_14

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and accumulation are the primary causes for the shoreline change. Shoreline notifies the developments and demolitions which occurred currently along the shore [1]. Approximately 80% of the worldwide coasts are deteriorating with erosion rates ranging from 1 cm/year to 10 m/year [2]. It is essential to investigate and recognize the change in shoreline for various field studies such as advancement of beachfront barrier, seaside zone administration design. The examination of erosion and accretion is necessary for assessment of sediment budgets and prediction of dynamic coastal morphology using conceptual modeling [3]. For coastal zone monitoring, extraction of shoreline is the imperative for national development and environmental protection by [4]. Shoreline is shaped by various geographical protests, for example, association, sediment silt discharge of rivers and seas, distinctive climate, and ocean conditions, and additionally the general human social and financial exercises by [5]. The shoreline is one among the 27 features identified by the IGDC (International Geographic Data Committee) [6]. Historically, calculation of long-term and medium variation in shoreline change rates which holds good in shoreline change [7]. Finally, change analysis of shoreline and its approaches have ripened and firmly recognized within both investigation and forecasting/decision-making domains. Unusually, there are two approaches used to analyze changes in shoreline. In the beginning, topographic techniques of the survey to form two-dimensional field-based techniques which are surveyed frequently which includes, survey of casting perpendicular profiles along shore [8]. Furthermore, Remote Sensing (RS) techniques coupled with Geographical Information System (GIS) tool is used to analyze for number of different time series of positions of shoreline, such as short-term and long-term. Particularly, from satellite images which are less time-consuming and used for historical analysis [1, 2, 4, 5, 7, 9–22]. To get detailed and accurate data, a field-based survey is carried out to achieve a high-level control over frequency of sampling (i.e., before and after storm events) extending to limited spatial coverage. In various cases [2], to obtain enriched analyses of short-term change of shoreline, it is better to couple fieldwork data with RS and GIS tools. Mapping of change in shoreline was approached based on remote sensing techniques, which are user-friendly worldwide [2]. The shorelines are easily interpreted from GIS tool packages and can be manually digitized for further analysis. Combination of vector-based analysis such as point, line, polygon options and aerial photographs including topographic survey data, cadastral survey maps in addition to satellite imagery which gives benefits to lead further analysis. Shoreline change rates were calculated using digitized shorelines of different time or years were obtained from image sources and analytical methods which are broadly used which are common along continental coasts [7]. In recent times, for monitoring coastline changes were carried by adopting RS and freely available satellite images from Landsat which is appreciated and cost operative tool [10]. Shoreline boundary is dynamic in nature which changes in no time, therefore, previous dry/wet boundary or high tide lines (HTL) considered as a shoreline, which can be actually seen to identify factors [15]. Most of the times, in coarse resolution of satellite images, tidal variations are safely neglected. But to proceed with improved accuracy, starting with medium and later high accuracy satellite products should be used to demarcate the positions of shoreline for historical

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change detection, short-term change detection and also cost benefits also should be considered [9]. The present study considered shoreline from a period of 5 years (2013–2017), using only Landsat-8 satellite data and Global Positioning System (GPS) shoreline track for 2017 of the Karwar coast. GIS, ERDAS Imagine coupled with an extension of Arc GIS Digital Shoreline Analysis System (DSAS) were used [21]. Net Shoreline Movement (NSM) was evaluated by adopting Digital Shoreline Analysis System (DSAS) tool. Statistical methods such as Weighted Linear Regression (WLR), Linear Regression Rate (LRR), and End Point Rate (EPR) were used to estimate the changes of shoreline [19].

2 Study Area and Data Products Karwar coast has two beaches, namely, in the northside Devbagh beach and in the southside Ravindranath Taghore beach which is separated by Kali river estuary, along with the west by the Arabian Sea and embarked by the Western Ghats in the east. The study area exists between 14° 48 00 –14° 52 30 N latitude and 74° 06 00 –74° 08 00 E longitude as shown in Fig. 1. The Karwar coast located in the north of Uttara Kannada coast which displays exclusively in nature. The seashore in this partition is uneven and the coast consists of sand beaches and most of the places covered with rocks, like natural breakwater type in sea. The river Kali is one of the major rivers, which meets the ocean in Uttara Kannada seashore which enters into the Karwar estuary which is also called as Kali estuary. About 96 kms of width the inland shelf spreads off Karwar [23]. Temperature in water varies from 28.77 to 29.87 °C in different vicinities of Karwar Bay [18]. The coast is experienced and receiving seasonally monsoon winds which reverse in nature, average annual rainfall is around 4209 mm, in which approximately 80% is experienced from June to August. The temperature variation extends from 21 to 36 °C from December to April [11]. In the study area, the tides fall under mixed semidiurnal, which upheaves in the north [12]. Significant wave height up to 6 m and less than 1.5 m has been verified during the monsoon and remaining period, respectively, along the Indian west coast [13]. Geometrically corrected and ortho-rectified Landsat-8 satellite data for pre-monsoon from 2013 to 2017 is used for shoreline analysis of Devbagh and Ravindranath Taghore beach, Karwar. The details of the remote sensing satellite data utilized in the study are provided in Table 1.

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Fig. 1 Study area Table 1 Specifications of satellite data and GPS data adopted in the study Sl. no. Satellite and Acquired date Path/row sensor 01 02 03 04 05

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3 Methodology In this present study, the estimation of the shoreline change rates were adopted from several authors [24] which includes digitization and extraction of the shoreline position and database generation. It comprises of the following different stages

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Fig. 2 Flowchart of shoreline extraction and analysis

of data operation: (1) GPS data for May month 2017 and Landsat-8, Operational Land Imager (OLI) and Thermal Infrared Sensor (TIRS) obtained from the United States Geological Survey (USGS) website covering the period 2013–2017, sensors were ortho-rectified (2) shoreline digitization and extraction, and (3) computation of shoreline erosion and accretion rates by using Digital Shoreline Analysis System (DSAS) (Fig. 2).

3.1 Image Preprocessing The obtained GPS data was differentially corrected using source data from the Indian Institute of Science. The errors were eliminated and finally data was set to be 85% of error-free data. Later, the GPS data was defined into World Geodetic System 1984 and reprojected to Universal Transverse Marcadum. GPS data then loaded as shapeline in Arc GIS 10.3 version. To remove distortions associated to scale variation, tilt, and lens distortion and to combine the selected bands in Tiff format; Geometric correction and Layer stack were carried out using ERDAS Imagine 2014 tool [2]. Later, obtained image is projected to the real-world coordinate Universal Transverse Mercator (UTM) northern hemisphere N43° with reference to WGS 1984 datum. Using Arc GIS 10.3 tool shoreline was digitized from geo-rectified images.

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3.2 Extraction of Shoreline From the many features of the coastal zone, the subaerial beach is also considered as shoreline [5]. The high water line (HWL) is more suitable for selection of shoreline, which has a smaller horizontal displacement than the swash terminus (ST) [25]. HWL is the extent of wave variation in the run-up on the beach slope [14]. HWL approximated closely by the wet/dry line [2]. Therefore, GPS track was carried out on basis of wet/dry line and considered as HWL, made differential correction and generated as shapeline which supports in ArcGIS 10.3. Shorelines were digitized from the satellite imageries manually for different years in ArcGIS 10.3. The geo-information base was then made in ArcGIS programming from these vectors shorelines. This geodatabase was analyzed with an ArcGIS extension tool Digital Shoreline Analysis System (DSAS) developed by USGS. Consequently, the rate of shoreline movement and changes were calculated. In the present study, the DSAS tool was conceded in the following steps: (1) shoreline creation, (2) baseline preparation, (3) transect casting, and (4) calculation of shoreline change rate [21]. In recent times, the uncertainty related to the calculation of the End Point Rate (EPR) is consequently ascertained in the utilization of DSAS. The consequence of this calculation is quantified as assurance of the endpoint rate calculation (ECI) [21].

3.3 Calculation of Rates of Erosion and Accretion There are a few information investigation methods that can be utilized to figure shoreline erosion and accretion rates, [21]. Present examination, shoreline change positions are figured using four information investigation methods. The End Point Rate (EPR) is basically completed through partitioning the separation isolating the two shorelines in the quantity of time duration (Eq. (1)). This is the most common basic strategy to figure shoreline development rates, and it is generally utilized by various seaside specialists [7]. EPR  D1 − D2 /t1 − t0

(1)

where D1 and D2 : distance between the shoreline and baseline. t0 and t1 : the time period of the position of two shorelines. Linear Rate Regression (LRR) is the second technique utilized to computing erosion rates. This technique comprises to fit a minimum squares relapse line to different position of shoreline focusing a specific transect [21]. The rate of change in shoreline along each transect for the period (2013–2017) was figured by plotting the focuses. The shorelines are crossed by transects and establishing the linear regression equation given by [2] (Eq. (2)).

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(2)

where (Y) denotes the length of the space from baseline, in meters (2013), (X) duration (years), (m) represents the rate of change in shoreline and (c) represents Yintercept [2]. The Weighted Direct Relapse (WLR), is a weightage toward deciding a best-fit line through a certainty interim of 99.9% [21]. The weighted linear regression rate is calculated by plotting the positions of shoreline for time. The weight (w) is characterized as a component of uncertainty in the estimation of fluctuation (e) (Eq. (3)). W  1/e2

(3)

where e  shoreline uncertainty value. The Net Shoreline Development (NSM) is the separation (in meters) between the antiquated and new positions of the shoreline at each transect. It shows a separation, instead of rate [2]. The negative values in the estimation of EPR, LRR, WLR, and NSM demonstrates landward relocation of the shoreline whereas positive estimation describes the movement toward the ocean [19].

4 Results and Discussion 165 transect generated through DSAS tool for Devbagh beach and 180 transect for Ravindranath Taghore beach were arranged by perpendicular lines to the baseline at 30 m separating beside 9.5 kms length of Devbagh–Ravindranath Taghore. Kali estuary region was not selected which is separating both these beaches. The rate of change in shoreline has been computed utilizing DSAS an extension Arc GIS tool with two diverse statistical systems, for instance, LRR and EPR. The baseline is developed 250 m remove from most recent 2017 shoreline, i.e., from GPS information and aggregate 345 transects are produced with 30 m dividing along 9.5 kms stretch of study zone. A transect map for Devbagh beach and Ravindranath Taghore beach shown in Fig. 3, shoreline change rate in terms of LRR and EPR m/year. The map explains about high erosion and accretion. Ravindranath Taghore beach considered shoreline change rate (EPR) and (LRR) from 2013 to 2017. At transect 126 maximum shoreline accretions of 15.29 m/year (EPR), 15.01 m/year (LRR) and 22.93 m/year (WLR). At transect 74 maximum shoreline erosion of −16.97 m/year (EPR) at transect 103, −11.37 m/year (LRR) and at transect 1, −25.72 m/year (WLR). Average erosion rate is −4.61 m/year (EPR), −1.49 m/year (LRR) and 0.19 (WLR). From the above results, it is evident that the shoreline change rate differs according to the different approaches (Figs. 4 and 5).

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Fig. 3 Transect map of Ravindranath Taghore beach

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Fig. 4 Graph shows shoreline change rate of Ravindranath Taghore beach

Fig. 5 Graph shows net shoreline movement of Ravindranath Taghore beach

Net shoreline movement from transect 1 to 10 and 25 to 10 show major movement toward landward movements. Transect from 110 to 160 shows toward seawards movements (Fig. 6).

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Fig. 6 Transect map of Devbagh beach

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Fig. 7 Graph shows shoreline change rate of Devbagh beach

Devbagh beach, considered shoreline change rate (EPR) and (LRR) from 2013 to 2017. At transect 25 maximum shoreline accretion of 10.16 m/year (EPR), 20.4 m/year (LRR) and at transect 24, 8.12 m/year (WLR) maximum shoreline erosion of −21.66 m/year (EPR), −20.09 m/year (LRR) and −23.77 m/year (WLR). Average erosion rate is −9.74 m/year (EPR), −7.53 m/year (LRR) and −11.55 m/year (WLR) (Fig. 7). Net shoreline movement from transect 1 to 22 and 28 to 165 shows major movement toward landward movements. Transect from 23 to 27 shows toward seawards movements.

5 Conclusion Remote sensing and geospatial techniques coupled with DSAS an extension Arc GIS tool will be useful for short-term shoreline analysis, including seasonal wise monitoring. It delivers a complete sight of erosion and accretion rate of the shore areas which is economically important. This study focuses on particularly Landsat-8 (OLI/TIRS) satellite data and latest GPS data for shoreline extraction. Overall there is a different change rate of shoreline found between two shorelines. Devbagh beach experiences average shoreline change rate of average erosion rate is −11.55 m/year (EPR), −7.53 m/year (LRR) and −9.74 m/year (WLR). Similarly, Ravindranath Taghore beach experiences average shoreline change rate of average erosion rate is −4.61 m/year (EPR) and −1.49 m/year (LRR) and 0.19 m/year (WLR). The shoreline

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Fig. 8 Graph shows net shoreline movement of Ravindranath Taghore beach

analysis acquired from this study can be helpful for the stakeholders, policymakers, coastal managers, scientists, and coastal livelihoods. With the increasing gathering of high-resolution satellite-based sensors and Digital Elevation Modules (DEM), the complex shoreline dynamics can resolve with better accuracy. Additionally, the study is required to determine the better results with regular occasions such as storms, regular variety in season and nearby ocean level rise (Fig. 8).

References 1. Salghuna NN, Bharathvaj SA (2015) Shoreline change analysis for northern part of the coromandel coast. Aquat Proc 4:317–324. https://doi.org/10.1016/j.aqpro.2015.02.043 2. Kermani S, Boutiba M, Guendouz M, Guettouche MS, Khelfani D (2016) Detection and analysis of shoreline changes using geospatial tools and automatic computation: case of jijelian sandy coast (East Algeria). Ocean Coast Manag 132:46–58. https://doi.org/10.1016/j.ocecoaman. 2016.08.010 3. Aedla R, Dwarakish GS, Reddy DV (2015) Automatic shoreline detection and change detection analysis of netravati-gurpurRivermouth using histogram equalization and adaptive thresholding techniques. Aquat Proc 4:563–570. https://doi.org/10.1016/j.aqpro.2015.02.073 4. Rasuly A, Naghdifar R, Rasoli M (2010) Monitoring of Caspian sea coastline changes using object-oriented techniques. Proc Environ Sci 2:416–426. https://doi.org/10.1016/j.proenv. 2010.10.046 5. Boak EH, Turner IL (2005) Shoreline definition and detection: a review. J Coast Res 21(4):688–703. https://doi.org/10.2112/03-0071.1 6. Berger AR (1996) The geoindicator concept and its application: an introduction. Geoindicators: assessing rapid environmental changes in earth systems, vol 1. AA Balkema, Rotterdam, p 14

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7. Ford M (2013) Shoreline changes interpreted from multi-temporal aerial photographs and high resolution satellite images: Wotje Atoll, Marshall Islands. Remote Sens Environ 135:130–140. https://doi.org/10.1016/j.rse.2013.03.027 8. Ruggiero P, Kaminsky GM, Gelfenbaum G, Voigt B (2005) Seasonal to interannual morphodynamics along a high-energy dissipative littoral cell. J Coast Res 21(3):553–578. http://www. jstor.org/stable/4299442 9. Dolan R, Fenster MS, Holme SJ (1991) Temporal analysis of shoreline recession and accretion. J Coast Res 7(3):723–744. http://www.jstor.org/stable/4297888 10. Gens R (2010) Remote sensing of coastlines: detection, extraction and monitoring. Int J Remote Sens 31(7):1819–1836. https://doi.org/10.1080/01431160902926673 11. Hegde AV, Akshaya BJ (2015) Shoreline transformation study of Karnataka Coast: geospatial approach. Aquat Proc 4:151–156. https://doi.org/10.1016/j.aqpro.2015.02.021 12. Kumar A, Jayappa KS (2009) Long and short-term shoreline changes along Mangalore coast, India. Int J Environ Res 3(2):177–188. https://doi.org/10.22059/ijer.2009.46 13. Kumar V, Pathak K, Pednekar P, Raju N, Gowthaman R (2006) Coastal processes along the Indian coastline. Curr Sci 91(4):530–536. http://www.jstor.org/stable/24093957 14. Lanfelder LJ, Stafford DB, Amein M (1970) Coastal Erosion in North Carolina. J Waterw Harb Coast Eng Div 96(2):531–545 15. Liu Y, Huang H, Qiu Z, Fan J (2013) Detecting coastline change from satellite images based on beach slope estimation in a tidal flat. Int J Appl Earth Obs Geoinf 23:165–176. https://doi. org/10.1016/j.jag.2012.12.005 16. Crowell M, Leatherman S, Buckley MK (1991) Historical shoreline change: error analysis and mapping accuracy. J Coast Res 7(3):839–852. http://www.jstor.org/stable/4297899 17. Moussaid J, Fora AA, Zourarah B, Maanan M, Maanan M (2015) Using automatic computation to analyze the rate of shoreline change on the Kenitra coast, Morocco. Ocean Eng 102:71–77. https://doi.org/10.1016/j.oceaneng.2015.04.044 18. Naik UG (1986) Studies on the plankton and productivity of Kali estuary and inshore waters of Karwar. http://hdl.handle.net/10603/93969 19. Natesan U, Parthasarathy A, Vishnunath R, Kumar GEJ, Ferrer VA (2015) Monitoring longterm shoreline changes along Tamil Nadu, India using geospatial techniques. Aquat Proc 4:325–332. https://doi.org/10.1016/j.aqpro.2015.02.044 20. Thieler ER, Danforth WW (1994) Historical shoreline mapping (II): application of the digital shoreline mapping and analysis systems (DSMS/DSAS) to shoreline change mapping in Puerto Rico. J Coast Res 10(3):600–620. http://pubs.er.usgs.gov/publication/70135638 21. Thieler ER, Himmelstoss EA, Zichichi JL, Ergul A (2009) The Digital Shorelne Analysis System (DSAS) version 4.0-an ArcGIS extension for calculating shoreline change (No. 2008–1278). US Geological Survey 22. Thom BG, Hall W (1991) Behaviour of beach profiles during accretion and erosion dominated periods. Earth Surf Proc Land 16(2):113–127. https://doi.org/10.1002/esp.3290160203 23. Bhat UG, Neelakantan B, Kusuma N, Naik UG (1988) Environmental characteristics of the marine and estuarine habitats of Karwar: an overview. J Indian Fish Assoc 18:401–412. aquaticcommons.org/id/eprint/15991 24. Ayadi K, Boutiba M, Sabatier F, Guettouche MS (2016) Detection and analysis of historical variations in the shoreline, using digital aerial photos, satellite images, and topographic surveys DGPS: case of the Bejaia bay (East Algeria). Arab J Geosci 9(1):26. https://doi.org/10.1007/ s12517-015-2043-9 25. Dolan R, Hayden B, Heywood J (1978) A new photogrammetric method for determining shoreline erosion. Coast Eng 2:21–39. https://doi.org/10.1016/0378-3839(78)90003-0

An Experimental Study on Surface Wave Modulation Due to Viscoelastic Bottom Dharma Sree, Adrian Wing-Keung Law and Hayley H. Shen

Abstract In the present study, we developed viscoelastic bottom layers of required rheological properties in the laboratory using a mixture of a polymer, polydimethylsiloxane with glycerol. The properties of the viscoelastic layers were quantified using oscillatory shear tests in a rheometer. Wave flume experiments with different viscoelastic bottom layers were then conducted under shallow water conditions. The synchronized time series data at seven locations along the direction of wave propagation were obtained using ultrasound sensors, which were used to determine the attenuation rate due to the presence of the bottom boundary. The results of the analysis showed that the attenuation rate of waves change with the variation of rheological property of bottom boundary, with the softer bottom attenuating the waves more significantly. Keywords Viscoelastic bottom · Attenuation · Shallow water

1 Introduction Increasing surface temperature and sea-level rise associated with global warming can reshape the shorelines around the globe by altering the climate-driven wave parameters including the wave height, wave period and wave direction [1]. A large portion of the muddy Indian coastline which is devoid of vegetation [2] can be D. Sree · A. W.-K. Law (B) · H. H. Shen Environmental Process Modelling Centre (EPMC), Nanyang Environment and Water Research Institute (NEWRI), Nanyang Technological University, 1 CleanTech Loop, CleanTech One, #06-08, 637141, Singapore e-mail: [email protected] D. Sree · A. W.-K. Law School of Civil and Environmental Engineering, Nanyang Technological University, 50 Nanyang Avenue 639798, Singapore H. H. Shen 132 Rowley Laboratories Civil and Environmental Engineering, Clarkson University, Potsdam, NY, USA © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_15

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susceptible to the changes in the direct wave action. This demands the need for a better understanding of the interaction of surface waves with the erodible seabed, including the muddy bottom. Several theories have been developed with various approximations made for the soft mud bottom. A two-layer viscous model with inviscid water above viscid bottom mud layer was developed by Gade [3] for shallow water conditions. This two-layer viscous model was subsequently modified for shallow and intermediate waters by Dalrymple and Liu [4], with the verification effort using kerosene over sugar solution [3]. The elastic model for mud by Mallard and Dalrymple [5] assumed mud as an infinitely deep elastic bottom layer underlying water of finite depth. This model was later improved by Dawson [6] with the inclusion of soil inertia for bottom layer. Recent work on the wave interaction with a bottom elastic plate was performed by Mohapatra and Sahoo [7], assuming the bottom layer as thin Euler Bernoulli beam. Muds with high sediment concentrations exhibit both viscous and elastic properties [8], and the energy dissipation thus needs to be included in coastal wave modelling. A generalized viscoelastic model [9–11] was subsequently proposed, which considered both properties. The linear viscoelastic model includes Voigt model and Maxwell model. The material testing of Kaolinite and mud in the laboratory by Maa [8] showed that Voigt model was suitable for soft mud. However, a substantial error was evident between the inversely calculated rheological properties from the experimental results and actual rheometric measurements by Soltanpour and Samsami [12] for multilayered viscoelastic models. The discrepancy drives the need for more detailed experimental studies for the verification of theoretical models and to identify possible missing factors. In other words, laboratory experiments need to be performed under controlled environment with similar viscoelastic conditions as in the theory. To the authors’ knowledge, wave interaction experiments with a real homogeneous viscoelastic bottom have not been done so far. In this paper, we will describe a laboratory study using a precisely controlled real viscoelastic bottom to quantify its influence on the modification of surface waves. The objective is to obtain measurement to verify the related theories in the future. Noted that the scaling of the laboratory parameters with respect to specific field conditions is not considered.

2 Material Preparation and Experimental Setup The 2.0 m long viscoelastic bottom boundary above the raised platform was made of glycerol-doped Polydimethylsiloxane (PDMS). PDMS was commercially available as Sylgard 184 Silicone Elastomer kit, consisted of a silicone oil base and curing agent/crosslinker. The specific gravity for PDMS was 1.02. Glycerol was added to increase the specific gravity of the bottom layer. The preparation procedures included the mixing of the three components (base, curing agent and glycerol) in required proportions, followed by degassing and curing. The fraction of glycerol added was

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M

calculated as m g (%)  Mg +Mbg+MC A ×100, where Mg is the mass of glycerol, Mb is the mass of base and MC A is the mass of curing agent. Similarly, the percentage of curing CA ×100. For the present study, m g  10% agent was calculated as, m C A (%)  MbM+M CA while two fractions of curing agent were used (m C A  1.5 and 2.0%) to alter the properties of the bottom layer. The curing period for m C A  1.5% was 32 days and that for m C A  2.0 was 18 days, which was determined using rheological tests. The rheological properties of the viscoelastic bottom were determined using small amplitude oscillatory shear tests in a rheometer (Anton Paar, MCR 302, Germany). Rheometry testing included two parts: (a) determination of linear viscoelastic regime (LVR) using frequency sweep analysis and (b) measurement of dynamic modulus of the material for the required frequency range within LVR. The dynamic modulus comprises of storage modulus (G  ) and loss modulus (G  ), which represents the elasticity and viscosity of the material, respectively. Figure 1 shows the variation of G  and G  with rotational frequency of rheometer (ω). Three samples were tested for each m C A to check the repeatability. The stability of the material property was ensured by conducting the tests within two weeks after the curing period. The G  and G  values were obtained by equating the wave frequency (σ ) to the rotational frequency of rheometer. Within the required range of frequency, G  was always greater than G  , with the dependence of G  on ω lesser compared to G  . Both G  and G  increased with m C A , and the rate of increase of G  was relatively larger than G  . The ratio G  /G  decreased with increase in m C A . The laboratory experiments were conducted in a wave flume (8.0 m long and 0.3 m wide), equipped with a piston-type wave generator, at the Environmental Process Modelling Centre (EPMC) Laboratory of Nanyang Environment and Water Resources Institute (NEWRI), Singapore. The wave flume was made of tempered transparent glass panels and was filled with fresh water up to a height, d  26.5 × 10−2 m. The inclined mesh type beach (slope 1.0V:1.25H) was provided to dissipate the reflected wave energy. The shallow water region was created with a raised platform, consisted of 2.0 m long horizontal section with slopes at both ends (see Fig. 2). The slope near the leading edge was 1.0V:1.8H whereas that near the trailing edge was 1.0V:1.0H. The

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Fig. 2 Schematic diagram of experimental setup Table 1 Test conditions and attenuation coefficients T (s) ko a α (rad/m) m C A (%) 0.6 0.8 1.0

0.08 0.11 0.11

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1.5

2.0

0.28 ± 0.16 0.47 ± 0.22 0.39 ± 0.20

0.20 ± 0.13 0.37 ± 0.19 0.31 ± 0.18

0.14 ± 0.03 0.23 ± 0.06 0.19 ± 0.08

slopes enabled the gradual change of water depth from 26.5 × 10−2 to 8.0 × 10−2 m above the horizontal section of the platform. The 2.0 cm thick viscoelastic layer was laid over the horizontal section which then reduced the water depth to 6.0 × 10−2 m. In the present study, regular monochromatic waves were generated. The test conditions are provided in Table 1. The surface wave displacement along the platform was determined using seven ultrasound sensors (US 325, General Acoustics), statically calibrated with different water depths. The synchronized surface displacement data from the ultrasound sensors were obtained using a data acquisition system (NI 9215), and the digitized data was collected using LABVIEW. The first sensor US1 was positioned at 0.2 m from the leading edge of the viscoelastic bottom. All other sensors were kept at 0.2 m interval as shown in Fig. 2. The position of the sensors, except US1, were shifted by 0.1 m once all the experiments with the initial position were done. Thus, for each test condition, displacement data at 13 locations were obtained.

3 Data Analysis and Discussion The sampling rate of the ultrasound sensors was 50 Hz. It was increased to 200 Hz using the PCHIP function in MATLAB. Only the first three fully developed waves were considered in the analysis so that the results were free from beach refection. The

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t (s) Fig. 3 Surface wave displacement (US4) for different wave periods, for m C A  1.5%. The three fully developed waves considered are enclosed in the rectangle box, the repeatability of test was confirmed using three experiments of the same test conditions (light grey solid line, dark grey dashed line and black solid line)

repeatability of the wave experiments was verified by conducting each experiment three times, see Fig. 3. Figure 4 shows the spectral analysis of the surface water displacement at different locations along the shallow water region with viscoelastic boundary. It is clearly visible that with an increase in wave period, a second peak corresponding to twice the input frequency to the wave generator (σ  2π/T ) became significant. The surface profile for T  0.6 s was linear; with an increase in wave periods, the nonlinearity became obvious (Fig. 3). For constant T , the height of the dominant peak increased from m C A  1.5 to 2% and then further increased for the rigid bottom case. For each constant T and fixed boundary condition, the wave height decreased along the distance of sensors from the leading edge of the viscoelastic bottom.

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The findpeaks function in MATLAB was used to identify the value of peaks from the surface displacement data. The attenuation of waves along the viscoelastic bottom was calculated by fitting the variation of wave height with an exponential curve as shown in Fig. 5. The exponential fitting equation is given by Hx  Ho e−αx , where Hx is the wave height at x distance from the leading edge, α is the attenuation coefficient and Ho is the wave height at x  0. The attenuation coefficients obtained for the different cases are included in Table 1, which shows that the bottom boundary properties significantly influenced the decay of wave height. For all the wave periods considered, the cases with m C A  1.5% showed notably higher attenuation compared to m C A  2% and lower for the rigid bottom. The maximum wave attenuation was for T  0.8 s and minimum for T  0.6 s. The viscoelastic bottom thus led to the attenuation of wave height for shallow water cases, like soft mud [13].

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4 Conclusions An experimental study was conducted to analyze the attenuation of surface waves due to the presence of the viscoelastic bottom under shallow water conditions. A novel method was developed to prepare a viscoelastic bottom layer in the laboratory using a polymer, Polydimethylsiloxane doped with glycerol. The wave experiments showed that the non-linear effects increased with wave period. The material property of the viscoelastic bottom G  /G  was found to be directly proportional to attenuation rate for a particular wave period. Acknowledgements This work is supported by US Office of Naval Research Grant #N0001413-1-0294 and US Office of Naval Research Global Grant No: N62909-15-1-2069. The authors would like to thank Mr. Peh Zhisheng at the Nanyang Technological University for assisting in the experiments.

References 1. Hemer MA, Fan Y, Mori N, Semed A, Wang XL (2013) Projected changes in wave climate from a multi-model ensemble. Nat Clim Change 3(5):471 2. Baba M, Nayak SR (2002) Chapter fifteen muddy coasts of India. Proc Mar Sci 4:375–390 3. Gade HG (1958) Effects of a nonrigid impermeable bottom on plane surface waves in shallow water. J Mar Res 16(2):61–82 4. Dalrymple RA, Liu PL (1978) Waves over soft muds: a two-layer fluid model. J Phys Oceanogr 8(6):1121–1131 5. Mallard WW, Dalrymple RA (1977) Water waves propagating over a deformable bottom. In: Offshore technology conference. Offshore Technology Conference 6. Dawson TH (1978) Wave propagation over a deformable sea floor. Ocean Eng 5(4):227–234 7. Mohapatra SC, Sahoo T (2011) Surface gravity wave interaction with elastic bottom. Appl Ocean Res 33(1):31–40 8. Maa PY (1986) Erosion of soft muds by waves. Coastal & Oceanographic Engineering Department, University of Florida 9. Hsiao SV, Shemdin OH (1980) Interaction of ocean waves with a soft bottom. J Phys Oceanogr 10(4):605–610

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10. Macpherson H (1980) The attenuation of water waves over a non-rigid bed. J Fluid Mech 97(4):721–742 11. Piedra Cueva I (1993) On the response of a muddy bottom to surface water waves. J Hydraul Res 31(5):681–696 12. Soltanpour M, Samsami F (2011) A comparative study on the rheology and wave dissipation of kaolinite and natural Hendijan Coast mud, the Persian Gulf. Ocean Dyn 61(2–3):295–309 13. Mathew J, Baba M, Kurian NP (1995) Mudbanks of the southwest coast of India. I: wave characteristics. J Coast Res 168–178

Spectral AB Simulations for Coastal and Ocean Engineering Applications R. Kurnia, P. Turnip and E. van Groesen

Abstract For simulating phase-resolved waves in large coastal and oceanic areas, as well as in confined coastal areas and ports, efficient, stable and accurate Boussinesq type of equations for irrotational flows are much desired. Results can also be used as input for CFD calculations on smaller domains when viscous and vorticial effects need to be included. In this contribution, we present examples of recent results using the AB (Analytic Boussinesq) model that has been developed based on consistent modelling of the Hamiltonian formulation of free surface waves. The pseudo-spectral AB code with various order of nonlinearity can deal with breaking waves and with spatial inhomogeneities such as bathymetry and harbour walls with fully or partially reflecting walls and breakwaters. A separate Radar Module can reconstruct and predict phase-resolved waves from radar images, and a Ship Module can deal with fully coupled wave–ship–structure interactions. In this paper, we illustrate the performance of simulations for three application areas: wave tank experiments, incoming waves in a harbour with deep access channel, and extreme, freak waves in Draupner seas as introduced in van Groesen et al., OEME 2017. Keywords Hamiltonian Boussinesq wave modelling · Harbour waves Freak waves · Wavetank simulations · Analytic Boussinesq model

1 Introduction In this paper, we show the performance of the Analytic Boussinesq (AB) code that has been designed to be applicable for various ocean and coastal applications. The implementation is relatively straightforward, but the underlying modelling uses in an efficient way the most compact description of waves, which is the Hamiltonian R. Kurnia · P. Turnip · E. van Groesen (B) LabMath-Indonesia, Bandung, Indonesia e-mail: [email protected]; [email protected] R. Kurnia · E. van Groesen University of Twente, Enschede, The Netherlands © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_16

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formulation of Zakharov [1] and Broer [2]. They discovered that the water wave problem, i.e. the irrotational flow of a layer of incompressible fluid with a pressurefree surface, can be described as a Hamiltonian system. This is a generalization of systems with a finite degree of freedom in Classical Mechanics, to the infinite dimensional system for water waves. Using only the elevation η and the potential φ at the free surface, the total energy serves as the Hamiltonian. Then the generalization of the classical description is the compact formulation of the exact continuity (mass conservation) and the Bernoulli equation at the surface. The main challenge for practical applications is to express the kinetic energy explicitly in terms of the canonical variables η and φ. Any approximation of this energy will retain the conservation of the approximated total energy, which, when positive definite, also implies a stability property. These are two properties that in other Boussinesq equations that do not start with the Hamiltonian formulation may get lost, or may be difficult to prove, although any Boussinesq model will give the computational benefit of the dimension reduction. The AB equation is an example of a so-called higher-order spectral method, initiated in [3]. The kinetic energy is calculated using truncations of the nonlinear Airy profiles in which the total depth is used, which leads to the need to use Fourier integral operators. In Kurnia and van Groesen [4], approximations up to fifth order are given. Extensions include a breaking scenario, and various localization methods to deal with partially or fully reflective walls [5]. The performance of the wave code has been tested for nearly 100 different study cases for which theoretical results or measurements were available. Applications run from tsunami simulations, wave tank applications, run-up on shores, bores, to waves in harbours with an access channel and freak waves in the North Sea. In recent times, we developed a radar module with which phase-resolved waves can be reconstructed and predicted some 1–2 min in advance, using radar images of standard ship X-band radars. For high waves and waves above bathymetry, the AB software is used. A fully dynamic, Hamiltonian, implementation for coupled wave— ship interactions is in development, for ship–ship and ship-structure interactions. In Sect. 2 a short description of the AB model is given, followed by an illustration of three-wave study cases. Discussion and conclusions finish the paper.

2 AB Model and Implementation In this section, we briefly describe the governing equation of the AB model and some aspects of the numerical implementation.

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2.1 Hamiltonian Structure The basic dynamics is described in the canonical variables η, the surface elevation, and φ, the surface potential, as ∂t η  δφ H (φ, η) and ∂t φ  −δη H (φ, η) + S The first equation is the continuity equation, and the second one the momentum equation. Here S is a collection of additional source terms for breaking and wave influxing and absorption described in the next subsections. For S  0 the equations are Hamilton equations. The notation δφ H and δη H denotes the variational derivatives with respect to the canonical variables of the Hamiltonian H . This is the total energy, sum of potential and kinetic energy K , written for notational convenience for one horizontal direction as H (φ, η)  1/2 ∫ gη2 d x + K (φ, η). The kinetic energy, the integral over the fluid domain of half the squared velocity, has to be considered as functional of η and of the surface potential of the internal irrotational fluid, which can only be achieved in an approximate way. In the AB model, this is explicitly done for equations up to fifth order [4]. Using such approximations, the fact that the dynamics is only for variables in the horizontal directions, without the need to solve the interior flow, makes these equations to be of Boussinesq type. The Hamiltonian structure guarantees that the total energy is conserved, and using positive definite approximations an inherent stability is achieved.

2.2 Breaking In many practical cases, one has to deal with breaking waves. In the AB equations, breaking is modelled as a sink term in the momentum equation that reduces the energy while leaving the horizontal momentum constant. For the energy dissipation, a variant of Kennedy’s eddy-viscosity model [6] is used, extended [4] to be applicable for exact dispersion. For the initiation, a kinematic breaking criterion is used, the quotient of fluid particle velocity in a crest and the crest speed. Values for this quotient are in the interval (0.7, 1) depending somewhat on the type of waves, but a deterministic method to determine this value is not yet available.

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2.3 Wave Generation and Boundary Damping Zones Most often, waves are generated by influx from a point or from a line; this influx method uses a source in the momentum equation that is related to the desired elevation at each position multiplied by a suitable directed acceleration [7]. Waves can also be generated from specified initial field values at an initial time over the entire simulation domain. To compensate for outflow in the simulation domain, in Sect. 3.3 we use data-assimilated influx, for which repeatedly known field data in a subdomain (instead of from a line) are merged with waves from an ongoing simulation in the complementary remaining domain [8]. Waves propagating towards outflow boundaries of the simulation domain are damped in small damping zones to prevent artificial reflection.

2.4 Spectral Implementation Spectral implementations are known to be very efficient and relatively simple to implement for linear equations if spatial inhomogeneities are absent. Nonlinear terms require generalizations to spatially dependent Fourier integral operators. Slowly varying spatial changes can be dealt with in quasi-homogeneous ways, but for nonlinear terms, and when walls or partially reflecting breakwaters are present, sharp transitions may lead to Gibbs’ phenomena. These problems have been overcome in the Fourier integral operators which may include step functions; retaining the (skew-) symmetry properties of the operators in the Hamiltonian is then of most importance to get the correct operators in the dynamic equations, see [4, 5].

3 Illustration of Wave Simulations In this section, we illustrate the performance of the AB model outlined above for three different coastal and engineering applications.

3.1 Wave Tank Simulations Most experiments in wave tanks aim to test ship behaviour in well-controlled circumstances. Then accurate generation of the desired waves is needed to obtain the correct positioning of all nonlinearly interacting wave phases and amplitudes at the position of the ship. This is illustrated here for an experiment executed at the wave tank of the Technical University of Delft [9, 10]. The tank is 142 m long, 4.22 m wide with water level of 2.13 m. Generated at one side by a single piston-type flap, the waves

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Fig. 1 Comparison of wave elevations (a) and the corresponding spectra (b) at wave probes W1–W6 between a-priori simulation (red, dashed line) and measurement (blue, solid line)

are absorbed at the other side at an artificial beach. Wave elevation measurements are located at W1  10.31 m, W2  40.57 m, W3  60.83 m, W4  65.57 m, W5  70.31 m and W6  100.57 m distance from the wave maker. By way of example, an experimental result, identified as TUD1403Foc6, is investigated here to show the quality of the generation in the tank of an a priori given (simulated) wave field in the basin, followed by an a posteriori reconstruction of the actually generated waves using the elevation at a first measurement point as influx for a simulation. The case to be considered is a focussing breaking wave group with peak period T p  1.89 s, peak wavelength λ p  5.52 m and focused at position W4. Figure 1 shows (red, dashed line) the simulation result of a priori designed wave elevations and the corresponding spectra at the measurement positions and (blue, solid line) the elevation and the corresponding spectra of the actually generated wave. The, rather small, discrepancies are mainly due to inaccuracies to translate the designed wave elevation at the wave maker position to the flap motions. This is confirmed by using as influx for a second simulation the actual laboratory elevation at the measurement position W1, and comparing the experimental result in Fig. 2 with the new simulations that show better agreement between the measurement and the simulation.

3.2 Harbour Simulations Simulations of harbour waves have to deal with the presence of walls, partially reflecting breakwaters, bathymetric changes and possibly bottom friction. A particularly difficult case for which accurate measurements have been performed at Deltares [11] is illustrated here. The lay-out and bathymetry of the harbour with access channel of

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Fig. 2 Same as in Fig. 1 but now for comparison between a-posteriori simulation (red, dashed line) and the measurement (blue, solid line)

21.3 m depth in real scale is shown in Fig. 3a; the outer boundaries at the east and west sides are hard walls. Waves with a designed spectrum with 20° spreading are influxed to the North at a depth of 21.3 m from the south, west of the access channel. Immediately after generation, the waves enter the shallower part of the western harbour over a slope 1:10 till 11 m depth. The sides of the access channel have slopes of 1:5. The directional spreading of the waves cause a variety of waves in the western part. Direction and wavelength of each individual wave determine, according to Snell’s law, whether it reflects at the access channel or will refract and cross the channel to end up in the shallower eastern part of the harbour. Measurements of wave conditions at positions indicated in Fig. 3a with resistant type (WHM) and directional type (GRSM) gauges are compared with simulations. In [12, 13] results for simulations with SWASH and MIKE BW show large deviations of significant wave height, with bias of −23.6% and −27.1% respectively and average deviations of 6.6% and 9.6% respectively for the case of nonbreaking waves (T01) with Hs  3 m, T p  9.43 s. Simulations with the AB code performed better for the same case, namely bias of −4.3% and deviation 2.8%. Also breaking waves, simulated only with AB, showed good results [14]. Here, we will show results for test case T02 with Hs  3.85 m, T p  11.90 s and an input spectrum as shown in Fig. 3b, c. Simulations are done using the AB2 code (accurate up to and including second order). The results of the significant wave height show a bias of 0.4% and an average deviation of 4.3%. Figure 4a shows the spatial distribution of the significant heights with the errors of simulation with respect to measurement, shown in percentage at the wave gauge positions. The relatively small errors indicate that the simulation is able to reconstruct the wave conditions in the wave-ward side of the channel, inside the channel and in the lee-ward side of the channel, with highest errors appearing at WHM01 and WHM07. From the Hs plot, it can be seen that most of the wave energy is concentrated along the wave-ward side

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Fig. 3 Shown are a the physical model setup of the harbour with the access channel making a complicated bathymetry as indicated by the colouring according to the colour bar, b the onedimensional input spectrum and c the two-dimensional wave spectrum for the generation of waves for test case T02 with contours lines enclosing various levels of energy

of the channel that leads to wave breaking in front of the breakwater, see Fig. 4b for a snapshot with wave breaking.

3.3 Freak Waves in Draupner Seas Scientific interest in high seas with abundant appearance of freak waves let us design and investigate ‘Draupner seas’ that resemble the sea at the moment that the wellknown Draupner wave of 18 m crest height was measured from the Draupner platform on 1 January 1995 in the north sea. Using new meteorological insights [15], the very wide spectrum has long wave lobes at the side as shown in Fig. 5 in which a rotation has been applied to have the main wave propagation from North to South. In [8] we simulated such seas in a large area, using data-assimilated influx of linear waves along a circular arc, and investigated details in a much smaller rectangular area of 15 km2 where nonlinear effects, including four-wave interaction, have

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Fig. 4 a Shown are the density plot of the spatially varying significant wave height. The error of the calculations compared to the measurement data are indicated at the wave gauge positions. b Snapshot of the elevation at t  1340 s; breaking waves are indicated by white foam (circles)

been developed. Here we show results of one of the in total 40 seas that have been simulated, identified as sea 17 m4. This sea has Hs  12.1 m and T p  15 s, and the largest crest height in the simulation of 200 waves for this sea was found to be a freak wave of 20 m crest height, more than 1.6 Hs . From statistical results [8], the probability of such a crest height in this sea is as high as 1.85 × 10−9 /m2 per period, i.e. can be expected on an area of 1 km2 almost once every 2 h. An impression of the sea elevation at the time of the freak event is shown in a neighbourhood of the freak wave in Fig. 6, and in the North–South direction at a transect through the freak position in Fig. 7. The time trace of the elevation at the freak position is given in Fig. 8.

4 Discussion and Conclusions The illustrations for various applications given in Sect. 3 show that accurate wave simulations are possible with the AB code. The a priori design of desired waves in a wave tank can be used to improve if needed, the software to steer the wave flap. The a posteriori simulation of generated waves can, for instance, be used to take the

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Fig. 5 The 2D spectrum as shown in [8] based on [16]

Fig. 6 Plot of the sea state at time 2048.7 s looking from south (bottom) to north over the whole observation area. The highest crest, with white cap, is positioned at x  350.7 m, y  456 m

quantitative results as input in a much smaller area for more precise CFD calculations on structures in that area. Simulation of waves in harbours are of profound importance

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Fig. 7 Plot of the elevation profile (red, solid line) at a cross-section along the y-axis at x  350.7 m at time of the freak wave event. The maximum and minimal temporal elevation is shown by the dashed line (black) and by dashed-dot line (cyan)

Fig. 8 Plot of the elevation time trace at the freak wave position, x  350.7 m, y  456 m

for the design of harbours and are a prerequisite for simulations of motions of moored ships in an existing harbour, which may also lead to more optimal performance for loading operations. Simulations of high waves in seas and oceans that include fourwave interactions are of interest to increase our knowledge about the various physical aspects that dominate the appearance and the 2D patterns of complicated wave crests. The wave software, under the name HAWASSI, see www.hawassi.labmathindonesia.org, is freely available after registration for university thesis work, and arrangements can be tailor-made for other purposes. A Radar Module is under development to predict waves, including freak waves as in Sect. 3.3, ahead of their appearance [16, 17]. A ship module for fully coupled wave–ship–structure interactions are being developed for future releases.

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Acknowledgements We are grateful for the use of data of measurements at TUD and Deltares in The Netherlands, and for information about the spectrum used for the Draupner seas from the European Centre for Medium-Range Weather Forecasts, Reading, UK. Riam Badriana contributed to simulations for the access channel. R.K. was partly funded by the Netherlands Organization for Scientific Research NWO, Technical Science Division STW Project 11642.

References 1. Zakharov VE (1968) Stability of periodic waves of finite amplitude on the surface of a deep fluid. J Appl Mech Tech Phys 9:190–194 2. Broer LJF (1974) On the Hamiltonian theory of surface waves. Appl Sci Res 29:430–446 3. Dommermuth DG, Yue DKP (1987) A high-order spectral method for the study of nonlinear gravity waves. J Fluid Mech 184:267 4. Kurnia R, van Groesen E (2014) High order Hamiltonian water wave models with wavebreaking mechanism. Coast Eng 93:55–70 5. Kurnia R, van Groesen E (2017) Localization for spatial-spectral implementations of 1D analytic Boussinesq equations. Wave Motion 72:113–132 6. Kennedy AB, Chen Q, Kirby JT, Dalrymple RA (2000) Boussinesq modeling of wave transformation, breaking, and runup. J Waterw Port Coast Ocean Eng 126:39–47 7. Lie SL, Adytia D, van Groesen E (2014) Embedded wave generation for dispersive surface wave models. Ocean Eng 80:73–83 8. Van Groesen E, Turnip P, Kurnia R (2017) High waves in Draupner seas, part 1: numerical simulations and characterization of the seas. J Ocean Eng Mar Energy 3:233–245 9. Kurnia R, van den Munckhov T, Poot CP, Naaijen P, Huijsmans RHM, van Groesen E Simulations for design and reconstruction of breaking waves in a wavetank. In: ASME 34th international conference on ocean, offshore and arctic engineering (OMAE). St. John’s, NL, Canada, ASME. OMAE2015–41633 10. Kurnia R, van Groesen E: Design of wave breaking experiments and A-Posteriori Simulations (Memorandum Department of Applied Mathematics; No. 2042), Enschede, University of Twente (2015) 11. Van der Werf IM, Hofland B (2012) Internal report. Deltares 12. Dusseljee D, Klopman G, van Vledder G, Riezebos HJ (2014) Impact of harbor navigation channels on waves: a numerical modelling guideline. Coast Eng Proc 1(34):58 13. Monteban D (2016) Numerical modelling of wave agitation in ports and access channels. Master Thesis, TU Delft 14. Kurnia R, Badriana M, van Groesen E (2018) Hamiltonian Boussinesq simulations for waves entering a harbour with access channel. J Waterw Port Coast Ocean Eng 144(2):04017047 15. Cavaleri L, Benetazzo A, Barbariol F, Bidlot J-R, Janssen PAEM (2017) The Draupner event: the large wave and the emerging view. Bull Am Meteor Soc 98:729–735 16. Wijaya AP, Naaijen P, Andonowati, van Groesen E (2015) Reconstruction and future prediction of the sea surface from radar observations. Ocean Eng 106:261–270 17. Van Groesen E, Wijaya AP (2017) High waves in Draupner seas, part 2: observation and prediction from synthetic radar images. J Ocean Eng Mar Energy 3:325–332

Nearshore Hydrodynamics Near an Open Coast Harbour at Gopalpur, Central East Coast of India U. K. Pradhan, P. Mishra, P. K. Mohanty, U. S. Panda and M. V. Ramana Murthy

Abstract Nearshore hydrodynamics of a particular region is largely controlled by the tide, current, local bathymetry and significantly modulated by the harbour and associated structures along the coastal front. Along the east coast of India, Gopalpur (19° 18 13 N; 84° 57 52 E), a minor seasonal harbour is under phases of renovation to a major all-weather port have ensued alarming changes along the coast. In view of the ongoing changes, water level and flow patterns along a 28 km stretch of the coastline for three different seasons viz., fair weather (December 2008), southwest (May 2009) and northeast (November 2009) monsoons were investigated. A numerical model was constructed to understand the spatiotemporal hydrodynamic regime for the region and future application from integrated coastal zone management perspectives. The study reveals that the tide is predominantly semidiurnal; M2 is the major tidal constituent contributing nearly half of the total tidal amplitude (0.48–0.55 m) followed by S2 constituent (0.20–0.25 m). The seasonal mean current speed was in the order of fair weather (20 cm/s) > southwest monsoon (19 cm/s) > northeast monsoon (15 cm/s). A two-dimensional hydrodynamic model was set-up, calibrated and the model performance was evaluated through various skill analyses. The correlation (r) for surface elevations were 0.96, 0.98 and 0.98 whereas 0.8, 0.96 and 0.75 in current during fair weather, SW and NE monsoons, respectively. The relative mean absolute error (RMAE) and index of agreement (IoAD) refer that the model works out to be ‘excellent’ for surface elevations and ‘very good’ for currents. Keywords Tide · Currents · Numerical modelling · East coast of India

U. K. Pradhan · P. Mishra (B) · U. S. Panda · M. V. Ramana Murthy National Centre for Coastal Research (NCCR), NIOT Campus, Pallikaranai, Chennai 600100, TN, India e-mail: [email protected] P. K. Mohanty Department of Marine Sciences, Berhampur University, Berhampur 760007, Odisha, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_17

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1 Introduction Tides and tidal currents are mainly produced by the interactive forces exerted on the ocean by the sun, and the moon and the tidal range is modulated as a function of geographical locations and substantially modified by the prevailing wind regime and wave set-up or set-down [1–3]. Exact prediction of tide and tidal currents are quite challenging even though in situ tidal records are available. Tidal predictions are made using the amplitude and phase of each tidal constituent, and these constituents are derived from harmonic analysis of each tidal frequency [4]. Typically, the tidal spectrum of an area consists of some constituents of varying amplitudes and phases that get distorted when they interfere with coastal structures and alter the local hydrodynamic regime. Thus, in coastal zone management and port developmental activities, navigations, the design of structures for coastal protection issues, analysis of tides and tidal currents and understanding nearshore hydrodynamics processes is crucial [5, 6]. Numerical models have proved to be reasonably useful to assess the impact of human interference on the natural environment and to address appropriate management solutions [7–10]. Along the Indian coast, various site-specific models are being used in the past to predict tidal regime and circulation for different applications, viz., assessment of coastal water quality, sediment transport, oil spill and pollutants trajectories [11–15]. The present investigation is a part of a shoreline management plan to assess the impact of a harbour development in an open coast high energetic environment along the east coast of India. The paper discusses the spatiotemporal variation of water levels, circulation patterns and examines the numerical model performance and its relevance for various coastal zone management issues of the coast.

2 Materials and Methods Gopalpur (19° 18 13 N; 84° 57 52 E), India is a straight coast with an orientation of 48° E to the true north, characterised by uninterrupted, sandy beaches, backed by continuous shore parallel dunes of 10–12 m high and few fishing hamlets (Fig. 1). The dunes are deposits of heavy-mineral concentrates, and an Indian Rare Earth (IRE) factory is mining and processing these sands. To cater the needs of IRE, a fair weather open coast port was constructed in 1987 by excavating the backshore basin and connecting through a 150 m channel supported by two piers of 400 m northern pier for dredgers operation (to keep the channel free from siltation) and 500 m southern pier for cargo handling. From 2007 to 2013, two perpendicular training walls of 370 m and 530 m length on north and south sides separated by 250 m, two breakwaters of 1735 m and 365 m length was constructed at 2.3 and 1 km, respectively, to the south of south training wall. These shore structures trapped the longshore sediment transport and resulted in significant changes along the coast, and

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Fig. 1 Map of the study area

in the south of the port, there was substantial accretion (~250 m) and severe erosion (~100 m) to the north of the port [16]. A groin field was constructed within 2.7 km from the north of the training wall to manage erosion on the northern side of the harbour. On 12 October 2013, a very severe cyclonic storm (VSCS), Phailin crossed near Gopalpur coast with a maximum sustained wind speed of nearly 215 km/h, devastated the south breakwater and about 650 m length got submerged and the northern groins partially washed out. The coast experiences inclement weather and tropical cyclones during southwest (SW) monsoon (May to September) and northeast (NE) monsoon (October–November) and relatively calm from December to April [17]. The average wind speed during summer, monsoon and winter are 14.8 km/h, 13.5 km/h and 10.3 km/h, respectively, and the average wind directions are S to SSW, SW and NE, respectively [16]. Waves predominately approach from the south (S) and southeast (SE). Based on the wave heights, the nearshore energetic regime is classified as very low (~0.53 m) for postmonsoon (DJF), low (~0.88 m) for northeast monsoon (ON), moderate (~1.06 m) for transition or pre-monsoon (MAM) and high (1.49 m) for southwest monsoon (JJAS) months [17]. The current direction was northeast (NE) or east–northeast (ENE) direction from January to June and southwest (SW) or south–southwest (SSW) from August to December. Reversal wind, high monsoonal wave action and high lit-

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toral drift interact with structures viz. groins and breakwaters resulted in significant changes in the coastal hydrodynamics. Due to lack of real-time information on water level and flow pattern for the region, field data were collected by deploying three Valeport pressure tide gauges and Andera RCM 9 current metres for 18 days at four locations representing three different seasons (based on wind pattern) (Fig. 1). The mooring locations were chosen within the 28 km length of the coastline based on the geographical settings, river inlet, coastal structures and model requirements. Standard protocols are followed for setting up the instruments, measurements, data retrieval and analysis; tide data were collected at a sampling frequency of 2 Hz, tide burst duration of 60 s, wave burst duration of 1024 s and wave measurement intervals of 30 min and data recording was maintained at 10 min intervals. The wind speed and direction measured at 3 h interval by Gopalpur-on-sea observatory, India Meteorological Department (IMD) is analysed. Depth (4–25 m) measurements at 500 m interval transects were made using a single beam Eco sounder (ODAM Hydrotrac, USA) interfacing with a DGPS and heave sensor. Tide gauge and current meter data are separated into tidal and non-tidal components, which is considered as an essential task in oceanic time series data analysis. The tidal signal is the sum of a finite set of sinusoids at specific frequencies related to astronomical parameters [18]. The measured water-level data were separated into tidal and non-tidal components, and tidal constituents are obtained using MIKEtool [19]. The observed depth-averaged current was split into zonal (cross-shore, u) and meridional (alongshore, v) components and tidal and non-tidal distribution. The absolute data sets were used for model calibration and validation. This tidal harmonic analysis provides individual amplitude and phase of the tidal constituents (Eq. 1). h  h0 +

n 

hi cos(ωt − ϕi )

(1)

i1

where h ho hi ϕi t

tidal level, amplitude at mean water level, amplitude of i-constituent, phase angle at i-constituent, time.

3 Numerical Modelling A 2-D depth-averaged, shallow water, finite difference numerical model, MIKE21HD capable of simulating flow is used [19]. The flow is computed in response to a variety of forcing parameters viz., bottom shear, wind shear, barometric pressure

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gradients, Coriolis force, momentum dispersion, sources and sinks, evaporation, flooding and drying and wave radiation stresses. The equation of continuity and depth-averaged momentum in both x and y directions are applied. The equation of continuity (mass conservation): ∂η ∂p ∂q + + S −e ∂t ∂x ∂y Momentum along x-direction:

⎡ 2 2 p   + qh2 ∂p ∂ p2 ∂  pq  ∂η ⎣ h2 + + + gh + g ∂t ∂x h ∂y h ∂x C2

p q

(2)

⎤ ⎦ − f V Vx − h ∂Pa − q − E  Six ρw ∂x

(3) Momentum along y-direction:

⎡ 2 p q2   2 + 2 ∂η ⎣ ∂q ∂  pq  ∂ q2 + gh + + + g h 2h ∂t ∂x h ∂y h ∂y C

p q

⎤ ⎦ − f V Vy − h ∂Pa − q − E  Siy ρw ∂y

(4) where p and q are the flux in the x and y directions, respectively, h the water depth, t the time, Pa the atmospheric pressure, ρ w the density of water, g the acceleration due to gravity, η the surface elevation, S the source magnitude, e the evaporation rate, C is defined as Chezy’s coefficient, f the wind friction factor, Ω the Coriolis force, S ix , S iy the source impulse in x and y directions and E the eddy viscosity coefficient, a time-varying function of the local gradient of the velocity, known as the Smagorinsky coefficient.

3.1 Model Set-up and Skill Analysis The model bathymetry was generated by integrating shoreline, sounding measurements, C-MAP charts and corrected with respect to local chart datum (1.1 m). The model domain (28 km × 8 km) is generated having 80 × 280 grids in x and y directions of uniform resolutions (100 m) with three open boundaries using finite difference technique. Tide and wind were used as forcing parameters; water-level data observed at 8 m depths on the north (RUS-8) and south (GPL-8) boundaries are assigned, and the offshore limit was set for free flux while observed wind recorded at Gopalpur IMD observatory is used as forcing. The model simulated for 15 days with a time step of 30 s following the Courant–Friedrich–Lewy (CFL) limit criteria. Several combinations of the calibration parameters were verified to achieve a better validation. The bed resistance coefficient (Chezy number 40 m1/2 s−1 ), the horizontal eddy viscosity (Smagorinsky formulation 0.5) and wind friction coefficient (fw  0.0016) were finalised. Flooding depth (the water depth at which the point will be

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re-entered into the calculation) and drying depth (minimum water depth allowed at a position before it is taken out of calculation) were assigned with 0.3 m and 0.2 m, respectively. The simulated water levels and current were validated with observed data at 8 m (PORT-8) and 18 m (PORT-18), respectively. Usually, the model performance is determined by the relative agreement between observed and simulated values; in the present study, five different skill tests were applied. The correlation coefficient (r) describes the degree of colinearity (Eq. 5), and their range is 1 to −1, is an index of the degree of leaner relationship between observed and predicted values. When r  1 or r  −1, a perfect positive and perfect negative relationship exists while for r  0 indicates no linear relationship [20]. rxy  Sxy /Sx Sy ,

(5)

where sx and sy are the sample standard deviations and sxy is the sample covariance. The relative mean absolute error (RMAE) gives the relative error between the observed and predicted values (Eq. 6) and extensively used to evaluate the numerical model performance [21]. RMAE 

||P| − |O|| , |P|

(6)

where P is simulated value, and O is observed value. The index of agreement (d) distinguished both additive and proportional differences in the observed and predicted means and variances (Eq. 7). The value of d closer to 1 is best and closer to 0 is bad. n |P − Oi |2 (7) d  1 −  i1    , n Pi − O ¯ 2 ¯  + O − O i1

where P is simulated value, and O is observed value. Refined index of agreement (RIoAd) is logically related to increases and decreases in mean absolute error (MAE); while the over-sensitivity of d to large errormagnitudes was reduced in d1, two aspects of d1 remain suboptimal. Its overall range (0 ≤ d1 ≤ 1) remained somewhat narrow to resolve adequately the great variety of ways that P can differ from O (Eq. 8). ⎧ n ⎪ i1 |pi −oi | ⎪ 1 , when ⎪ c ni1 |oi −¯o| ⎪ ⎪ ⎪ n ⎪ n ⎨ ¯| i1 |pi − oi | ≤ c i1 |oi − o dr  (8) n |o | c −¯ o ⎪ ⎪ n i1 i − 1 when ⎪ |p | −o ⎪ i i1 i ⎪ ⎪ ⎪ ⎩ n |p − o | > c n |o − o¯ | i i1 i i1 i

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The values of d are closer to 1 is best and closer to 0 is bad for model evaluation. The Nash–Sutcliffe efficiency (R) is a normalised statistic (Eq. 9), which determines the relative magnitudes of the residual variance compared to the observed data variance [22]. R in between 0 and 1 are viewed as acceptable levels of performance, whereas values < 0 indicates that the mean observed value is a better predictor than the simulated value, which indicates unacceptable performance.   n (oi − pi )2 (9) NSE  1 − n i1 2 i1 (oi − omean )

4 Results and Discussion Wind data collected by the Indian Meteorological Department (IMD) based at Gopalpur is analysed (Fig. 2). During December 2008, northerly wind predominates; 40% is contributed from southeast quadrant with speed varying between 1 and 4 m/s. In May 2009, wind predominately (80%) approach from south and southwest with speed ranging from 2 to 8 m/s and during November 2009, wind shifts to northerly with a varying speed of 2–4 m/s.

4.1 Water Level Oceanic tides produce sea level oscillations and currents in the coastal zone at different tidal frequencies, i.e., semidiurnal (twice a day), diurnal (once a day) or a combination of the two [23]. Along the east coast of the Indian peninsula, tides are semidiurnal, whereas predominately mixed, semidiurnal along the west coast; continuously amplified while moving from south to north and tidal range varying from 0.5 m at the peninsular tip of India to 8.5 m at Bhavnagar, Gulf of Khambhat [24]. These differences are due to the interaction between the forcing and the natural frequencies of the tidal basin [25].

Fig. 2 Windrose diagram for a NE monsoon, b SWM and c NEC

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The annual water-level data for Gopalpur shows that the highest spring and lowest neap tidal ranges are 2.39 m and 0.85 m, respectively, and the maximum water level was recorded in August, associated with cyclonic disturbances; whereas the minimum was observed during the fair weather (January) month [16]. The waterlevel variations along the coasts are principally due to astronomical tides and nontidal viz., atmospheric forcing and hydrological regime. Based on tidal range, the coast can be characterised as micro-tidal or lower meso-tidal [26]. The tide and non-tide (residual) components measured off Gopalpur port for three periods are shown in Fig. 3. The seasonal variability, i.e., the SW monsoon (May) tide level is comparatively high (1.79 m) than fair weather (December) low (1.59 m) value and the residual follows a similar trend, i.e., high (0.7 m) in May than December (0.62 m) and November (0.36 m). The amplitude and phase of tidal constituents for different time and space were given in Table 1. The lunar semidiurnal constituent, M2 is 0.55 m during November and 0.48 m in December. On an average, M2 contributes 50% of the total tidal amplitude.

Fig. 3 Astronomical and residual tide at GPL-8 a NE monsoon, b SW monsoon and c post-monsoon

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Table 1 Spatio-temporal variation in amplitude (meters) and phase (degree) of major tidal constituents in the model domain Location

M2 (0.0805)

S2 (0.0833)

O1 (0.0387)

K1 (0.0418)

Form no O1 + K1 /M2 + S2

Post

SW

NE

Post

SW

NE

Post

SW

NE

Post

SW

NE

Post

SW

NE

GPL-8

Amplitude (m)

0.48

0.52

0.48

0.20

0.24

0.18

0.04

0.04

0.05

0.15

0.13

0.14

0.29

0.23

0.23

Phase (°)

239

241

234

284

264

261

321

319

336

336

318

311

PORT-8

Amplitude (m)

0.49

0.53

0.53

0.21

0.22

0.23

0.04

0.04

0.05

0.14

0.14

0.14

0.27

0.24

0.24

Phase (°)

247

242

241

262

266

256

331

325

331

321

321

316

RUS-8

Amplitude (m)

0.48

0.52

0.55

0.21

0.24

0.25

0.05

0.04

0.04

0.14

0.14

0.14

0.28

0.22

0.23

Phase (°)

239

244

241

284

266

255

328

323

331

336

320

318

The solar semidiurnal, S2 component varies between 0.18 and 0.24 m, with an average of 0.21 m contributing to the total height. The diurnal constituents K1 and O1 do not differ significantly on the spatiotemporal scale ranges between 0.13–0.14 m and 0.04–0.05 m, respectively. Phase differences for semidiurnal (M2 ) constituents are of 13°, varying 234°–247° and for S2, it is 29° with a range of 255°–284°. The diurnal constituents O1 and K1 , phase differences varied from 319° to 336° and 311° to 336°, respectively. Tide form no, i.e., the ratio between the diurnal and semidiurnal constituents (F  O1 + K1 /M2 + S2 ) exhibits that the tide is mixed semidiurnal (F > 0.25) [27] during December and semidiurnal (F < 0.25) in other two months, i.e., May and November (Table 1). During December (winter), tide behaves mixed semidiurnal because in the northern hemisphere, the sun is at its maximum declination south (winter solstice). The vernal equinox, ushering in spring for the northern hemisphere, occurs on March 21st when the sun passes over the equator on its apparent trip north, which produces diurnal tidal frequencies because of two tidal bulges caused by the sun [28].

4.2 Coastal Water Currents Coastal currents are coherent water masses in motion flow in between the coast and the edge of the continental shelf [25]. Along the east coast of India, reversible monsoons, i.e., southwest (SW) and northeast (NE) play an essential role in current and circulation pattern. The observed current direction fluctuates from WSW to NNE parallel to shore with a maximum current speed of 48 to 54 cm/s, 31 to 54 cm/s and 49 to 70 cm/s for December’08, May’09 and November’09, respectively (Table 2). However, mean currents do not vary significantly (~20 cm/s and flow at PORT-18 (Offshore) was swift and stable (49–55 cm/s) in all the three seasons.

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Table 2 Measured in situ water currents speed and direction during three representative seasons Location

Post-monsoon

SW monsoon

NE monsoon

Average (cm/s)

Average (cm/s)

Average (cm/s)

Maximum Direction (cm/s) (°)

Maximum Direction (cm/s) (°)

Maximum Direction (cm/s) (°)

GPL-8

12

54

WSW

23

49

NNE

16

58

WSW

PORT-18

20

55

WSW

20

54

NNE

23

49

WSW

RUS-8

14

48

WSW

14

31

NNE

21

70

WSW

Table 3 Details of observed, tidal and non-tidal currents Time

December 2008

May 2009

November 2009

Location Observed current

Tidal component

Non-tidal component

υ-velocity

ν-velocity

υ-velocity

ν-velocity

υ-velocity

ν-velocity

GPL8

0.09 (−0.44 to 0.17)

0.07 (−0.34 to 0.18)

0.05 (−0.11 to 0.03)

0.04 (−0.09 to 0.04)

0.08 (−0.35 to 0.22)

0.07 (−0.25 to 0.21)

PORT18

0.13 (−0.48 to 0.23)

0.11 (−0.35 0.20)

0.10 (−0.20 to 0.05)

0.08 (−0.17 to 0.04)

0.09 (−0.29 to 0.29)

0.09 (−0.24 to 0.25)

RUS8

0.12 (−0.42 to 0.41)

0.06 (−0.17 to 0.25)

0.03 (−0.08 to 0.02)

0.02 (−0.07 to 0.02)

0.12 (−0.35 to 0.43)

0.06 (−0.15 to 0.25)

GPL8

0.18 (−0.25 to 0.37)

0.14 (−0.18 to 0.31)

0.16 (0.06 to 0.27)

0.13 (0.04 to 0.22)

0.06 (−0.36 to 0.21)

0.05 (−0.28 to 0.18)

PORT18

0.15 (−0.28 to 0.42)

0.11 (−0.19 to 0.39)

0.13 (0.03 to 0.25)

0.10 (0.01 to 0.19)

0.07 (−0.31 to 0.28)

0.06 (−0.24 to 0.26)

RUS8

0.13 (−0.23 to 0.28)

0.05 (−0.13 to 0.14)

0.10 (−0.01 to 0.20)

0.04 (−0.01 to 0.09)

0.07 (−0.30 to 0.16)

0.03 (−0.14 to 0.10)

GPL8

0.11 (−0.35 to 0.26)

0.10 (−0.34 to 0.25)

0.08 (−0.17 to 0.05)

0.06 (−0.15 to 0.04)

0.08 (−0.30 to 0.31)

0.07 (−0.26 to 0.27)

PORT18

0.17 (−0.44 to 0.22)

0.13 (−0.28 to 0.28)

0.14 (−0.29 to 0.04)

0.10 (−0.22 to 0.02)

0.10 (−0.34 to 0.31)

0.07 (−0.19 to 0.32)

RUS8

0.17 (−0.59 to 0.33)

0.10 (−0.34 to 0.18)

0.13 (−0.30 to 0.06)

0.08 (−0.18 to 0.04)

0.11 (−0.44 to 0.36)

0.07 (−0.25 to 0.20)

The cross-shore (υ) and alongshore (ν) components indicate the relative dominance of onshore–offshore flows than shore parallel flows (Table 3). Further, the tidal and non-tidal (residual) components are analysed to assess their seasonal variability. The current was predominantly westward (-υ) in the northeast (November’09) and post-monsoon (December’08) whereas eastward (υ) during the southwest monsoon. The υ was quite stronger during May’09 (0.5 m/s at RUS-8 to 0.14 m/s at GPL-8) followed by NEM (0.10 m/s to 0.13 m/s at GPL-18). The tidal currents were stronger during May’09; υ component is easterly dominated with a magnitude 0.10–0.16 m/s, whereas ν is northerly varying from 0.04 to 0.13 m/s. The tidal current observed at PORT-18 was quite stronger than other two locations. However, υ and ν currents were opposite and predominated by westward and southward flows during Novem-

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229

ber’09 and December’08, respectively. The non-tidal υ current is always stronger than ν; residual υ is higher (0.08–0.12 m/s) in December’08 and November’09 than May’09 (0.06–0.07 m/s) and the residuals ν also follows the same.

4.3 Model Result and Validation In hydrodynamic models, friction and turbulent diffusion/dispersion coefficients are adjusted to achieve a reasonable result. The simulated surface elevation and the flow regime due to tidal forcing and coastal structures are compared with the field data, and the performance was evaluated. Comparison of tidal constituents of the observed and simulated is a quantification technique to assess the performance of any tidal model [29]. Along the east coast of India, tides are mainly semidiurnal and M2 , S2 , K1 and O1 are the major tidal constituents for the Bay of Bengal region [30]. In the present study, the observed and model tidal constituents anomalies show an excellent agreement for tidal amplitudes (1–2 cm/s) and phases (1–12°) (Table 4). The model results of surface elevation and current velocities (υ and ν) for three different time periods are validated with the Port-8 water level and Port-18 current data (Figs. 4, 5 and 6). Figure 4 shows the graphical validation of sea-level changes (a), current u-velocity (b) and v-velocity (c); depicts that u component current is

Table 4 Tidal constituent’s comparison for observation (O) and simulation (S) Phase-I (DEC-08)

Phase-II (MAY-09)

Phase-III (NOV-09)

Amp (m)

Phase (°)

Amp (m)

Phase (°)

S

O

S

O

S

O

S

O

S

247

239

0.527

0.532

242

243

0.530

0.524

241

253

0.231

129

281

0.223

0.243

266

266

0.231

0.237

256

263

0.143

0.138

259

335

0.143

0.133

321

318

0.135

0.133

316

321

O1

0.043

0.043

252

324

0.040

0.034

325

316

0.045

0.048

331

334

MSF

0.063

0.083

261

266

0.036

0.018

309

200

0.098

0.077

207

175

SK3

0.010

0.008

230

67

0.010

0.007

48

27

0.005

0.005

50

74

M4

0.006

0.007

41

93

0.005

0.009

26

70

0.004

0.003

27

29

M3

0.004

0.003

358

121

0.006

0.008

335

253

0.003

0.007

346

25

S4

0.001

0.014

329

66

0.004

0.021

283

241

0.002

0.002

114

44

M6

0.002

0.000

112

144

0.004

0.008

294

125

0.002

0.005

133

6

MS4

0.001

0.016

163

75

0.002

0.013

99

202

0.002

0.007

175

111

Amp (m)

Phase (°)

Name

O

S

O

M2

0.486

0.487

S2

0.209

K1

2MK5

0.001

0.008

148

75

0.002

0.011

299

286

0.001

0.002

38

25

2MS6

0.002

0.005

173

263

0.006

0.006

282

27

0.002

0.011

86

302

2SK5

0.001

0.002

182

5

0.003

0.010

189

168

0.001

0.009

89

225

2SM6

0.004

0.003

131

354

0.001

0.004

286

290

0.002

0.005

194

209

M8

0.001

0.003

184

39

0.003

0.004

47

149

0.001

0.003

89

336

3MK7

0.002

0.003

139

317

0.000

0.004

355

7

0.001

0.001

54

280

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Fig. 4 Validation of a tide, b υ-current and c ν-current during post-monsoon

westward (−ve) with a range of 0 to −15 cm/s and v component current is southward (−ve) within a range of 0 to −12 cm/s. Figure 5 shows the validation plots of water level (a), both u-velocity (b) and v-velocity (c) current during SWM, which conclude that the current u-velocity is mostly eastward (+ve) within a range from −12 to 18 cm/s and v-velocity is mostly northward (+ve) with a range of −8 to 15 cm/s. The graphical validation of sea-level changes (a), current u-velocity (b) and vvelocity (c) are shown in the Fig. 6 and conclude that current u component is westward (−ve) with a range of 0 to −25 cm/s and v component current is southward (−ve) within a range of −4 to −18 cm/s. Various skill tests adopted for observed and simulated values for surface elevation and current components (zonal: υ and meridional: ν) are consolidated and compared (Table 5). Good agreement is achieved between observed and simulated water levels for all periods and signifies the efficiency of the model. The R values were 0.96–0.98 for surface elevation, 0.72–0.97 for υ velocity and 0.74–0.94 for ν velocity is defined as close to perfect model performance, though the R  1 and R  −1 is perfect positive and perfect negative and above 0.5 is acceptable [20]. The

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Fig. 5 Validation of a tide, b υ-current and c ν-current during SW monsoon

RMAE value indicates that the model is excellent for simulation of surface elevation (RMAE  0.08–0.14) and good for simulating the υvelocity (RMAE  0.24–0.38) and ν velocity (RMAE  0.24–0.30). The IoAd value most closer to 1 in case of tide (0.91–0.99), υ velocity (0.82–0.95) and ν velocity (0.85–0.94) classify the model performance is good [31]. The RIoAd analysis described the performance good for tide (0.84–0.89) and both υ velocity (0.66–0.79) as well as ν velocity (0.63–0.72) though, it closer to 1 [31]. Based on NSE, the model is acceptable as the values for all simulations (tide  0.91–0.97, υ velocity  0.46–0.82 and for ν velocity  0.44–0.72) falls in between 0 and 1 [22]. The surface elevations are in good agreement as compared to velocity components. In all the three seasons, the surface elevation agreement is excellent and very good, whereas May month gives better agreement than December and November simulations. The υ velocity has a ‘good’ agreement for May’09 than December’08 and November’09; whereas, ν velocity of May’09 has a ‘well’ agreement than November’09 and December’08. Overall model performance is evaluated as ‘excellent’ for water level and ‘better’ for tidal current simulations.

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Fig. 6 Validation of a tide, b υ-current and c ν-current during NE monsoon Table 5 Skill test results υ-velocity

Tide

ν-velocity

R

RMAE IoAd RIoAd NSE R

RMAE IoAd RIoAd NSE R

RMAE IoAd RIoAd NSE

0.96

0.14

0.91

0.85

0.91

0.85

0.24

0.91

0.71

0.63

0.74

0.28

0.85

0.63

0.44

May’09 0.98

0.09

0.99

0.84

0.97

0.97

0.38

0.95

0.79

0.82

0.96

0.30

0.94

0.73

0.72

Nov’09 0.98

0.08

0.99

0.89

0.94

0.72

0.28

0.82

0.66

0.46

0.77

0.24

0.84

0.68

0.50

Dec’08

The snapshots of simulated flow patterns for three different time periods, i.e., postmonsoon (December’08), SW monsoon (May’09) and NE monsoon (November’09) are shown in Figs. 7, 8 and 9 respectively. In December’08, the flow direction is towards southerly, and shore parallel. Currents near to the structures get fluctuated and anticyclonic (clockwise) eddy formed between the south groin and north breakwater. The main harbour area and on the lee side of the southern breakwater remains calm (Fig. 7b). The flow direction during May 2009 is reversed, and it is comparatively high and northerly. A clockwise flow is formed within the central harbour area, and the relatively stronger flows are formed at the tip of structures (Fig. 8b). The flow vectors indicate that the streams get concentrated at 8–12 m depth off northern groin, and stronger currents reach on the north side of the port.

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Fig. 7 Simulated flow for post-monsoon a whole model domain and b port region

During November’09, the flow is predominantly southerly and stronger than December’08; stronger flow vectors are seen outside of the port at a depth of 10–12 m (Fig. 9b). The current flow regime is almost similar in direction and strength during NE and post-monsoon and opposite to southwest period and relatively weak.

4.4 Particle Tracking The coastal current is seasonal and reversal along the east coast of India, thus understanding of circulation pattern, and sediment transport near coastal structures becomes essential for port maintenance and operation. Particle-tracking simulation was carried out to evaluate the sediment drift; three point locations were selected, one within the harbour and on north and south side of the harbour to determine the drift path (Fig. 10). The particles were released for 24 h for December’08 and 12 h

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Fig. 8 Simulated flow for SW monsoon a whole model domain and b port region

for other two periods as it was observed that relatively the current is swifter in both SW and NE monsoon months than post-monsoon month. In post-monsoon, particles outside harbour at a rate of 8.7 cm/s and the particle inside the harbour area moved anticlockwise and flew out at a rate of 3 cm/s along the breakwater in a southerly direction (Fig. 10a). Following the current, during SW, the particles moved northerly at a rate of 11.6 cm/s, and the particles released inside the harbour moved clockwise and drifted at a rate of 7 cm/s (Fig. 10b). During NE, the particle released on the extreme north drifted southerly at a rate of 12.7 cm/s, and inside the port, the displacement rate was 8 cm/s and takes an elliptical path on the lee side of the south breakwater (Fig. 10c).

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Fig. 9 Simulated flow for NE monsoon a whole model domain and b port region

5 Conclusions The tidal characteristics vary seasonally from semidiurnal in a monsoon to mixed semidiurnal in post-monsoon months; mostly dominated by the semidiurnal constituents, M2 (0.48–0.55 m) followed by S2 (0.18–0.25 m) with a phase difference of 13° and 29° throughout the year. The diurnal constituents are comparatively less significant with amplitude variation of O1 (0.04–0.05 m) and K1 (0.13–0.15 m) with a phase difference of 17° and 25°, respectively. The average current speed is within 15–20 cm/s in all the seasons except north–northeast during SW monsoon, west–southwest in NE, and minimum south–southwest in post-monsoon. Predominant northerly wind triggers shore parallel southerly current during NE and post-monsoon, whereas southerly wind during SW monsoon reverses the flow to northerly. A sitespecific model for a highly dynamic coastal environment was set-up and validated with the seasonal tide, and current observations and model sensitive analysis confirm a good agreement. In the absence of real-time data, the model-derived constituents

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Fig. 10 Particle tracking during a post-monsoon, b SWM and c NEM

can be used for tidal prediction and port operation. The particle-tracking experiment deciphering the circulation pattern is found to be useful for sediment transport computation and other coastal applications. Acknowledgements The study is supported by the Ministry of Earth Sciences (MoES), Government of India. We are thankful to Secretary, MoES for his constant support and encouragement. The help rendered by IMD, Gopalpur, Berhampur University and Gopalpur port authorities are duly acknowledged. This work is a part of the doctoral thesis of the first author.

References 1. Mofjeld HO (1976) Tidal currents. In: Stanley DJ, Swift DJP (eds) Marine sediment transport and environmental management. Wiley, New York, pp 53–64 2. Bowden KF (1983) Physical oceanography of coastal waters. Ellis Horwood Ltd, Chichester 3. Flemming BW (2005) Tidal environments. In: Schwartz ML (ed) Encyclopedia of coastal science. Encyclopedia of earth science series, pp 954–958 4. Shetye SR (1999) Tides in the Gulf of Kutch, India. Cont Shelf Res 19:1771–1782 5. Godin G (1991) Frictional effects in river tides. In: Tidal hydrodynamics. Hoboken, NJ, Wiley, pp 379–402

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6. Herman A (2007) Numerical modelling of water transport processes in partially connected tidal basins. Coast Eng 54:297–320 7. Byun DS, Wang XH, Holloway PE (2004) Tidal characteristic adjustment due to dyke and seawall construction in the Mokpo Coastal Zone, Korea. Estuar Coast Shelf Sci 59:185–196 8. Liu JF, Mauzerall DL, Horowitz LW (2005) Analysis of seasonal and inter annual variability in transpacific transport. J Geophys Res 110:D04302. https://doi.org/10.1029/2004JD005207 9. Sousa MC, Dias JM (2007) Hydrodynamic model calibration for a mesotidal lagoon: the case of Ria de Aveiro (Portugal). J Coast ResSI 50:1075–1080 10. Mirfenderesk H, Tomlinson R (2007) Numerical modelling of tidal dynamic and water circulation at the Gold Coast Broadwater, Australia. J Coast Res SI 50:277–281 11. Unnikrishnan AS, Gouveia AD, Vethamony P (1999) Tidal regime in the Gulf of Kutch, west coast of India by a two-dimensional numerical model. J Waterw Port Harb Eng ASCE 125(6):276–284 12. Gupta I, Dhage S, Chandorkar AA, Srivastav A (2004) Numerical modeling for Thane creek. Environ Model Softw 19:571–579 13. Babu MT, Vethamony P, Desa E (2005) Modelling tide driven currents and residual eddies in the Gulf of Kachchh and their seasonal variability a marine environmental planning perspective. Ecol Model 184:299–312 14. Vethamony P, Reddy GS, Babu MT, Desa E, Sudheesh K (2005) Tidal eddies in a semi-enclosed basin: a model study. Mar Environ Res 59:519–532 15. Kankara RS, Mohan R, Venkatachalapathy R (2013) Hydrodynamic modelling of Chennai coast from a coastal zone management perspective. J Coast Res 29(2):347–357 16. Mohanty PK, Patra SK, Bramha S, Seth B, Pradhan UK, Behera B, Mishra P, Panda US (2012) Impact of Groins on beach morphology: a case study near Gopalpur Port, east coast of India. J Coast Res 28:132–142 17. Mishra P, Pradhan UK, Panda US, Patra SK, Ramana Murthy MV, Seth B, Mohanty PK (2014) Field measurements & numerical modelling of nearshore processes at an open coast port on the east coast of India. Indian J Geo-Mar Sci 43:1277–1285 18. Pawlowicz R, Beardsley B, Lentz S (2002) Classical tidal harmonic analysis including error estimates in MATLAB using T_TIDE. Comput Geosci 28:929–937 19. Danish Hydraulic Institute (DHI) (2007) Mike 21 & Mike 3 hydrodynamic and transport module: scientific document. DHI Water and Environment. Horsholm, Denmark 20. Moriasi DN, Arnold JG, VanLiew MW, Bingner RL, Harmel RD, Veith TL (2007) Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Am Soc Agric Biol Eng 50(3):885−900, ISSN 0001−2351 21. Fernandes EHL, Dyer KR, Niencheski LFH (2001) TELEMAC-2D calibration and validation to the hydrodynamics of the Patos Lagoon (Brazil). J Coast Res 34:470–488 22. Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models: Part 1. A discussion of principles. J Hydrol 10(3):282–290 23. Komar PD (1998) Beach processes and sedimentation, 2nd edn. Prentice Hall 24. Sanilkumar V, Pathak KC, Pednekar P, Raju NSN, Gowthaman R (2006) Coastal processes along the Indian coastline. Curr Sci 91(4):530–536 25. Gelfenbaum G (2005) Coastal currents. In: Schwartz ML (ed) Encyclopedia of coastal science. Encyclopedia of earth science series, pp 259–260 26. Davies J (1964) A morphogenic approach to world shorelines. Z Geomorphol 8:127–142 27. Doodson AT (1921) The harmonic development of the tide-generating potential. Proc R Soc Lon Ser A. (Containing papers of Mathematical and Physical character) 100(704):305–3029 28. Parker BB (2007) Tidal analysis and prediction. NOAA special publication, NOS CO-OPS 3, Silver Spring, Maryland, Library of Congress Control Number: 2007925298 29. Dias JM, Lopes JF (2006) Calibration and validation of hydrodynamic, salt and heat transport models for Ria de Aveiro Lagoon (Portugal). J Coast Res SI 39:1680–1684 30. Murty TS, Henry RF (1983) Tides in the Bay of Bengal. J Geophys Res 88:6069–6076 31. Willmott CJ, Scott M, Robeson Matsuura K (2012) Short communication a refined index of model performance. Int J Climatol 32:2088–2094

Improving Hydraulic Conditions to Preserve Mangroves at Hazira V. B. Sharma, A. K. Singh and Prabhat Chandra

Abstract The Forest and Environment Department (FED), Government of Gujarat was concerned about protecting the 22-hectare mangrove patch in the vicinity of causeway approaching Land-Based Drilling Platform (LBDP) of NIKO Resources Ltd (NRL) and behind the reclaimed land of Hazira Port Private Ltd (HPPL), Hazira in Gujarat state. In this regard, the studies were carried out to simulate tidal flow in existing conditions with a culvert of 12 m width at HPPL side and two open pipes of 1 m diameter each at +6 m level on LBDP side. In order to improve the hydraulic conditions in this channel, the studies were carried out by incorporating the 8 m wide culvert at different sill levels on LBDP side using MIKE-21 software. Culvert with sill level at +4.5, +4.0, +3.5 and +2.5 m was incorporated in the computational model, and tidal flow was simulated for each condition. The studies revealed that channel would be hydraulically more active when the sill level of culvert at LBDP side is +2.5 m but it would require dredging of channel up to +2.5 m depth contour beyond LBDP bund on seaside. This area on seaside is prone to siltation and would need regular maintenance dredging which may not be cost-effective. Keeping this in mind, a culvert of width of 8 m with sill level at existing bed level on seaside (i.e. +4.0 m) at LBDP bund has been suggested, which would keep the channel hydraulically active both during spring and neap tides, and at the same time, it would not require dredging of channel beyond LBDP bund on seaside. The existing culvert level on HPPL side which is at +4.5 m is found to be adequate for tidal flow in the channel on port side. Even though the channel would get sufficient water during spring and neap tide, the submergence of Mangroves, which are at +5 to +7 m, would occur only during spring tide. Channels in the mangrove area were also suggested. Keywords Mangrove · Tide · Sill level · MIKE-21 · Hydraulic condition Revival V. B. Sharma (B) · A. K. Singh · P. Chandra Central Water and Power Research Station, Khadakwasla, Pune 411 024, India e-mail: [email protected] A. K. Singh e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_18

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1 Introduction The HPPL has reclaimed an area of about 19800 m2 with levels maintained at above +8 m in front of mangroves which runs about 1350 m along the coast (Fig. 1). The mangroves behind this reclaimed area are not receiving water from the seaside causing their degradation. In order to provide water to the mangroves, HPPL provided a culvert on the port side and dredged a channel all along the mangrove patch on the roadside up to NRL bund. The existing bed level at the culvert is +4.5 m and the bed level of the channel is between +4.5 and +5 m. On the southern side, an approach to the LBDP of NRL restricts the free flow of water from Tapi estuary side to the mangrove patch. The NRL has also provided two Hume pipes with nonreturn valves which open only towards the mangrove patch, to connect the channel dredged by HPPL and the sea. However, the bottom of these pipes is located at +6 m allowing tidal water to flow only during spring tides and that too, after mid-tide level. The existing mangrove level behind reclamation is between +5 and +7 m. It is understood that for sustenance of mangroves, there should be supply of seawater for at least once in a day. With the present level of channel and culverts, the water comes in this region only during spring tide and that too only for few hours in a tidal cycle. Thus, mangroves are getting supply of seawater only for a few hours in 15 days during spring and no supply of water for the period during neap tides in a month. It is felt that there is a need to study the feasibility of improving hydraulic conditions in the mangrove region by carrying out mathematical model studies.

2 Prototype Data Analysis Analysis of data is the most important part of model studies as the accuracy of model results depends on the accuracy of data. The basic inputs for model studies are bathymetry data, tidal data, current data, sediment characteristics, suspended sediment concentration, etc. The field data provided by the client is briefly discussed below. The hydrographic charts provide bathymetric information near the project site. The depth contours show that there is a wide stretch of tidal flats and also shoals in front of the proposed project site. As the tidal range is more than 6 m, a large area is subjected to flooding and drying. The bathymetry under the existing conditions digitized from the hydrographic chart is shown in Fig. 2. The detailed hydrographic chart shows that the 6–20 m depth contours converge at an offshore distance of 1.5 km indicating sudden steep bed beyond 5 m depth contour. The contours towards the south are spread apart indicating wide tidal flats. The spring tidal range at Hazira is of the order of 7.0 m while during neap tide, it is about 3.4 m. It is reported that the currents in this channel are directed NNW during flood and SSE during ebb. Peak currents in spring tide during flooding phase of tide are 2.3 m/s while during ebb, the peak currents are 1.8 m/s. During neap tide, the peak flood currents are of order of 1.6 m/s while during ebb, it is 1.2 m/s.

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HAZIRA

HPPL Culvert

NRL Bund

Fig. 1 Location plan showing existing scenario

Fig. 2 Computational model with nested grid

NRL Hume Pipes

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The bed sediment reported in the approach channel is sand with low percent of silt and clay. The bed sediment in the harbour area is silty clay. The concentration of suspended solids is very high. The maximum suspended solids (SS) concentration recorded is of the order of 1000 mg/l. The average sedimentation is of the order of 400 mg/l.

3 Modelling Approach MIKE-21 software developed by DHI, Denmark [1] is used to establish flow behaviour in the Hazira region. The shallow water equations derived from Navier–Stokes equations by integrating over the depth are solved by Alternating Direction Implicit (ADI) scheme in this software. The model is discretized using staggered grid system. These discretized variables and derivatives are derived from Taylor’s series approximation ignoring higher order terms. In ADI scheme, a system of equations is generated which solves space differences variables at the unknown time levels using boundary conditions. This computationally efficient scheme is widely used to solve shallow water equations. The solution of Shallow Water Equation results in hydrodynamic parameters at different time steps which are further used to simulate the flow conditions over a period of time at every grid point.

3.1 Setting Up of Computational Model The computational model considered for tidal flow simulation covers an area of 5.5 km × 7 km. The model limit extends up to 25 m depth contour in the offshore direction. The model area covers entire HPPL, reclaimed land and NRL approach bund to LBDP. The bathymetry of the area is digitized from the hydrographic charts available with CWPRS. The complete model area was discretized in three levels considering coarse and fine grids to reproduce mangrove patch, culvert dimensions and channel sections in detail. The coarse grid with 36 and 12 m grid size covers the Outer Hazira region and Port region. The mangrove patch and channel region are covered by a fine grid of 4 m grid size. The coarse grid model with 36 m grid size was set up to cover the entire model area consisting of 160 × 205 grids in x and y directions, respectively. The next coarse grid model with 12 m grid size was set up to cover Port area consisting of 350 × 240 grids in x and y directions, respectively. In order to reproduce the narrow channel dredged for the supply of saline water to mangrove patch and 12 m wide culvert a fine grid model of 4 m grid size was set up consisting of 450 × 515 grids in x and y directions, respectively. All the three computational models were nested together.

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4 Simulation of Flow In order to simulate flow conditions in the vicinity of mangrove region, it is required to simulate flow field in the entire port area using Nested Grid Model. The tide data provided by HPPL was used as boundary information to simulate flow field during spring and neap tide conditions. The hydrodynamic studies were carried out for improving the channel condition and by lowering the culvert sill level at LBDP bund side. Initially, channel bed level was considered at +4.5 m, which is the same as the culvert level at HPPL side. Subsequently, the studies were conducted varying the dredged level and Sill levels at LBDP side to +3.5 m and then to +2.5 m. The width of the proposed culvert at LBDP was considered as 8 m.

4.1 Flow Simulation for Existing Scenario Initially, the studies were carried out for existing condition both for spring and neap tide considering the following conditions: Culvert bed level at HPPL: + 4.5 m, Pipe bottom level at LBDP bund: + 6 m, Opening at HPPL: 12 m wide culvert, Opening at LBDP: 1 m dia. Pipe 2 nos. The flow simulations were carried out for both spring and neap tides for existing conditions considering the recent development of HPPL. Typical flow fields during flood and ebb during spring tide in the coarse grid model are shown in Fig. 3.

Fig. 3 Flow pattern during high water and low water spring tide

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Water levels were monitored at three locations, viz. at HPPL culvert, at the centre of the channel and at LBDP opening. Figure 4 shows water levels at three locations during different tidal stages. The time series the minimum water depth available during a tidal cycle at these locations could be seen.

FOR EXISTING CHANNEL AND SILL LEVEL OF + 6.0 mat LBDP BUND Fig. 4 Time history of tidal levels at three monitoring points for the existing channel and sill level of +6.0 m at LBDP bund

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4.2 Flow Simulation with Channel Bed Level and LBDP Sill Level at +4.5 m The studies were carried out considering the following conditions: Culvert at HPPL: 12 m width Culvert at LBDP: 8 m width Sill level at HPPL: +4.5 m, Sill level at LBDP bund: + 4.5 m, Channel bed level: +4.5 m Channel width: 12 m The simulations carried out for the above condition shows that the water also enters from the NIKO bund side and the channel gets filled after mid-tide. The draining from both the outlets was observed. However, there is no significant change in the time of submergence of the mangrove patch. Figure 5 shows the time history of water levels at monitoring points. It could be seen that the water remains in the channel for 4 h during a spring tidal cycle. Comparing Figs. 4 and 5, it can be observed that there is a slight improvement in the hydraulic conditions in the channel inside the mangrove area.

4.3 Flow Simulation with Channel Bed Level and LBDP Sill Level at +3.5 m The studies were repeated for following conditions where channel level and sill level of LBDP bund are maintained at +3.5 m for both spring and neap tides: Culvert at HPPL:12 m width Culvert at LBDP:8 m width Sill level at HPPL: + 4.5 m, Sill level at LBDP bund: + 3.5 m, Channel Bed level: + 3.5m Channel width: 12 m The results show that there would be free flow of water in the channel, which gets filled after tide reaching +3.5 m level. The draining from both the outlets was also observed. It is seen that the water remains in the channel during the complete tidal cycle. The model was simulated for channel bed level and LBDP Sill Level at +3.5 m. The studies were repeated for the neap tide.

4.4 Flow Simulation with Channel Bed Level and LBDP Sill Level at +2.5 m The model was further simulated for sill and bed level at +2.5 m. It is seen that even during neap tide, seawater enters the channel as soon as the tidal level reach +2.5 m provided a channel is dredged between LDBP culvert level to +2.5 m depth contour

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FOR CHANNEL DREDGED TO+ 4.5 m AND SILL LEVEL OF+ 4.5 m at LBDP BUND Fig. 5 Time history of tidal levels at three monitoring points for channel dredged to +4.5 m and sill level of +4.5 m at LBDP bund

in the sea. It could be seen from Fig. 6 that the seawater remains in channel even during neap tide. This condition is hydraulically very efficient but this area is highly prone to siltation resulting in huge maintenance dredging. In order to avoid high maintenance dredging, sill at +4.0 m was considered, and the model was simulated for this condition.

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FOR CHANNEL DREDGED TO + 2.5.0 AND SILL LEVEL OF + 2.5 m at LBDP BUND Fig. 6 Time history of tidal levels at three monitoring points for spring tide for channel dredged to +2.5.0 and sill level of +2.5 m at LBDP bund

4.5 Flow Simulation with Channel Bed Level and LBDP Sill Level at +4.0 m The simulations carried out have shown that there is a significant exchange of flow from the NIKO (LBDP) bund side, and the channel gets filled after mid-tide. The draining from both the outlets was observed. It is seen that the flow enters mangrove

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FOR CHANNEL DREDGED TO + 4.0 m AND LEVEL OF + 4.0 m at LBDP BUND

Fig. 7 Time history of tidal levels at three monitoring points for neap tide for channel dredged to + 4.0 m and level of +4.0 m at LBDP bund

region only after mid-tide and drains out after 6 h. The area of submergence during different tidal phases could be seen in Fig. 7. During neap tide, mangroves near HPPL only, get water for few hours. But in the other region, there would be no supply of water to mangroves even though there would be 1–2 m depth of water in the channel. It may be possible to retain the water in the channel by providing control structures on both the sides. This would avoid

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Fig. 8 a–d Area of submergence of mangrove region during different tidal phases

draining out of water during ebb. The flow field in the vicinity of the mangrove area simulated in the fine grid model is shown in Fig. 8a–d. It can be observed that the saline water enters the channel from both sides and also drain out from both openings. The maximum velocity in the channel would be 0.4 m/s at HPPL side and 0.6 m/s at LBDP side. However, in the middle of the channel, the velocities are hardly 0.02 m/s. The flow is mainly due to a rise in tidal levels and no other forcing factors drive the flow. As the water is entering the channel both through Port and from LBDP bund side through culverts, the sediment entering due to bed movement is not significant as it gets arrested below culvert sill level. However, the depth of sedimentation due to suspended sediment would be 0.3–0.5 m over a period of 1 year. This estimation does not include windblown sedimentation. The sedimentation in this region is dominated by windblown sediments from the

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reclamation area. Thus, it may not be possible to quantify the maintenance dredging considering wind effect. However, the actual loss in depth can be found out by regular survey of the channel at least once in a year. Accordingly, the necessary dredging may be carried out to maintain the desired channel levels in the mangrove area.

5 Conclusions Under the existing conditions with a culvert of 12 m width at HPPL side and two open pipes of 1 m diameter each at +6 m level on LBDP side, the mangroves are getting supply of seawater only for a few hours in 15 days during spring and no supply of water for the period during neap tides in a month. The model was further simulated for sill and bed level at +2.5 m. This condition is hydraulically very efficient but this would involve dredging a channel up to +2.5 m from the existing levels of +4.0 to +4.5 m and would further require heavy maintenance dredging. In order to avoid high maintenance dredging, sill at +4.0 m was considered, and the model was simulated for this condition. The opening on the HPPL side with 12 m width and bed level at +4.5 m and a culvert of 8 m width with sill level at existing bed level +4.0 m on LBDP bund side would ensure tidal flow in the channel both during spring and neap tide to a certain extent which would suffice for the revival of mangroves. The advantage of this proposal is that it would not require dredging of the channel on the seaside beyond LBDP bund.

Reference 1. MIKE 21 Flow Model, Hydrodynamic module. Scientific Documentation

Hydrodynamic Modelling for Development of a Port in an Estuary A. K. Singh , L. R. Ranganath

and M. Karthikeyan

Abstract Sharavathi River originates and flows entirely within the state of Karnataka in India. It is one of the few westward flowing rivers of India with huge discharge during monsoon, and the major part of the river basin lies in the Western Ghats. The total length of the Sharavathi River is around 128 km, and it joins the Arabian Sea at Honnavar in Uttara Kannada district of Karnataka. The present study deals with the development of port for providing berthing facilities for coal and iron ore-carrying vessels of 10,000 DWT capacity in the basin of the Sharavathi River estuary. The channel as well as harbour area is proposed to be dredged up to −10.0 m depth. A computer-based numerical model was developed for the port in the Sharavathi Estuary to examine the hydrodynamic characteristics of the region. The model highly resolved the region of interest and predicted sea level, currents in response to the effects of tides and slow sea level changes. Such a model could be used to predict the movements of sediments throughout the vicinity of the proposed harbour. Tidal hydrodynamic simulations reveal that the flow field is conducive without significant circulation with the suggested modified layout. The annual deposition of sediment is expected, in the approach channel. The capital dredging for proposed port development is estimated to be about 4.0 M Cum, and the total maintenance dredging is estimated to be about 1.0 M Cum. Results from the model show that the currents in the estuary are predominantly due to the effects of the tide; the tidal range is around 1.58 m. These tides can generate currents, with current speeds reaching up to 1.3 m/s in the vicinity of Badagani Estuary in the North and up to 0.8 m/s in the

A. K. Singh (B) · L. R. Ranganath · M. Karthikeyan Central Water and Power Research Station, Khadakwasla, Pune 411024, India e-mail: [email protected] L. R. Ranganath e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_19

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vicinity of Sharavathi Estuary in the south. The simulations generated by the model and associated analyses provide a first-order picture of the flow and distribution characteristics of the port environment which may aid in management decision processes and provide an enhanced understanding of the oceanography of the region. Keywords Tides · Current · Sediment transport · Hydrodynamics · Harbour

1 Introduction Honnavar lies on the coast of the Arabian Sea and on the banks of the river Sharavathi, forming an estuary. It lies midway between Panaji and Mangalore (Fig. 1). There is a proposal for the development of a port at Honnavar, Karnataka for providing berthing facilities for coal and iron ore-carrying vessels of 10,000 DWT capacity. The proposed layout (Fig. 2) consists of a northern breakwater of 820 m length and southern breakwater of 865 m length having a clear gap of 360 m in between them. The iron ore berth, coal berth and multipurpose berth are located inside the creek. The channel as well as harbour area is proposed to be dredged up to −10.0 m depth. Mathematical model studies were carried out to assess the flow field and sedimentation pattern in the proposed harbour along with two alternative layouts. This paper describes the mathematical model studies carried out to understand the tidal hydrodynamic behaviour of flow and probable siltation pattern in the harbour area of the proposed development of port at Honnavar.

Fig. 1 Study location

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Fig. 2 Layout of the proposed port

2 Site Condition 2.1 Bathymetry Bathymetric survey of the nearshore region at the proposed site near Honnavar was obtained (Fig. 3) and used. The nearshore bathymetry was superimposed on the C-MAP bathymetry to cover the model region for hydrodynamic studies.

2.2 Tidal Levels Tidal observations were done at Honnavar Jetty during 1–17 April 2011 at an interval of one hour. The data analysis indicated that the observed tidal range was 1.8 m during High tide and about 1.0 m during Low tide and the same was considered initially and further it was extrapolated to longer duration. The tide used for model studies is shown in Fig. 4 and the corresponding values are in Table 1.

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Fig. 4 Observed tide

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Table 1 Tidal levels at Honnavar Tidal levels Mean Higher High Water (MHHW)

+1.8 m

Mean Lower High Water (MLHW)

+1.5 m

Mean sea level Mean Higher Low Water (MHLW)

+1.2 m +1.0 m

Mean Lower Low Water (MLLW)

+0.4 m

2.3 Current Observations Currents observed at three locations (Fig. 5) one in the open sea and the other two inside the Sharavathi River covering spring and neap tide for a duration of 2 weeks during 1–17 April 2011. The current observations were taken at every 20 min interval and at a water depth of 2.6 m below the surface. The analysis of the data indicated that there is a reversal of flow during flood and ebb phase and the average currents at C1 location in outer sea varied from 0.05 to 0.25 m/s with an average value of 0.1 m/s. At C2 location inside the river, the average currents were of the order of 0.55 m/s with a peak value of about 1.2 m/s. Similarly at C3 location inside the river, the average currents were of the order of 0.27 m/s with a peak value of about 0.8 m/s.

Fig. 5 Model region with field observation point

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Table 2 The sediment size distribution at Honnavar Locations Soil D50 Sand (%) description (mm) Coarse sand River

Open sea

River

Medium sand

Silt and Fine sand clay (%)

S1 S2 S3 S4 S5 S6

Coarse sand Fine sand Fine sand Coarse sand Coarse sand Silt and clay

0.52 0.18 0.43 0.60 0.52 0.17

54.03 18.72 22.71 68.31 52.17 22.55

31.88 3.93 47.71 25.15 33.60 8.48

13.77 56.30 28.86 6.28 13.33 36.14

0.20 19.04 0.45 0.20 0.40 31.30

S7

Silt and clay 0.17

18.07

11.90

39.59

29.69

S8 S9 S10 S11 S12

Fine sand Fine sand Coarse sand Fine sand Coarse sand

13.23 16.36 55.33 16.63 53.28

40.03 34.87 26.31 39.28 35.82

23.51 29.17 17.05 35.77 9.92

19.92 15.96 1.00 7.76 0.70

0.32 0.31 0.53 0.28 0.52

2.4 Sediments Water samples were collected at 12 different locations during spring and neap tides at the site. Total 120 samples were analysed and the suspended sediment concentration varied from 15 to 195 mg/l during different phases of tide and water depth. The average value of 0.01 kg/m3 was considered in the model studies. The average D50 value of the sediments at the site was considered as 0.40 mm for simulation. Table 2 shows the sediment size distribution observed at Honnavar.

3 Mathematical Model Studies for Tidal Hydrodynamics The mathematical model studies were carried out using MIKE 21 software developed by Danish Hydraulic Institute, Denmark. The hydrodynamic and siltation studies were carried out with the help of MIKE 21 HD and MIKE 21 MT modules, respectively.

3.1 Model Description In order to examine the tidal flow conditions and dynamics of sediments, it is necessary to compute hydrodynamics of water body in terms of velocity and water level fluctuation. The appropriate governing equations for studying water movement in

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coastal areas are the 2-D shallow water equations. These are obtained by vertically integrating the 3-D Navier–Stokes equations of motion making the following simplified assumptions: • • • •

The flow is incompressible. The flow is well mixed (no variation in density). Vertical accelerations are negligible. Bed stress can be modelled.

Simulation of hydrodynamics is based on the shallow water equations given below (continuity equation): ∂z ∂uh ∂vh + +  0. ∂t ∂x ∂y Equation of motion in x-direction: ∂u ∂u ∂u ∂z +u +v +g − C f v + τbx − E c ∇ 2 u  0. ∂t ∂x ∂y ∂x Equation of motion in y-direction: ∂v ∂v ∂z ∂v +u +v +g + C f u + τ by − E c ∇ 2 v  0, ∂t ∂x ∂y ∂y where z u v d h Cf τb EC

water surface elevation above the datum, X-component of velocity, Y-component of velocity, depth of flow below datum, total depth of flow (d + z), Coriolis force, bed shear stress and eddy viscosity coefficient.

The governing equations are solved by finite difference technique using Alternating Direction Implicit (ADI).

3.2 Computational Model A 2-D mathematical model was developed using bathymetry from the recent hydrographic survey carried out during April 2011. The mathematical model domain consists of open sea portion up to −21 m contour and a portion of Sharavathi River influenced with tidal fluctuation. A uniform square grid of 20 m × 20 m was considered for the entire model area of 19 km × 11 km to cover the entire proposed harbour

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Fig. 6 Computational model area

and surrounding area. The model consists of 900 grid points along x-direction and 550 grid points along y-direction. The bathymetry data extracted from the C-MAP was reproduced in mathematical model for the existing conditions along with superimposition of Hydrographic survey data of the nearshore region at Honnavar and is shown in Fig. 6.

4 Literature Survey Nayak et al. [1] inferred that during flooding, sediments move into the estuary, and during ebbing, they flow seaward resulting in erosion and formation of shoals. Sediment-dispersal patterns largely follow wind and wave patterns, a characteristic feature of the mesotidal coast. Dora et al. [2] carried out Grain character analysis of beach sediments along three selected beaches (Pavinkurve, Kundapura and Padukare) of Karnataka coast, west coast of India. Grain characteristics varied spatially and temporally along with beach orientation, foreshore slope and wave action. The study shows that the sedimentary environment at Kundapura was influenced by relatively high wave action compared to Padukare and Pavinkurve beach, and the beaches were under erosion or non-deposition with strong blow upon the process.

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5 Discussions Mathematical model studies were carried out using MIKE21-HD and MIKE21-MT models to assess the changes in coastal hydrodynamics and siltation pattern due to the proposed harbour at Honnavar. From the model studies using the data available, it was found that with the existing conditions the magnitude of currents varied in the range of 0.2–0.3 m/s indicating that the currents are weak in offshore and near the proposed harbour region during entire tidal cycle except at the Sharavathi River inlet where the magnitude of currents are of the order of 1.0 m/s (Fig. 7). The typical flow during different phases of tide is shown in Fig. 8 Similarly, simulations were carried out for monsoon season by increasing the river discharge to 300 m3 /s and keeping all other conditions same. The typical flow during different phases of tide is shown in Fig. 9. The magnitude of currents did not change much in the offshore region and varied in the range of 0.2–0.3 m/s. At the inlet near river mouth and estuary, the magnitude of currents increased considerably due to the river discharge and reached up to 1.0 m/s. It is observed that the average depth of sediment deposition varies from 10 to 40 cm during monsoon season. From the sedimentation studies, it could be seen that the zone of deposition is mainly in front of the river inlet and a tendency of sandbar formation is prevailing. It is observed that the average depth of sediment deposition varies from 10 to 25 cm during non-monsoon season (Fig. 10). It is observed that the average depth of sediment deposition varies from 10 to 40 cm during monsoon season.

Fig. 7 Comparison of currents (observed vs. computed)

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Peak Ebbing

Peak Flooding

Fig. 8 Flow field in existing condition (non-monsoon)

Peak Ebbing

Peak Flooding

Fig. 9 Flow field in existing condition (monsoon)

Non Monsoon

Monsoon

Fig. 10 Siltation pattern over a period of 1 month

With the proposed layout, the magnitude of currents varied in the range of 0.2–0.33 m/s indicating that the currents are weak in offshore which is similar to the existing condition. For monsoon conditions, the magnitude of currents did not change much in the offshore region which varied in the range of 0.2–0.3 m/s. At the river inlet and inside the estuary the magnitude of currents increased considerably due to the river discharge and reached up to 1.15 m/s (Fig. 11).

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Monsoon

Fig. 11 Flow field during peak ebb (proposed)

Non Monsoon

Monsoon

Fig. 12 Siltation pattern over a period of 1 month (proposed)

A typical siltation pattern over a period of 1 month during non-monsoon with the proposed port layout is shown in Fig. 12. It could be seen that the zone of deposition is mainly in the approach channel extending up to –8.0 m contour, specifically after the tip of the proposed breakwater and towards the offshore region which ranges from 0.5 to 10 cm, this may be attributed to the sudden change in depth of the channel when compared to the adjacent contours, also there is a tendency of erosion at the tip of the breakwater which may be attributed to the sudden variation in the flow condition, i.e. increase in flow velocity which acts as a jet facilitating removal of sediments in the channel. Inside the harbour, there is a slight tendency of sediment deposition over the shadow region of the basin which is very marginal. But inside the river, i.e. just behind the inlet, there is a trend of deposition and may be of the order of 10–25 cm. From the sedimentation studies conducted for monsoon conditions the depth of deposition in the approach channel extended up to –8.0 m contour, specifically after the tip of the proposed breakwater and towards the offshore region which ranges from 10 to 30 cm. Inside the harbour also, there is a slight tendency of sediment deposition. In the estuary, the trend of deposition has further intensified, and it is of the order of 10–40 cm.

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Non Monsoon

Monsoon

Fig. 13 Flow field during peak ebb (alternative I)

Similarly, studies were conducted by reducing the length of the breakwater by about 30%, to optimize the breakwater length shown in Fig. 13 (alternative I). Model simulations for both non-monsoon and monsoon conditions indicated that the magnitude of currents in the offshore varied in the range of 0.2–0.30 m/s. In the proposed harbour basin, the current magnitude has reduced further due to the increased opening at the tip of the north and south breakwaters near channel entrance. It is also observed that there is no tidal circulation or eddy formation inside the harbour. It could be seen that the zone of deposition is mainly in the approach channel, specifically after the tip of the proposed breakwaters the deposition trend is more and towards the offshore region up to a depth contour of about −8 m which ranges from 0.5 to 10 cm, it reduces gradually and stabilizes, this may be attributed to the sudden change in depth of the channel when compared to the adjacent contours, also there is a tendency of erosion at the tip of the breakwater which may be due to the sudden change in the flow condition, i.e. an increase in flow velocity. Inside the harbour, there is a reduction in tendency of sediment deposition. But inside the river, i.e. just behind the inlet, there is a trend of deposition and may be of the order of 10–25 cm indicating that there is no impact of reduction in length of breakwater on sedimentation. Further studies were conducted for monsoon conditions. The trend of sediment deposition in the channel continues with a further increase in the depth of deposition in the approach channel extending up to –8.0 m contour, specifically after the tip of the proposed breakwater and towards the offshore region which ranges from 10 to 30 cm. Inside the harbour also, there is a clear increase in tendency of sediment deposition in the channel as well as in the shadow region of the basin when compared with full length of breakwater. Inside the river, i.e. just behind the inlet the trend of deposition has further intensified and may be of the order of 10–40 cm. Overall, it is clear that reduction in length of the breakwater has not reduced the quantum of siltation and is shown in Fig. 14. The magnitude and direction of flow along with flow pattern were observed. The magnitude of currents in the offshore varied in the range of 0.2–0.30 m/s indicating

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Monsoon

Fig. 14 Siltation pattern over a period of 1 month (alternative I)

Non Monsoon

Monsoon

Fig. 15 Flow field during peak ebb (alternative II)

that the currents are weak in offshore similar to that of original proposal but in the proposed harbour basin the current magnitude has reduced further due to the increased opening at the tip of the north and south breakwaters near channel entrance. It is also observed that there is no tidal circulation or eddy formation inside the harbour. Similarly, simulations were carried out for monsoon conditions. A typical flow during different phases of tide is shown in Fig. 15. The magnitude of currents did not change much in the offshore region. At the harbour entrance, the magnitude of currents has reduced when compared with the original proposal with full-length breakwater. A typical siltation pattern over a period of 1 month during non-monsoon and monsoon with the proposed port layout is shown in Fig. 16. It could be seen that the zone of deposition is mainly in the approach channel, specifically after the tip of the proposed breakwaters the deposition trend is more and towards the offshore region up to a depth contour of about −8 m which ranges from 0.5 to 10 cm which is similar to that of full-length breakwater of the proposed layout but there is a slight increase in depth of deposition. Inside the harbour, there is not much change in the trend of sediment deposition when compared to the original proposal. Sedimentation pattern inside the river also remains similar to that of the original layout. Overall impact of shifting the southern breakwater on sedimentation pattern is not significant.

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Non Monsoon

Monsoon

Fig. 16 Siltation pattern over a period of 1 month (alternative II)

However, it may be noted that the sediment transport studies are more qualitative than quantitative. The exact quantification of the sedimentation in the coastal region is difficult as the process becomes complex due to continuous changes in the tide, currents and waves throughout the year.

6 Conclusions From the hydrodynamic studies, it can be concluded that the flow field is conducive without significant circulation with the original proposal of port development and also with the two alternatives. Sedimentation studies reveal that the quantum of sediment deposition is minimal with the original port layout when compared with other two alternative layouts. Hence, the original port layout was found to be feasible. Only with the requirement of additional harbour area, the proposal of alternative II may be taken up. The annual deposition of sediment is expected, in the approach channel. However, provisions may be made for the periodical maintenance dredging to maintain adequate depths in the channel and basin. The capital dredging for proposed port development is estimated to be about 4.0 M Cu m, and the total maintenance dredging is estimated to be about 1.0 M Cu m. This maintenance dredging quantity is about 0.4 M Cu m in the approach channel and 0.6 M Cu m in the basin including turning circle. This estimate is based on the model study and literature survey of ports along the west coast.

References 1. Nayak SR, Hegde VS, Shalini R, Rajawat AS, Ali M, Venkateshwarlu B, Ramana IV (2012) Application of satellite remote sensing for investigation of suspended sediment dispersion pattern in the near shore region: a case study from the central west coast of India. J Coast Res 28(2):399–406. https://doi.org/10.2112/JCOASTRES-D-10-00190.1 2. Dora GU, Kumar VS, Philip CS, Johnson G, Vinayaraj P, Gowthaman R (2011) Textural characteristics of foreshore sediments along Karnataka shoreline, west coast of India. Int J Sedim Res 26, 364–377

Wave Interaction with Multiple Submerged Porous Structures V. Venkateswarlu and D. Karmakar

Abstract In the present study, two submerged porous structures under the action of ocean waves are analysed to understand the wave control performance due to porosity parameter. The studies in the first case consider the submerged porous structure kept at finite depth backed by rigid wall at a distance L. The second case explains the two submerged porous structures with sea wall. The numerical study is performed considering the velocity potentials in (i) open water region (seaside), (ii) porous region (primary porous structure), (iii) open water region (in between the porous structures), (iv) porous region (second porous structure) and (v) open water region (lee side). The linearized wave theory is used to analyse the wave interaction with submerged porous structures. The matching conditions are adopted based on continuity of mass and velocity, and the orthogonality condition is used to formulate the boundary value problem, and the eigenfunction expansion method is adopted for the determination of reflection, transmission coefficients, energy loss and wave forces on submerged porous structures. Numerical computation is performed for predicting the wave reflection and transmission from the submerged porous structures for different structure width and angle of incidence conditions. The existence of the porosity and friction causes energy loss and minimum friction; maximum porosity results in high wave transmission and less wave reflection. The significant difference is observed when submerged porous structure is divided into two submerged porous structures with rigid wall. In all the cases, the width of the porous structure is considered similar and is observed to play a predominant role in wave reflection, transmission and stability of the structure. The study will help in the novel economic design of the submerged porous structures for the protection of coastal facilities. Keywords Submerged porous structure · Linearized wave theory · Wave forces Energy absorption

V. Venkateswarlu · D. Karmakar (B) Department of Applied Mechanics and Hydraulics, National Institute of Technology Karnataka, Surathkal, Mangalore 575025, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_20

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1 Introduction Submerged porous structures are frequently used as a breakwater to control the wave attack on gently sloping beaches, ports and harbours. Practical problems arising dayto-day life has motivated to investigate the wave interaction with submerged porous structures considering different conditions. Porous structures are not only constructed for controlling the tremendous wave power generated due to wave propagation but also essential in the attenuation of wave height and protection of coastal structures. Tremendous wave attack causes coastal erosion and creates a disturbance to the artificial and man-made structures. Submerged porous structures are one of the solutions to mitigate the coastal-related problems from high wave trains with less maintenance and long life period. Wave reflection from the structures plays a predominant role in the prediction of wave climate in harbours and wharfs. The significance of the submerged porous structures is studied by numerous researchers using numerical and experimental models. Numerical models are developed based on linear wave theory to investigate the submerged porous structure kept in various conditions with various key role parameters like porosity, friction, inertia, width of the porous structure and angle of wave attack. Sollitt and Cross [15] performed an elaborated study on the rectangular porous structure for finding the reflection and transmission coefficients in the presence of evanescent waves. Eigenfunction expansion method is used to relate the velocity potentials for finding the unknowns. Finally, the theoretical values are compared and validated with numerical values. Dattatri et al. [7] analysed the behaviour of the vertical, rectangular and trapezoidal submerged permeable and impermeable breakwaters with experimental study. The wave reflection due to the presence of vertical permeable porous structure is presented in Madsen [12] for shallow water waves. The detail derivation for the wave absorption due to the vertical homogeneous porous structure under the action of shallow water waves is performed. Further, Sulisz [17] examined a rubble-mound breakwater kept in infinite water depth and the reflection and transmission characteristics for the multi-layered breakwater of arbitrary cross section is analysed using boundary element method. The numerical method was validated with Sollitt and Cross [16] for the rectangular porous structure. Dalrymple et al. [2] used the eigenfunction expansion method to examine the submerged rectangular porous structure and porous structure backed by a rigid wall existing in the finite depth. The numerical study was performed for the plane wave and long wave approximation. An extensive numerical study has been performed on the wave absorption by rectangle porous barrier. The performance of the seawall protected by a submerged porous bar was examined by Reddy and Neelamani [14]. The wave force reduction on the caisson type breakwater due to the presence of submerged structure was investigated experimentally. Chen et al. [1] presented the numerical solution for submerged porous structure with seawall using time-dependent mild-slope approximation. A detailed comparison of the existing analytical model and the developed numerical approach was performed and presented on the effect of geometric configuration and permeability properties of the porous structure on the wave reflection. The

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reflection and transmission characteristics of two submerged horizontal plates were examined by Liu et al. [11]. Liu and Luo [10] developed a numerical model to examine the two submerged breakwater using long wave approximation. The variation in the width of the breakwater and depth of the two submerged breakwaters are analysed. Das and Bora [3] examined the damping of an elevated porous structure away from impermeable wall and the numerical model is developed for submerged porous structure near to the impermeable wall and far away from the impermeable wall. The matched eigenfunction expansion method is utilized for finding the reflection characteristics of the porous structure and rigid wall. The study was extended for the vertical porous structure placed on elevated bottom and multiple submerged structures by Das and Bora [4–6]. The study on the wave trapping by submerged porous structure is well examined by the researchers for the attenuation of wave height. The generalized solution for the submerged multi-layer horizontal porous plates was examined analytically and experimentally by Fang et al. [8] using matched eigenfunction expansion method. An effective practical designing criterion was developed due to the effect of porosity, width and number of plates. Zhao et al. [18] developed a numerical model for the vertical impermeable wall protected with submerged porous bar. The partial reflection from the impermeable wall is computed and compared with BEM solution and experimental data. Further, Zhao et al. [19] extended the study for analysing the multiple porous bars in the presence of end wall. Recently, Zhao et al. [20] examined the oblique wave scattering by submerged porous structure supported with seawall. The eigenfunction expansion method and multi-domain BEM approach are used to examine the wave behaviour. In the present study, a numerical model is developed for the wave interaction with single and multiple submerged porous structures with impermeable wall. The study demonstrates the wave reflection, transmission, wave forces and energy loss due to porous structures in finite water depth. The eigenfunction expansion method and continuity of velocity and pressure are used to analyse the effectiveness of the submerged porous structure.

2 Mathematical Formulation The wave absorption due to the presence of the submerged porous structure is analysed in the presence of impermeable wall under the assumption of linearized wave theory. The study is performed considering single porous structure in the presence of wall Fig. 1a and two porous structures in the presence of end wall (Fig. 1b). The monochromatic wave is incident along the positive x-direction. A two-dimensional coordinate system is considered in the analysis with x-axis being the horizontal and the z-axis considered vertically downward negative. The fluid domain in Fig 1a is divided into three regions, upstream open water region at −∞ < x < 0, −h < z < 0 as region 1, the porous structure region at 0 < x < U, −h < z < 0 as region 2 and downstream domain at U < x < U + L , −h < z < 0 as region 3.

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Fig. 1 a Submerged porous structure and b two porous structures with impermeable wall

In Fig. 1b, two submerged porous structures of width u and w are placed at a distance L from the end wall. The distance between the porous structures is considered to be V . Assuming that the wave elevation is simple harmonic in time with frequency ω, the velocity potential i (x, y, z, t) and the surface deflection ζi (x, t) can be written as i (x, y, z, t)  Re{φi (x, z)}e−i(λy−ωt) and ζi (x, t)  Re{ηi (x)}eiωt where Re denotes the real part with λ  k0 sin θ represents the progressive wave mode, θ is the angle of incidence and k0 is the progressive wave number. The spatial velocity potential, φi (x, y, z), satisfies the Helmholtz equation given by ∂ 2 φi ∂ 2 φi + − λ2 φi  0 for ∂x2 ∂z 2

− h ≤ z ≤ 0.

(1)

The linearized free surface boundary condition in each of the regions is given by

i ∂φi − φi  0 at z  0, i  1, 2, 3 . . . ∂z h where 1  3  5  ωgh and 2  4  ω The bottom boundary condition is given by 2

2

(2)

h(s+i f ) . g

∂φi  0 at z  −h. ∂z

(3)

In the free surface and the porous structure region, the progressive wave number satisfies the dispersion relation of the form ω2  gk0 tan hk0 h,  −gkn tan kn h

n  1, 2, 3 . . .

ω2 h(s + i f )  gp0 h tan hp0 h  −gpn h tan pn h

n  1, 2, 3 . . .

(4)

(5)

where g is acceleration due to gravity, k 0 is progressive wave number, k n is evanescent wave numbers in open water region, h is water depth, p0 is progressive wave number

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pn is evanescent wave numbers in porous structure region, f is linear friction factor, s is inertial term, i is imaginary number and ω is wave frequency. The dispersion relation for the open water region is solved with Newton–Raphson method and for the porous structure region perturbation method [13]. The effect of inertia and friction is considered in the dispersion relation for calculating the imaginary wave number in the porous water region. In the present study, porosity is considered as 40% and friction factor is considered as 0.25 [2, 3, 15]. The inertia force is given by the following equation:   1−e , (6) s  1 + Am e where s is inertia, e is porosity and Am is added mass due to wave propagation. The inertial effect, s is considered as unity [15, 16] and the friction factor is considered to be 0.25 [3, 4]. The porous structures are immovable which suggests that the porous structures are in static condition and the added mass is considered negligible.

3 Method of Solution The numerical model is developed in order to analyse the submerged porous structure in the presence of rigid wall. The wave reflection coefficient, transmission coefficient and energy loss from the porous structure are analysed using the eigenfunction expansion method.

3.1 Single Porous Structure with End Wall The velocity potentials φi (x, y) for i  1, 2, 3 satisfies the governing Eq. (1) along with the boundary condition (2) and (3) as defined in Sect. 2. The velocity potentials φi (x, y) for i  1, 2, 3 are of the form ∞  √ 2 2 √ 2 2  √ 2 2  Rn e−i (kn −λ )x In (z), φ1  ei (k0 −λ )x + R0 e−i (k0 −λ )x I0 (z) + n1

at − ∞ ≤ x ≤ 0 ∞   √ 2 2 √ 2 2  φ2  An ei ( pn −λ )x + Bn e−i ( pn −λ )(x−U ) Pn (z),

(7) at 0 ≤ x ≤ U

(8)

n0

φ3 

∞  

Tn ei

√

( pn2 −λ2 )(x−U )

+ Dn e−i

√

( pn2 −λ2 )(x−U −L)



In (z), at U ≤ x ≤ U + L ,

n0

(9)

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where Rn , n  0, 1, 2 . . . , An , Bn , n  0, 1, 2, . . . . and Tn , Dn , n  0, 1, 2, . . . . are the unknown constants to be determined. The eigenfunctions In (z) for n  0, 1, 2, . . . and Pn (z) for n  0, 1, 2, . . . given by ig cosh kn (h + z) for n  0 and In (z)  ω cosh kn h ig cosh pn (h + z) Pn (z)  for n  0 and Pn (z)  ω cosh pn h In (z) 

ig cos kn (h + z) for n  1, 2, . . . ω cos kn h ig cos pn (h + z) for n  1, 2, . . . , ω cos pn h

(10a) (10b)

where kn and pn for n  0, 1, 2, . . . are the eigenvalues. These eigenvalues satisfy the dispersion relation as defined in Eqs. (4) and (5). It may be noted that the eigenfunctions In (z)’s and Pn (z)’s satisfy the orthogonality relation as given by   0 for m  n, 0 for m  n, Im , In  j1,3  and Pm , Pn   Cn for m  n, Cn for m  n, with respect to the orthogonal mode-coupling relation defined by 0 Im In  

0 Im (z)In (z)dz and Pm , Pn  

−h

where Cn 



−g 2 ω2



Pm (z)Pn (z)dz, −h

2kn h+sinh 2kn h 4kn cosh2 kn h



and Cn 



−g 2 ω2



2 pn h+sinh 2 pn h 4 pn cosh2 pn h



.

The continuity of velocity and pressure at the interface x  0 and x  U , −h < z < 0 is given by φ1x  eφ2x and φ1  Gφ2 at x  0, eφ2x  φ3x and Gφ2  φ3 at x  U, (11a) The wall condition is adopted for obtaining the full wave reflection [9]: φ3x  μk0 φ3 , μ  i

1 − Kw at x  b + L , 1 + Kw

(11b)

Using the progressive wave mode, the solution for the boundary value problem considering the matching conditions and orthogonal mode-coupling relation for submerged porous structure with end wall is obtained as 

 i(1 − m 2 ) sin b p02 − λ2 KR  (12) 



  , 2m cos b p02 − λ2 + i(1 + m 2 ) sin b p02 − λ2 2me−ib( p0 −λ ) . 



  2m cos b p02 − λ2 + i(1 + m 2 ) sin b p02 − λ2 2

KT  



e

i L (k02 −λ2 )



2 1/2

(13)

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Considering both progressive and evanescent wave mode, the solution for the boundary value problem considering the matching conditions and orthogonal modecoupling relation for submerged porous structure with end wall is obtained as   0 N

k 2 − λ2  n  {1 − R0 } I0 (z)In (z)dz − Im (z)In (z)dz Rn k02 − λ2 i0 −h −h  ⎤ ⎡  0 N

p 2 − λ2  n   e⎣ (An − Bn Un ) Pn (z)In (z)dz ⎦, k02 − λ2 n0 0

(14)

−h

0 {1 + R0 }

I0 (z)In (z)dz +

N 

0 Rn

i0

−h

Im (z)In (z)dz −h

⎡ ⎤ 0 N   G⎣ (An + Bn Un ) Pn (z)In (z)dz ⎦, i0

(15)

−h

 ⎡ ⎤  0 N N

k 2 − λ2   n  ⎣ ⎦ e (Tn − Dn L n ) (An Un − Bn ) Pn (z)In (z)dz  p02 − λ2 i0 i0 −h

0

(16)

In (z)In (z)dz, ⎡ G⎣

N  i0

0 (An Un + Bn )

⎤

−h

Pn (z)In (z)dz ⎦ 

0

N 

(Tn + Dn L n )

i0

−h

In (z)In (z)dz,

(17)

−h

N  

  0 N   2 2 iμk0 + kn − λ L n Tn iμk0 − kn2 − λ2 Dn In (z)2 dz +

i0

i0

−h

0 In (z)2 dz  0,

(18)

−h

      where Un  exp iU (kn2 − λ2 ) , Vn  exp i V (kn2 − λ2 ) , L n       0 p02 −λ2 e 2 2 exp i L (kn − λ ) , m  s+i f , G  s + i f and Pn (z)In (z)dz)  2 2 k −λ 0

g(s+i f −1) . ( pn2 −kn2 )

−h

The infinite series sums of the algebraic equations as presented in (14)–(18) are obtained and the solution is obtained for the system of (5N + 5) equations. The velocity potentials in each of the three regions consist of (5N + 5) unknown coefficients such as Rn , Tn , n  0, 1, 2, . . . , N , An , Bn , Dn , n  0, 1, 2 . . . , N . The full solution is obtained by solving the system of linear equations in terms of wave reflection and transmission coefficients as

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K R  |R0 | and K T  |T0 |, Energy loss  1 −

(K R2

+

(19a)

K T2 ).

(19b)

3.2 Multiple Porous Structure with End Wall In the case of two porous structures in the presence of end wall, the velocity potentials φi (x, y) for i  1, 2, 3, 4, 5 satisfies the governing Eq. (1) along with the boundary condition (2) and (3) as defined in Sect. 2. The velocity potentials φi (x, y) for i  1, 2, 3, 4, 5 are of the form  √ 2 2 √ 2 2  φ1  ei (k0 −λ )x + R0 e−i (k0 −λ )x I0 (z) +

∞ 

Rn e−i

√

(kn2 −λ2 )x

In (z), at −∞ ≤ x ≤ 0

(20)

n1

φ2 

∞  

A n ei

√

( pn2 −λ2 )x

+ Bn e−i

√

( pn2 −λ2 )(x−u)



Pn (z), at 0 ≤ x ≤ u,

(21)

n0

φ3 

∞   √ 2 2 √ 2 2  1 Cn ei (kn −λ )(x−u) + Dn e−i (kn −λ )(x−V ) In (z), at u ≤ x ≤ V 1 , (22) n0

φ4 

∞  

E n ei

√

( pn2 −λ2 )(x−V 1 )

+ Fn e−i

√

( pn2 −λ2 )(x−W 1 )



Pn (z), at V 1 ≤ x ≤ W 1 ,

n0

(23) φ5 

∞  

Tn ei

√

(kn2 −λ2 )(x−W 1 )

+ Jn e−i

√

(kn2 −λ2 )(x−W 1 −L)



In (z) at W 1 ≤ x ≤ W 1 + L .

n0

(24) where V 1  u + V and W 1  u + V + w. The continuity of velocity and pressure at the interface x  0, x  u, x  u + V and x  u + V + w at −h < z < 0 is given by φ1x  eφ2x and φ1  Gφ2 at x  0,

eφ2x  φ3x and Gφ2  φ3 at x  u, (25a)

φ3x  eφ4x and φ3  Gφ4 at x  V 1 , eφ4x  φ5x and Gφ4  φ5 at x  W 1 . (25b) Using the orthogonal mode-coupling relation and the continuity of velocity and pressure with wall condition, the unknowns for the submerged porous structure with

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end wall is determined. The system of equation is represented for n  0, 1, 2, . . . , N , as   0 N  kn2 − λ2 {1 − R0 } I0 (z)In (z)dz − Rn Im (z)In (z)dz k02 − λ2 i0 −h −h ⎤ ⎡  0   N 2 2  pn − λ  e⎣ (An − Bn u n ) Pn (z)In (z)dz ⎦, 2 2 k 0 −λ n0 0

(26)

−h

0 {1 + R0 }

I0 (z)In (z)dz +

−h

⎡  G⎣

N  i0

N 

0 Rn

Im (z)In (z)dz −h

0 (An + Bn u n )

n0

⎤ Pn (z)In (z)dz ⎦,

(27)

−h

⎤  0 ∞ 2 − λ2  p n e⎣ (An u n − Bn ) Pn (z)In (z)dz ⎦ 2 2 p − λ 0 n0 −h ⎡ ⎤ 0   2  2 kn − λ ⎣ (28) (Cn − Dn Vn ) In (z)In (z)dz ⎦, p02 − λ2 −h ⎤ ⎡ ⎤ ⎡ 0  0 N N   (Cn + Dn Vn ) In (z)In (z)dz ⎦, G⎣ (An u n + Bn ) Pn (z)In (z)dz ⎦  ⎣ ⎡

n0



−h

⎡ ⎣

N 



i0

i0

−h

⎤  0 kn2 − λ2 (Cn Vn − Dn ) In (z)In (z)dz ⎦ k02 − λ2

(29)

−h

⎡ ⎤   0 N 2 2  pn − λ ⎣ (30) (E n − Fn wn ) Pn (z)In (z)dz ⎦, 2 2 k 0 −λ n1 −h ⎤ ⎡ ⎤ ⎡ 0  0 N N   ⎣ (Cn Vn + Dn ) In (z)In (z)dz ⎦  G ⎣ (E n + Fn wn ) Pn (z)In (z)dz ⎦, i0

−h

n0

−h

(31)

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⎡ e⎣

N 

0 (E n wn − Fn )

n0

−h

⎤

  N  kn2 − λ2 (Tn − Jn L n ) Pn (z)In (z)dz ⎦  pn2 − λ2 i0 0 In (z)In (z)dz,

⎡ G⎣

N 

0 (E n wn + Fn )

n0

⎤ Pn (z)In (z)dz ⎦ 

iμk0 +

i0

N 

0 (Tn − Jn L n )

i0

−h N  



(32)

−h



In (z)In (z)dz, (33)

−h

0

kn2 − λ2 L n Tn

In (z)2 dz −h

  N   iμk0 − kn2 − λ2 Jn In (z)2 dz  0, + 0

i0

(34)

−h

where In (z)and Pn (z), are eigenfunctions in open and porous water regions, 0   f −1) G  s + i f, Pn (z)In (z)dz)  g(s+i , u n  exp iu( pn2 − λ2 )1/2 , Vn  pn2 −kn2 −h       exp i V (kn2 − λ2 )1/2 , wn  exp iw( pn2 − λ2 )1/2 and L n  exp −i L(kn2 − λ2 )1/2 . The infinite series sums of the algebraic equations as presented in (26)–(34) are obtained and the solution is obtained for the system of (9N + 9) equations. The expansion formulae for each of the three regions consist of (9N + 9) unknown coefficients such as Rn , Tn , n  0, 1, 2, . . . , N , An , Bn , n  0, 1, 2, . . . , N , Cn , Dn , n  0, 1, 2, . . . , N , E n , Fn , Jn , n  0, 1, 2, . . . , N . The full solution is obtained by solving the system of linear equations in terms of wave reflection and transmission coefficients as in Eq. (19a,19b).

4 Numerical Results and Discussions The wave interaction with submerged porous structures are considered in two different conditions (i) submerged porous structure with end wall (ii) multiple submerged porous structures with end wall at a distance. Wave reflection, transmission, wave forces and energy loss from the porous structures are analysed and presented for both single and double porous barrier. Present study elaborates the importance of porosity, friction, angle of wave attack, width between the porous structures and non-dimensional width of the structure. The convergence in the wave reflection is observed with the increase in the evanescent wave modes N.

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4.1 Submerged Porous Structure Supported with Seawall Porous structure supported with sea wall is examined and the behaviour of the structure is analysed. Reflection coefficient depends upon porosity, angle of incidence, non-dimensional width of the porous structure and friction. Hence, in the first trial, the effect of angle of incidence is studied. Various values of angle of incidences 0°, 15°, 30°, 45° and 60° are considered and variation in reflection coefficient is studied. Maximum reflection is observed for lower values of angle of incidence and oscillation in reflection coefficient is observed for lower values of k 0 h. For higher values of angle of incidence, oscillation in reflection coefficient vanishes. The increase in the angle of incidence Θ causes variation in transmission coefficient. Energy loss from the porous structure is presented for various values of Θ. Figure 2a demonstrates the variation of reflection coefficient versus k 0 h for U/h = 0.5, f = 0.25 and e = 0.4 for various angles of wave incidence. In the case of k 0 h = 3, variation in wave reflection is observed at an angle of incidence 0°. An 1.12% reduction in reflection coefficient is noticed at 15°, 4.93% reduction at 30°, 13.078% reduction at 45° and 30.28% reduction at 60° angle of incidence. Figure 2b demonstrates the minimum variation in transmission coefficients for various values of angle of attack. Variation in angle of incidence causes minimum variation in energy absorption due to the sufficient width of the porous structure. In Fig. 2c, the variation in energy loss against k 0 h for various angle of incidences is presented, and Fig. 2d demonstrates the variation in wave forces against k 0 h. Increase in angle of incidence shows considerable variations in the wave forces. For angle of incidence 0° and 15° , a similar trend is noticed. For angle of incidences 30°, 45° and 60°, the trend of the wave forces is different compared with 0° and 15°. If the adopted porosity is unity, then the transmission coefficient is one K T = 1, which causes complete reflection at D0 = 1 [3] and complete reflection is observed due to end wall at x = 0. Due to total reflection from end wall, for minimum k 0 h values, maximum transmission (K T = 1) and maximum reflection (K R = 1) due to end wall at x = 0 are observed.

4.2 Two Submerged Porous Structures with Seawall In the present section, the discussion on wave interaction with two submerged porous structures is presented. Variation in wave reflection characteristics, transmission characteristics and energy loss are studied for various non-dimensional width of the porous structure. In Fig. 3a, for U/ h  0.5, maximum wave reflection is observed at k0 h  2.5, and again for U/ h  0.125, maximum reflection coefficient is observed at k0 h  5.5. Comparison between the U/ h  0.125 and 0.5 is that U/ h  0.5 is able to reflect the long waves and U/ h  0.125 is able to reflect the moderate waves. Figure 3b presents the wave reflection from the second porous structure. Minimum

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(a)

(b)

1.0

1.0 θ=00 θ=150 θ=300 θ=450 θ=600

0.8 0.6

0.6

KT

KR

0.8

θ=00 θ=150 θ=300 θ=450 θ=600

0.4

0.4

0.2

0.2 0.0

0.0 0

1

2

3

4

5

6

7

0

8

1

2

3

(c)

5

6

7

8

(d)

100

200000

θ=00 θ=150 θ=300 θ=450 θ=600

60 40

θ=00 θ=150 θ=300 θ=450 θ=600

180000 160000

Wave forces

80

Energy loss (%)

4

k 0h

k 0h

20 0 -20

140000 120000 100000 80000

-40

60000

-60

40000

-80

20000 0

-100 0

1

2

3

4

k 0h

5

6

7

8

0

1

2

3

4

5

6

k 0h

Fig. 2 Effect of angle of incidence on a reflection coefficient, b transmission coefficient, c energy loss and d wave forces for U/h = 0.5, f = 0.25 and e = 0.4

wave reflection is observed at 6 < k0 h < 7 from the first porous structure and maximum wave reflection is observed at k0 h ≥ 7 from the second porous structure. Hence, the maximum transmission from the first porous structure is reflected from the second porous structure. Falling trend in wave transmission Fig. 3c is observed in the presence of two submerged porous structures with end wall for all U/ h. Increase in width of the porous structure causes a decrease in wave transmission and an increase in energy loss. The oscillations in wave reflection and transmission vanish with the increase in width of the porous structure.

5 Conclusions In the present study, the importance of submerged porous structures on wave reflection, transmission, energy loss and wave forces is studied. The study is performed considering (a) single porous structure and (b) two porous structures in the presence of end wall. The monochromatic wave is incident on along the positive x-direction.

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(a)

277

(b)

1.0

1.0

U/h =0.125 U/h =0.25 U/h =0.375 U/h =0.5

0.8

0.8

0.6

K R2

K R1

0.6

0.4 0.2

0.4 0.2

0.0

U/h =0.125 U/h =0.25 U/h =0.375 U/h =0.5

0.0 0

1

2

3

4

5

6

7

8

0

1

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3

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4

5

6

(c)

8

(d)

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100

U/h =0.125 U/h =0.25 U/h =0.375 U/h =0.5

75

Energy loss (%)

0.8

KT

0.6 0.4 0.2

50 25 0 -25 -50

U/h =0.125 U/h =0.25 U/h =0.375 U/h =0.5

-75 -100

0.0 0

7

k0h

1

2

3

4

k 0h

5

6

7

8

0

1

2

3

4

5

6

7

8

k0h

Fig. 3 Effect of non-dimensional width of the structure on reflection from a structure 1 and b structure 2, c transmission coefficient and d energy loss for f  0.25, s  1, e  0.4 and Θ = 0°

The matched eigenfunction expansion method is adopted to solve the boundary value problem. • In the first case, the submerged porous structure with end wall is examined. Porosity is considered as 0.4, friction factor is considered as 0.25 and angle of wave attack is varied from 0° to 60°. • Oscillations are observed in reflection coefficient for lower values of angle of wave attack. Wave reflection is maximum for lower angle of wave attack and minimum for higher angle of wave attack. • Maximum wave reflection is observed at Θ = 0°, 30% reduction in reflection coefficient is observed at Θ = 60° compared with Θ = 0°. Very less variation in transmission coefficients is noticed for various values of angle of attack. • In the second case, the width of the submerged porous structure modelled in the first condition is divided into two porous structures. Similar relations are observed in reflection characteristics, transmission characteristics and energy loss. • The width of the submerged porous structure is varied from U/ h  0.125 − 0.5. Maximum reflection coefficient from the structure for all values of U/ h is 0.74 but an increase in width of the porous structure is able to reflect the long waves.

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From Fig. 3a for U/ h  0.5, maximum wave reflection is observed at k0 h  2.5, similarly for U/ h  0.125, maximum reflection coefficient is observed at k0 h  5.5. • The advantage of the two porous structures is that the transmitted wave from the first porous structure is reflected by the second porous structure. Acknowledgements The authors are thankful to National Institute of Technology Karnataka Surathkal and MHRD for providing necessary support. The authors also acknowledge Science and Engineering Research Board (SERB), Department of Science & Technology (DST), Government of India for supporting financially under the Young Scientist research grant no. YSS/2014/000812.

References 1. Chen HB, Tsai CP, Chiu JR (2006) Wave reflection from vertical breakwater with porous structure. Ocean Eng 33(13):1705–1717 2. Dalrymple RA, Losada MA, Martin PA (1991) Reflection and transmission from porous structures under oblique wave attack. J Fluid Mech 224:625–644 3. Das S, Bora SN (2014) Wave damping by a vertical porous structure placed near and away from a rigid vertical wall. Geophys Astrophys Fluid Dyn 108(2):147–167 4. Das S, Bora SN (2014) Reflection of oblique ocean water waves by a vertical rectangular porous structure placed on an elevated horizontal bottom. Ocean Eng 82:135–143 5. Das S, Bora SN (2014) Reflection of oblique ocean water waves by a vertical porous structure placed on a multi-step impermeable bottom. Appl Ocean Res 47:373–385 6. Das S, Bora SN (2014) Damping of oblique ocean waves by a vertical porous structure placed on a multi-step bottom. J Mar Sci Appl 13(4):362–376 7. Dattatri J, Raman H, Shankar NJ (1978) Performance characteristics of submerged breakwaters. Coast Eng 2153–2171 8. Fang Z, Xiao L, Peng T (2017) Generalized analytical solution to wave interaction with submerged multi-layer horizontal porous plate breakwaters. J Eng Math 105(1):117–135 9. Isaacson M, Qu S (1990) Waves in a harbour with partially reflecting boundaries. Coast Eng 14(3):193–214 10. Liu HW, Luo JX (2013) An analytical solution for linear long wave reflection by two submerged rectangular breakwaters. J Mar Sci Technol 21(2):142–148 11. Liu Y, Li YC, Teng B, Dong S (2008) Wave motion over a submerged breakwater with an upper horizontal porous plate and a lower horizontal solid plate. Ocean Eng 35(16):1588–1596 12. Madsen PA (1983) Wave reflection from a vertical permeable wave absorber. Coast Eng 7(4):381–396 13. Mendez FJ, Losada IJ (2004) A perturbation method to solve dispersion equations for water waves over dissipative media. Coast Eng 51(1):81–89 14. Reddy MM, Neelamani S (2005) Hydrodynamic studies on vertical seawall defenced by lowcrested breakwater. Ocean Eng 32(5):747–764 15. Sollit CK, Cross RH (1972a) Wave reflection and transmission at permeable breakwaters. MIT, RM persons laboratory technical report, pp 147–235 16. Sollitt CK, Cross RH (1972b) Wave transmission through permeable breakwaters. Coas Eng 1827–1846 17. Sulisz W (1985) Wave reflection and transmission at permeable breakwaters of arbitrary crosssection. Coast Eng 9(4):371–386

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18. Zhao Y, Liu Y, Li H (2016) Wave interaction with a partially reflecting vertical wall protected by a submerged porous bar. J Ocean Univ China 15(4):619–626 19. Zhao Y, Liu Y, Li H, Chang A (2017) Oblique wave motion over multiple submerged porous bars near a vertical wall. J Ocean Univ China 16(4):568–574 20. Zhao Y, Li HJ, Liu Y (2017) Oblique wave scattering by a submerged porous breakwater with a partially reflecting sidewall. J Mar Sci Technol 25(4):383–392

Beyond the Data Range Approach to Soft Compute the Reflection Coefficient for Emerged Perforated Semicircular Breakwater Suman Kundapura, Arkal Vittal Hegde and Amit Vijay Wazerkar

Abstract Prediction of reflection coefficient (Kr ) for emerged perforated semicircular breakwater (EPSBW) using artificial neural network (ANN) and adaptive neurofuzzy inference systems (ANFIS) is carried out in the present paper. A new approach has been adopted in the present work using ANN and ANFIS models for the prediction of the reflection coefficient (Kr ) for the wave periods beyond the range of the dataset used for training the network. The experimental data obtained for a scaled down EPSBW model from regular wave flume experiments at Marine Structure laboratory of National Institute of Technology Karnataka, Surathkal, Mangaluru, India was used. The ensemble was segregated such that certain higher ranges of wave periods were excluded in the training, and possibility of prediction was checked. The independent input parameters (Hi , T, S, D, R, d, hs ) that influence the reflection coefficient (Kr ) are considered for training as well as testing, where Hi is the incident wave height, T is the wave period, S is the spacing of perforations, D is the diameter of the perforations, R is the radius of the breakwater, d is the depth of the water and hs is the structure height. The accuracy of predictions of reflection coefficient (Kr ) is done based on the coefficient of determination (R2 ), root mean square error (RMSE), and mean absolute error (MAE). The study shows that ANN and ANFIS models may be used for prediction of reflection coefficient Kr of semicircular breakwater for beyond the data range of wave periods used for training. However, ANFIS outperformed ANN model in the prediction of Kr in the case of beyond the data range segregation method. Keywords Semicircular breakwater · ANN · ANFIS · Reflection coefficient Beyond the data range · Conventional data segregation

S. Kundapura (B) · A. V. Hegde · A. V. Wazerkar Department of Applied Mechanics and Hydraulics, National Institute of Technology Karnataka, Surathkal, Mangalore 575025, Karnataka, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_21

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1 Introduction Coastal environment is dynamic in nature and among the several challenges in the coastal environment wave attack on the beaches is prime. Emerged semicircular breakwaters are coastal structures that protect the lagoon area from the sea waves. Physical model studies on the breakwater are carried out in the laboratory to evaluate the hydrodynamic characteristics which are tedious and time-consuming. The quantum of research available in this area since the advent of semicircular breakwater is less. Few researchers have studied the performance of emerged and submerged semicircular breakwaters under regular and irregular wave conditions, by varying the perforation percentages [1–6]. From the literature, it is found that artificial intelligence has been successfully applied to study various wave parameters and to solve the coastal related problems. Prediction of hydrodynamic performance of several coastal structures has also been studied in the recent decades [7–12]. Though ANN models can efficiently model the nonlinear relationships between inputs and outputs, fuzzy logic better estimated the damage ratio as it closely mimics the environment. Modeling damage ratio as function of wave height, wave period, wave steepness, and breakwater slope is done as a substitute for generating a typical regression equation [7]. The stability number forecasting of the conventional rubble mound structures by fuzzy logic approach was found accurate, as it deals with the uncertainties not accounted for by empirical formulae. The input parameters to the developed FL model are permeability of structure, slope angle of breakwater, number of waves, surf similarity parameter, and damage level are used together to predict the stability number. Along with these parameters in Van der Meer’s equations, the nondimensional parameter, i.e., depth to significant height ratio (d/Hs), at the structure toe is also used so as to consider the effect of foreshore breaking waves. The spectral shape parameter is not considered in the study. The fuzzy logic model developed to predict the stability number of conventional rubble mound breakwater was superior compared to Van der Meer’s approach and Mase et al.’s ANN model. Van der Meer has tested for a wide range of conditions; under these circumstances, the current algorithm can be used anywhere in the world [8]. Forecasting of ocean wave parameters using a Takagi–Sugeno rule-based fuzzy inference system (FIS) based on the wind speed and direction, and the lagged-wave characteristics is possible using subtractive clustering method [13]. The wave transmission coefficient of horizontally interlaced multilayer moored floating pipe breakwater was found by ANFIS model. With a prior application of PCA, the most influential parameter on the wave transmission coefficient was found to be S/D [14]. Estimation of coefficient of reflection for several coastal and harbor structures using ANN was found to be more effective in comparison with the empirical formulae [15]. Wave reflection coefficient for emerged quarter circular breakwater for beyond the ranges of data (for wave period) with ANFIS model outperformed the ANN model. ANFIS performed reasonably well for the conventional method with dimensionless parameters in comparison with dimensional parameters [12].

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The study focusses on the prediction of the reflection coefficient for beyond the range of input data of wave periods that is not fed while training the network. Here, the prediction of reflection coefficient of semicircular breakwater (SBW) for higher ranges of wave period not fed while training ANN and ANFIS is done. The performance assessment of the proposed ANN, ANFIS models is based on the error metrics coefficient of determination, root mean square error, and mean absolute error.

2 Experimental Setup 2.1 Wave Flume and Data Acquisition The data was obtained from the experiments performed in a regular wave flume (Fig. 1) at the Department of Applied Mechanics and Hydraulics, NITK, Surathkal, Mangaluru, India [16–19]. The monochromatic wave flume setup with an emerged seaside perforated semicircular breakwater is considered for the study. Following are the characteristics of the wave flume: • • • • • • •

Wave flume length 45 m, Wave flume width 0.75 m, Wave flume depth 1.0 m, Type of wave flume two-dimensional, Wave generator used hinged flap type, Wave type monochromatic type, and Wave absorber type rubble mound.

The wave generating chamber is 6.3 m long, 1.4 m wide and 1.1 m deep with a gradual transition provided by a ramp between the flume bed and wave generation chamber. Also, a wave filter consisting of asbestos cement sheets spaced 100 mm apart was arranged parallel along the length of the flume to dampen the effect of successive reflections. Table 1 represents various wave and structural parameters.

Motor

Wave filter

Semicircular breakwater

Wave probe

Spending Beach Spending Beach

Bottom hinged wave flap

Fig. 1 Experimental setup of wave flume used

L/3

L/3

L

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Experimental range of values

Height of the incident wave, Hi (m)

0.06–0.22

Wave period, T (s)

1.4, 1.6, 1.8, 2.0, 2.2, 2.5

Water depth, d (m)

0.35, 0.40, 0.45

Semicircular breakwater radius, R (m)

0.45, 0.60

Semicircular breakwater height, hs (m)

0.502, 0.652, 0.730

Diameter of perforations, D (m)

0.012, 0.016

Spacing of perforations, S (m)

0.032, 0.048, 0.064, 0.096, 0.128

2.2 Data Segregation In the study, an attempt is made to predict the wave reflection coefficient for emerged perforated semicircular breakwater (SBW) for beyond the data range of wave periods (T) which is not trained into ANN and ANFIS. The entire dataset (consisting of 1044 input–output data points) is called global data (GD) and is sorted in the increasing order of wave periods (T). The line diagram in Fig. 2 shows the data segregation: the lower ranges of wave period (15%) and higher ranges of wave period (15%), i.e., a total of 30% is segregated. The inner 70% of the data (consisting 736 datasets) is randomized and is called curtailed data (CD) of which 70% is used to train and the remaining 30% is used to test the network. In this 30% test data, a part is replaced by the available 15% of higher ranges of data, and it is named as “beyond the range”. The network is expected to predict the reflection coefficient for those ranges not involved in the training.

Fig. 2 Typical data segregation procedure for performance prediction of SBW for incident wave period (T)

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2.3 ANN—Artificial Neural Network Model The basic artificial neural network (ANN) has input, hidden, and output layers. Learning of an ANN is called as training of the input–output pair, thus obtaining the connection weight values in the hidden layer and bias [20]. In the current study, the prediction of Kr for emerged perforated semicircular breakwaters (SBW) for beyond the data range of wave periods is done. Figure 3 shows a feed-forward back-propagation neural network (FFBPNN). The Levenberg–Marquardt algorithm having transfer functions like “tansig” (hidden layer) and “purelin” (output layer) is used here. A single hidden layer will suffice for nonlinear problems. However, the number of neurons in every layer is determined by trial and error method [8, 21, 22]. In the current study, several ANNs were trained altering the neuron number in the hidden layer. The best network is the one with the highest coefficient of determination with the experimental data and least error. The artificial neural network model predicts well provided there is no overfitting of the data. The parameters influencing the reflection coefficient (Kr ) are taken as input into the ANN models in the dimensional form. Here, xi yj zk wij , wjk bj , bk

input vector, hidden layer neuron, output vector, the weights, and bias values.

Fig. 3 A feed-forward back-propagation network [8]

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In a feed-forward network, xi the input layer neurons is transmitted on to the hidden layer neurons yj . The received values are further multiplied by its weight wij and add a bias value bj, i.e., (netj   xi wij − bj ). This is fed to transfer function to get the output from individual hidden layer neuron. Here, the transfer functions used is “tansig” (hidden layer) and “purelin” (output layer). The output vector zk is mapped to target vector tk as closely as possible by a back-propagation algorithm. A feed-forward back-propagation neural network back-propagates the error (E in Eq. 1) to update their weights (wij as in Eq. 2) in opposite direction to the way activities propagate in a network. Here, the “trainlm” is a training function that adjusts the weight and bias values in line with Levenberg–Marquardt optimization. The process of training is continued until predicted outputs and targets are acceptable.  (1) E (z k − tk )2 P

P

where P number of output neurons and P number of training patterns. wij (n)  α wij (n − 1) − ε

∂E ∂wij

(2)

where wij (n) and wij (n − 1) are the incremental weights between input and hidden layer during nth and (n − 1)th steps. α the momentum factor speeds up training in very flat regions of the error surface and avoids oscillations in the weights, and ε takes care of train process trapping in local minima instead of global. The network is trained until the model prediction and targets coincide for a given tolerance limit.

2.4 ANFIS—Adaptive Neuro-Fuzzy Inference System Model The present study involves an ANFIS structure generating a Sugeno-type fuzzy inference structure using “genfis2” (subtractive clustering). The genfis2 does not suffer the curse of dimensionality it can handle high dimension of input data unlike “genfis1” (grid partitioning method) which has as a limitation [23] and uses Gaussian membership function as the input membership function. A model generated from subtractive clustering method was found accurate compared to the one generated by FCM algorithm [24]. Subtractive clustering is a quick, one-pass algorithm for finding the cluster number and cluster center in the dataset automatically [25]. Only

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Sugeno fuzzy systems can be generated using subtractive clustering. In this type of clustering if data scale is set to “auto”, the genfis command considers the actual highest and lowest values in the dataset that to be clustered. Each data point zj  (xj , yj ) is assigned a potential Pj , with respect to its position from the rest of the data points [26, 27]. Pi∗



n 

e−α||xi −x j ||

j1

α Pi∗ α x γ ra

2

γ ra

(3) (4)

is the potential-value cluster center, is the weight between i-data to j-data, is the data point, is variable, and is cluster radius.

The highest potential data point, denoted by Pi∗ , is taken as the first cluster center c1  (d1 , e1 ). Further, the potential is recalculated for the rest of the points by not considering the first cluster center influence as in Pi∗  Pi∗ − Pk∗ ζ ζ e

−β||xi −ck ||2

(5) (6)

γ β 2 rb

(7)

rb  ra ∗ η

(8)

where P*I P*k c β ri η

new potential-value i-data, potential-value data as cluster center, cluster center of data, weight of i-data to cluster center, distance between cluster center, and is the quash factor. The highest potential data point is considered to be the next cluster center ck , if dmin Pk∗ + ∗ ≥1 ra P1

(9)

where d-min is the least distance between c1 and all cluster centers found before, and t data point is still accepted as the next cluster center c1 . New cluster centers c2 are found by further iterations. The cluster center is rejected by setting its potential to 0, when a cluster center does not satisfy the above conditions. The next highest potential

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data point P∗k is chosen as the new cluster center and retested. This clustering process terminates when the below mentioned condition is fulfilled: PK∗ < ε Pi∗

(10)

where ε is the reject ratio. The suggested ra , η, ε, and* can be found from the literature. Every cluster center is taken as a fuzzy rule describing the system behavior. The degree to which a rule i is fulfilled is defined in terms of a common form of subtractive clustering μikj  e

 2   −α x ij −ckj 

(11)

The best results are used to build input/output fuzzy models and then applied to the original data to build the system model.

3 Results and Discussion The application of ANFIS, subtractive clustering technique for the prediction of reflection coefficient (Kr ) of emerged perforated semicircular breakwater (EPSBW) for the wave periods beyond the data range used for training the network is carried out in the present study. The results are further compared with predictions made by artificial neural network (ANN). The details of data segregation corresponding to “beyond the data range” are as described in Sect. 2.2. The accuracy of both the ANN and ANFIS models during training and testing is validated using the performance index like R2 , MAE, and RMSE. The coefficient of determination (R2 ) shows the degree of association between model prediction and actual experiment values. Mean absolute error (MAE) is the average of absolute error between the predicted and actual values; here all the individual differences have equal weight. Root mean square error (RMSE) is the square root of the average of squared differences between the predicted and actual values. The RMSE gives high weight to large errors as the error is squared before taking the average.

3.1 Training and Testing of ANN Model for Prediction Beyond the Data Ranges of Wave Periods The prediction of wave reflection coefficient (Kr ) for beyond the data ranges of wave period used for training the network for emerged perforated semicircular breakwater (EPSBW) was carried out with different architectures of ANN. The ANN was fed

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with seven inputs and to predict 1 output. The neurons in the only set hidden layer are obtained on a trial and error basis with respect to the error metrics. Among the different model architectures tested, the model with one hidden layer consisting of 17 neurons predicted the wave reflection coefficient (Kr ) with the least error. The values of the measure of error are presented in Table 2. The coefficient of determination (R2 ) was found to be 0.94 indicating a good fit of the model. Figure 4 shows the comparison of model prediction and actual values of the reflection coefficient for various data points for beyond the data range testing using ANN.

3.2 Training and Testing of ANFIS Model for Prediction Beyond the Data Range of Wave Periods Training data loaded to generate input membership function consisted of seven inputs and one output data. In this case, the “genfis2” is used for training the data with a step size of 0.1 and the number of epochs 20. The ANFIS model has been trained for several radii and found that the model gave better results with an R2  0.96 for a radius of 0.9. The performance of the ANFIS model for beyond the data range is validated by error measures as shown in Table 2. The quantitative comparison between ANN and ANFIS model was done and there has been an improvement found in ANFIS model prediction with respect to ANN model prediction. The actual reflection coefficient and the ANFIS model prediction are plotted for various data points in Fig. 5. Figure 6 represents the input–output network of the ANFIS model for prediction beyond the data range. The application of subtractive clustering method

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has improved the prediction of reflection coefficient consuming less time for running the model as well.

4 Conclusions The study with a new approach of predicting beyond the ranges of the trained wave periods using soft computing techniques has been carried out. The obtained results for the complex nonlinear systems are reasonably good, and the following conclusions are arrived:

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i. The study shows that the prediction of wave reflection coefficient of emerged seaside perforated semicircular breakwater for ranges beyond the wave period used for training the network is possible by ANN and ANFIS models. ii. Lower RMSE, lower MAE, and higher coefficient of determination between the ANFIS model prediction and observed values in comparison with ANN model prediction demonstrated that the ANFIS model outperformed the ANN model.

References 1. Sundar V, Ragu V (1998) Dynamic pressures and run-up on semicircular breakwaters due to random waves. Ocean Eng 25(2–3):221–241. https://doi.org/10.1016/S0029-8018(97)000073 2. Dhinakaran G, Sundar V, Sundaravadivelu R (2002) Dynamic pressures and forces exerted on impermeable and seaside perforated semicircular breakwaters due to regular waves. Ocean Eng 29:1981–2004. https://doi.org/10.1016/S0029-8018(01)00106-8 3. Yuan D, Tao J (2003) Wave forces on submerged, alternately submerged, and emerged semicircular breakwaters. Coast Eng 48:75–93. https://doi.org/10.1016/S0378-3839(02)00169-2 4. Dhinakaran G, Sundar V, Sundaravadivelu R, Graw KU (2009) Effect of perforations and rubble mound height on wave transformation characteristics of surface piercing semicircular breakwaters. Ocean Eng (Elsevier) 36(15–16):1182–1198. https://doi.org/10.1016/j.oceaneng. 2009.08.005 5. Young DM, Testik FY (2011) Wave reflection by submerged vertical and semicircular breakwaters. Ocean Eng (Elsevier) 38(10):1269–1276. https://doi.org/10.1016/j.oceaneng.2011.05. 003 6. Kudumula SR, Mutukuru MRG (2013) Experimental studies on low crested rubble mound, semicircular breakwaters and vertical wall system. 4(3):213–226. http://journals.sagepub.com/ doi/pdf/10.1260/1759-3131.4.3.213 7. Yagci O, Mercan DE, Cigizoglu HK, Kabdasli MS (2005) Artificial intelligence methods in breakwater damage ratio estimation. Ocean Eng 32(17–18):2088–2106. https://doi.org/10. 1016/j.oceaneng.2005.03.004 8. Erdik T (2009) Fuzzy logic approach to conventional rubble mound structures design. Expert Syst Appl (Elsevier Ltd.) 36(3):4162–4170. https://doi.org/10.1016/j.eswa.2008.06.012 9. Mandal S, Patil SG, Hegde AV (2009) Wave transmission prediction of multilayer floating breakwater using neural network, International conference in Ocean Engineering (ICOE 2009). IIT Madras, Chennai, India 10. Deo MC (2010) Artificial neural networks in coastal and ocean engineering. Indian J GeoMarine Sci 39(December):589–596. http://nopr.niscair.res.in/handle/123456789/10807 11. Kim DH, Kim YJ, Hur DS (2014) Artificial neural network based breakwater damage estimation considering tidal level variation. Ocean Eng Elsevier 87:185–190. https://doi.org/10.1016/j. oceaneng.2014.06.001 12. Raju B, Hegde AV, Chandrashekar O (2015) Computational intelligence on hydrodynamic performance characteristics of emerged perforated quarter circle breakwater. Procedia Eng (Elsevier B.V.) 116(1):118–124. https://doi.org/10.1016/j.proeng.2015.08.272 13. Sylaios G, Bouchette F, Tsihrintziz VA, Denamiel C (2009) A fuzzy inference system for wind wave modeling. Ocean Eng 36:1358–1365. https://doi.org/10.1016/j.oceaneng.2009.08.016. https://doi.org/10.1016/j.oceaneng.2009.08.016 14. Patil SG, Mandal S, Hegde AV, Alavandar S (2011) Neuro-fuzzy based approach for wave transmission prediction of horizontally interlaced multilayer moored floating pipe breakwater. Ocean Eng (Elsevier) 38(1):186–196. https://doi.org/10.1016/j.oceaneng.2010.10.009

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15. Zanuttigh B, Mizar S, Briganti R (2013) A neural network for the prediction of wave reflection from coastal and harbor structures. Coast Eng (Elsevier B.V.) 80:49–67. http://dx.doi.org/10. 1016/j.coastaleng.2013.05.004 16. Sooraj M (2009) Sliding stability and hydrodynamic performance of emerged semicircular breakwater. M. Tech Thesis, NITK, Surathkal, Mangaluru, India 17. Sreejith (2015) Sliding stability and hydrodynamic performance of emerged semicircular breakwater. M. Tech Thesis, NITK, Surathkal, Mangaluru, India 18. Vishal K (2010) Hydrodynamic performance characteristics of one side and two side perforated semicircular breakwater. M. Tech Thesis, NITK, Surathkal, Mangaluru, India 19. Nishanth N (2008) Sliding stability and hydrodynamic performance of emerged semicircular breakwater M. Tech Thesis, NITK, Surathkal. Mangaluru. India 20. Azamathulla H, Asce M, Ghani AA (2011) ANFIS-Based approach for predicting the scour depth at culvert outlets 2(February), pp 35–40. https://doi.org/10.1061/(asce)ps.1949-1204. 0000066 21. Karsoliya S (2012) Approximating number of hidden layer neurons in multiple hidden layer BPNN architecture 3:714–717. http://ijettjournal.org/volume-3/issue-6/IJETT-V3I6P206.pdf 22. Panchal FS, Panchal, M. (2014) Review on methods of selecting number of hidden nodes in artificial neural network 3(11):455–464. http://www.ijcsmc.com/docs/papers/November2014/ V3I11201499a19.pdf 23. Hiremath S, Patra SK (2010) Transmission rate prediction for cognitive radio using adaptive neural fuzzy inference system. In: 2010 international conference on industrial and information systems (ICIIS). http://ieeexplore.ieee.org/document/5578727/ 24. Bataineh KM, Naji M, Saqer M (2011) A Comparison study between various fuzzy clustering algorithms. Jordan J Mech Indust Eng 5(4):335–343. http://jjmie.hu.edu.jo/files/v5n4/JJMIE230-09.pdf 25. Hiremath SM, Patra SK, Mishra AK (2012) Extended date rate prediction for cognitive radio using ANFIS with Subtractive Clustering. In: 5th International conference on computers and devices for communication (CODEC), Kolkata, pp 1–4. http://dspace.nitrkl.ac.in/dspace/ bitstream/2080/1821/1/Paper_cordic.pdf 26. Rahmat OK, Hassan A, Alauddin M, Ali M (2005) Generation of fuzzy rules with subtractive clustering. J Teknologi 43(D):143–153. https://doi.org/10.11113/jt.v43.782 27. Vernieuwe H, Georgieva O, De Baets B, Pauwels VRN, Verhoest NEC, De Troch P (2005) Comparison of data-driven Takagi—Sugeno models of rainfall—discharge dynamics. J Hydrol 302:173–186. https://doi.org/10.1016/j.jhydrol.2004.07.001

Design of a Reef for Coastal Protection P. V. Chandramohan

Abstract The beach at Pudussery has been badly eroded. The rock armour placed there to stop the erosion marred the beauty of the beach. An agency was commissioned to go into the matter and suggest remedies. The scheme suggested by them included a reef on the northern side. The three components of this scheme were a raised work area, a rubble bed for a wedge to be installed and a triangular-shaped wedge. The bed is submerged and was designed based on the formulations of Van der Meer. Engineering design of the components had to be carried out before execution. It was decided to use steel for fabrication of the wedge for easiness of construction. The paper deals with the engineering design of the components. Keywords Reef · Wedge · Submerged structure · Base pressure · Wave force

1 Introduction Pudussery had been a favourite spot of beach going public for years. But during recent times, the beach at Pudussery started eroding. This went to the extent that there was no beach left for the patronising public. For stopping the onward progress of erosion further into the land, large rock pieces were dumped at the interface with waves. This has slowed down the advance of erosion but intruded into the beauty of the beach. In any case, the beach could no more be patronised as a picnic spot. Please see Fig. 1. A study was conducted to restore the beach to its original glory. This study was done by M/s Sanctuary beach. After elaborate model studies, they had proposed certain activities to be taken up. One of the recommendations of the study was the formation of a reef at the northern side of the location. This would have reversed the erosion process and would have resulted in beach building.

P. V. Chandramohan (B) Navayuga Engineering Company Ltd., Plot 379, Road #10, Hyderabad 500033, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_22

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Fig. 1 Beach eroded away

2 General Arrangement of Components The shape of the reef and its components was arrived at by the agency which made the morphologic/oceanographic study. Engineering design of these components was to be carried out before execution. Please see Fig. 2. The reef consisted of three parts. One is the work area to be filled up at the coast. The second is a rock bed about 2 m high to act as bed for a wedge-shaped box. The third is the wedge to be fabricated with steel. The total length of the reef projecting into sea is 171 m. The work area is 52.75 m from the shoreline into the sea. Its width at the shore end is 108 m and that at the seaward end is 64 m. Top level of this area has been kept at +3.0 m. Please see Fig. 3. On the seaward side of the work, area is a rubble bed for locating the wedge. This bed is triangular in plan similar to the shape of the wedge. Deepest bed level is at −4.5. The shape of the caisson is triangular in plan. But in order to appreciate the 3-D shape, please see Fig. 4.

3 Hydraulic Parameters and Design Tidal range at the location was given as 1.0 m. A storm surge of another 1 m has also to be considered.

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3.1 Work Area This is mainly a raised platform with soil that has to be retained by a rubble wall. This is located in the surf zone and the top portion of the walls will be acted upon by breaking waves. It is proposed to use rubble mound to retain the soil. The size of the stones was arrived at by Hudson’s formula as per Shore protection manual [1]. Since it is very near to the shore, wave heights were small. A stone weight of 500 kg was used.

3.2 Rubble Bed for Wedge This is a submerged structure. Bed level varies from −4.5 to −1.5. Top of the bed is at −2.5. The low water level is 0.0. This means that there will be at least a water cushion of 2.5 m on top of the bed. In the transition area between the caisson and the work area, the rubble mound has a top level of 0.0. Structures with water cushion are often called submerged structure. Hudson’s formula will overestimate the size of stones. Van der Meer provides a procedure for the design of a submerged structure. This has been utilised here. But wave heights vary along the length of the bed as breaking wave heights are governed by the water depth. Breaker height varies with the stage of the tide as well. For example, wave height at high water at a bed level of −1.5 is 2.81 m while that at low water is 2.02 m. Water cushion also varies with

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the stage of the tide. So, for doing the design, a computer program was developed. Breaking wave height at high water varied from 2.81 to 5.1 m. Besides, the weight of armour stones varies with the ratio of structure height to water depth. This ratio varies with the stage of the tide as well. Please see Fig. 5. This shows the variation of the above ratio with water depth and also its oscillation with the stage of the tide. Envelopes have been constructed to show the values of the ratio at high water and low water. Please see Fig. 6. The weight of the stones arrived at by Van der Meer’s method is plotted against the water depth. Because of the water cushion present over the structure, wave energy was moderated to minimise the increase in stone weight. From the above analysis for various wave and tide conditions, maximum stone weight was arrived at as 1.52t. This was provided all through though this could be less on the leeward side. To get an idea about the effect of submergence on the weight of armour, a graph was plotted for constant wave parameter with varying submergence. Please see Fig. 7. Armour weight goes on reducing with an increase in submergence. This is to illustrate the role of water cushion on stone weight.

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3.3 Wedge As can be seen in Fig. 4, the wedge is triangular in plan. It is triangular in cross section as well. Length of the wedge is 60 m. Its width at the base is 50 m. As mentioned earlier it is triangular in cross section. Height at the apex is 2.5 m. Since the bed is at −2.5, the apex will be at 0.0. Initially, it was decided to make it as concrete caisson that could be floated out into position. But this posed problems in handling and flotation. So, the material was altered to steel. Please see Fig. 8 for the general arrangement of the wedge on the bed. Please see Fig. 9. Various sections of the wedge are shown. The wedge will always be under water. Externally it will be acted upon by wave forces like a submerged structure. The structure is taken as being acted upon by waves from one side. Breaking wave formulation by Takahashi et al. [2] was used to quantify the pressures and forces. The original formulation was for an exposed structure. This was slightly modified for a submerged structure. Besides, the pressures had to be reduced to an inclined surface. This was done using the formulation given in the Shore Protection Manual. It may be noted that the side angle of the wedge is only 5.71°. This is almost equivalent to a beach slope. So, the resultant horizontal forces were found to be much less. One salient feature of the force configuration is that the wave force acts only on the seaward side. Please see Fig. 10. Because of the flat angle of 5.71°, vertical forces were predominant. To resist the forces, 25 mm thick steel plates were used. Longitudinal stiffeners were provided at a spacing of 1.5625 m c/c, and cross stiffeners were provided at 1.875 m c/c. These plates were analysed based on the provisions of IS: 5620–1985 Structural design criteria for low head slide gates [3]. Stresses in the skin plates were limited to 99.26 MPa against 140, allowable. Stiffener beams were also made of plates and stresses were limited to 56 MPa. Stability of the wedge against external forces was investigated. Since forces on the leeward side were predominant, the overturning moment is towards the seaside. But as the base width is very large, 50 m, factor of safety against overturning came 45000

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out to be 7.6 and that against sliding, 567. As can be imagined bearing pressures at the base were very low. Two conditions were investigated. One is when the object

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is subjected to wave action from the seaside and the other, when there is no wave action. The base pressures are given in Fig. 10. Total weight of the wedge came to 737t.

4 Present Position Construction of the work area is in progress. Please see Fig. 11. This component is critical as fabrication of the wedge is to be carried out on this platform. After fabrication, the proposal is to slide the empty wedge down on to the wedge. Top of the work area is at +3.0 and will be above water level. It has to be installed at a base level of −2.5 under water. The project is slated to be completed within a few months.

5 Conclusion The shape of the reef was arrived at by model studies by morphologists/oceanographers. The task of the engineers is to design the various components of the scheme and implement it at the site. Constant interaction with the proponents was necessary during the design stage in order to achieve the desired results. One important point was that the work had to be carried out in marine conditions. Most of the components were located under water. The design had to take into account the

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construction aspects and had to be modified to suit the construction requirements. Changing over from concrete to steel was one such requirement.

References 1. U.S. Army Corps of Engineers (1984) Shore protection manual, pp 7–175 2. Takahashi, Tanimoto, Shimosako (1990) Wave and block forces on a caisson covered with wave dissipating block, Report of Port and Harbour research institute, Yokosuka, Japan, vol 30, no 4, pp 3–34 (in Japanese) 3. Bureau of Indian Standards (1985) IS: 5620–1985 Recommendations for Structural design criteria for low head slide gates

Assessment of Littoral Drift and Shoreline Changes for Fisheries Harbour on East Coast of India S. N. Jha and J. Sinha

Abstract Establishment of fishing harbour and fish landing centre is the most important activity for the development of marine fisheries infrastructure. However, littoral drift can be seriously impacted by the construction of fishing harbour and if due consideration is not given during construction of breakwaters, it may result in severe siltation on one side of harbour and erosion on the other side. This can eventually lead to complete failure of the harbour and result in a huge economic loss. To prevent such situation, mathematical modelling tools can play a significant role in estimating quantum and extent of littoral drift and assessing shoreline changes. Emphasis should also be given to corroborate the findings of mathematical modelling with actual field data. In this paper, a mathematical model study of shoreline changes has been undertaken for a proposed fishery harbour at Juvvaladinne on the east coast of India. It was found that annual northward and southward drift were of the order of 0.297 million cum and 0.001 million cum (almost negligible), respectively, while net and gross transports were estimated as 0.297 million cum and 0.298 million cum, respectively. Net transport was towards the north. It was also observed that northward transport was dominant during all periods. After 10 years, maximum cross-shore advancement is expected to be about 170 m on the southern side of the harbour while the maximum recession is expected to be about 130 m on the northern side of the harbour. The corresponding longshore effect of deposition and erosion was felt for 1500 m and 1300 m, respectively. Keywords Harbour · Littoral drift · Shoreline changes

S. N. Jha (B) · J. Sinha Central Water and Power Research Station, Khadakwasla, Pune 411024, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_23

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1 Introduction Development of marine fisheries infrastructure has gained considerable importance in recent years. Establishment of fishing harbour and fish landing centre is the most important activity for the development of such infrastructure. However, the natural course of shoreline can be seriously impacted by the construction of coastal hydraulic structures essential for the development of ports and harbours. If due consideration is not given during construction of hydraulic structures, it may result in severe siltation on one side of structure and erosion on the other side. This can eventually lead to complete failure of the harbour and result in a huge economic loss. In this paper, littoral drift and shoreline changes have been assessed due to the proposed development of a fishery on the east coast of India. The study area (Fig. 1a) with geographical coordinates 8° 47 15 N and 76° 40  7 E is located at Juvvaladinne in Nellore district of Andhra Pradesh state in the east coast of India where a fishery harbour is proposed to be developed for channelizing fishing activities. The proposed layout plan of the fishery harbour (Fig. 1b) consists of facilities like fish handling area, boat repairing yards, workshops, administrative office, etc. on the shore side while on the water side the facilities include two long training walls and a navigational channel of width 110 m and depth −4.0 m in between them. Training walls having length 835 and 619 m are proposed to be constructed normal to the shoreline up to −5.0 m depth contours in the deep sea. In the present study, the seasonal and annual littoral drift rates were estimated based on ship observed offshore wave data transformed into nearshore data, and shoreline changes were assessed due to the proposed training walls along the creek inlet.

Fig. 1 a Proposed location of fishery harbour at Juvvaladinne and b proposed development (schematic diagram)

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2 Site Conditions and Literature Review 2.1 Offshore Wave Climate For simulation of littoral drift and shoreline changes, nearshore wave data are essential. The wave data observed by the ships plying in the offshore region of Juvvaladinne reported by India Meteorological Department (IMD) during the past 30 years were considered to arrive at nearshore wave data. The rose diagram wave climate during the entire year in the offshore region of Juvvaladinne is presented in Fig. 2. These data indicate that the predominant wave directions in deep water are south-west, north-east, NNE and WSW with the maximum wave height of the order of 4.5 m. In order to get the nearshore wave climate, the deep water wave data were transformed at a location of −10 m depth contour near the proposed fishery harbour at Juvvaladinne using the SW module of MIKE 21 software.

Fig. 2 Rose diagram for wave heights in offshore region of Juvvaladinne for annual period (January–December)

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2.2 Tidal Levels and Currents The maximum tidal range at the study area was of the order of 1.1 m and it was also observed that the maximum current in the vicinity of Juvvaladinne was of the order of 0.5 m/s while the average current was of the order of 0.35 m/s.

2.3 Sediment Characteristics The bed material in the vicinity of Juvvaladinne was mainly composed of fine sand and clayey silt, having mean grain size, D50 , of the order of 0.10 mm.

2.4 Littoral Drift and Shoreline Changes Longshore sediment transport rates near Visakhapatnam coast are estimated by Panigrahi [1]. They estimated the annual net transport of 0.4–0.6 million m3 (northward) and gross transport of 1.64 million m3 at Visakhapatnam. The longshore sediment transport study [2] also showed that the general direction of longshore transport was towards the north-east during March to October and south-west during November to February. The longshore transport rate was high during the south-west monsoon period from June to September. Based on the measured data, wave height and current speed, longshore sediment transport rates were estimated by Sanil Kumar et al. [3] wherein which it was reported that along the east coast, longshore transport was southerly from November to February, northerly from April to September and variable during March and October. Vandana Kumari [4] reported net northerly drift of 0.35 M m3 near Kondurupalem inlet which is about 25 km south of Juvvaladinne. They also inferred that the increase in wave energy during July to September causing the maximum growth of the sand spit observed in the field. Recently, Kannan et al. [5], using the remote sensing data for a period of 1989 to 2015, inferred that in Juvvaladinne shoreline was accreting on the south side of the creek at the rate of 10 m/year while the shoreline was getting eroded on the northern side at the rate of 20 m/year. This also suggests that the net sediment transport at the study area is towards the north. Field observation at the site further revealed the combined effect of the water discharge from the creek and the littoral drift resulting into the shifting of the inlet mouth of the creek in the range of 1 km during the year.

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3 Modelling Techniques Bathymetry in the offshore region of Juvvaladinne consists of almost parallel contours from −10 m depth up to −100 m depth. The bathymetric data in the offshore were taken from CMAP database. It was found that the bed slope in the vicinity of the proposed site is very mild 1:850 till the depth of −1 m and then increases sharply to 1:100 till the depth of −8 m. Wave transformations from deeper water to shallow water region were computed using the MIKE 21 Spectral Wave (SW) model. This model can compute the growth, transformation and decay of wind-generated waves and swells in both offshore and coastal areas. MIKE 21 SW [6] model is based on unstructured meshes, which can handle non-linear wave–wave interaction and all other important wave phenomena like wave breaking, bottom friction, wave diffraction, refraction and shoaling effects, etc. This model will provide the important wave parameter like significant wave height, mean wave direction and radiation stresses at the chosen point or region in the shallower depth. Wave action balance equation is solved using cell-centred finite volume method. In horizontal Cartesian coordinates, wave action balance equation is given as S ∂N → + ∇ · (ν N)  ∂t σ

Nomenclature → N( x , σ, θ, t) t → x (x, y) → ν (Cx, Cy, Cσ, Cθ) S ∇

the action density, time (s), Cartesian coordinates, propagation velocity of a wave group in four→ dimensional phase space x , σ and θ , source term for the energy balance equation, → the four-dimensional differential operator in x , σ and θ.

In the present study, an area of 250 km alongshore and 50 km cross-shore with an unstructured mesh was considered for the simulation using MIKE 21 SW model. The cross-shore region was adopted from high water line near the shore to −100 m depth contour in deep sea. The model was run for incident waves of wave height 4 m for all the predominant wave directions in deep sea, viz. NW, NNW, North, NNE, NE, ENE, East, ESE, SE, SSE and South. Wave heights and wave directions at −10 m depth contour near the location of the proposed training walls were extracted from the model results for all the incident wave directions. The extracted information of wave heights and directions at −10 m

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Fig. 3 Rose diagram for wave heights at Juvvaladinne for annual period (January–December)

depth contour was applied to seasonal and yearly offshore wave climate to obtain the frequency distribution of wave heights and wave directions near the location of the existing training walls as depicted in Fig. 3. From the figure, it can be seen that the wave climate for the annual period indicates that the predominant wave directions are from East, ENE and ESE with the maximum wave height of the order of 3.5 m and the percentage occurrence of 6%, 36% and 28%, respectively, for the annual period.

4 Model Simulations and Results Some of the most important parameters that need to be accounted in the simulation of littoral drift are waves (both regular and irregular), currents induced by the tide, wind effect, type and size of sediments and bottom friction. Further, wave breaking, wave refraction and wave shoaling influence the quantum and distribution of the drift. LITPACK model [7], which takes into consideration all the above parameters for an arbitrary beach profile, was used for the present study. Details of the method of computation and model capabilities are available in the reference. In the model, wave condition obtained from the SW model was taken as input for different seasons. Suspended load and bedload under the influence of wave breaking

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(a) SW Monsoon

(b) NE Monsoon

(c) Non Monsoon

(d) Annual Period

Fig. 4 Cross-shore distribution of littoral drift for different periods

and current condition were computed for each incident wave. To compute total annual drift, sediment transport obtained from each incident waves was combined. Crossshore sediment transport was computed using sediment profile and bathymetry of Juvvaladinne. The model assumes the depth contours parallel to the seashore. Figure 4 shows the beach profile (cross-shore bed profile) near the Juvvaladinne site at Andhra Pradesh which is used for the littoral drift computation. The profile covers a distance of 3.0 km extending up to about −10 m depth contour. It was found that −5 m depth contour is about 1.25 km from the coastline. The profile is discretized into 320 grid points with a uniform grid size of 10 m. Littoral drift at the Juvvaladinne site was simulated using LITDRIFT module of LITPACK, which takes into account the cross-shore profile, the sediment characteristics and the wave climate as input. The general orientation of the coastline at the proposed fishery harbour is NNWSSE making an angle of about 67° with respect to north. Further, depending on the wave direction with respect to the coastline, the littoral drift will be either directed northward or southward along the shoreline. The model was simulated for the crossshore profiles for the seasonal and the annual wave climates. Based on the simulation of littoral drift, the annual net and the gross transports were estimated to be of the order of 0.297 and 0.298 million m3 , respectively. The model was also used to compute seasonal transport rates. The distribution of littoral

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Table 1 Transport rates (million cum) Period Northward Southward SW monsoon NE monsoon Non-monsoon Annual

0.146 0.076 0.077 0.298

0.002 0.001 0.000 0.001

Net

Gross

−0.144 −0.075 −0.077 −0.297

0.148 0.077 0.077 0.299

transport rates for the three seasons and for the annual period. It may be noted that the northward drift is indicated as negative and the southward drift is indicated as positive in the figures. It could be seen from Fig. 4a that during south-west monsoon, northward transport (0.146 million cum.) is more than the southward transport and the transport occurs within a range of 1700 m from the shoreline. It could also be seen that main drift moves within a range of 1250 m from the coastline. The peak of the drift is observed at that depth of −3 m. During north-east monsoon also, northward transport (0.076 million cum) is more than southward transport and the transport is mainly confined to a range of 1400 m from the shoreline (Fig. 4b). However, the peak of the drift is observed at that depth of −2 m. During the non-monsoon period, the northward transport is predominant (0.077 million cum), and the peak of the littoral drift is observed at less than −1 m of depth (Fig. 4c). It can be seen from Fig. 4 (d) that for the entire annual period sediment drift moves within a range of 1250 m from the shoreline and peak of the littoral drift transport occurs at the depth of −3 m. Further, it could be seen that the northward transport is dominant during all the seasons. It could also be seen that about 75% transport occurs between 750 and 1250 m from the shoreline, i.e. between −0.5 and −4.0 m depth contours. Annual and seasonal net and gross littoral drift were estimated using LITDRIFT model. The northward and the southward drift are calculated based on the gross and the net littoral drift [8]. The littoral drifts are reported in Table 1. It could be seen from the table that the annual northward and southward drift are 0.297 million cum and 0.001 million cum, respectively, while the net and the gross transports are 0.296 million cum and 0.298 million cum, respectively. The net transport is towards the north. It is also observed that the major northward transport occurs during SW monsoon. For predicting coastline changes over a period of years, LITLINE module of LITPACK [7] modelling system was used. This model can simulate the effect of various coastal structures on natural sediment transport and predict accretion or erosion in the coastal region. The continuity equation used in the model allows the introduction of source or sink in the model as per the site condition. The input parameters consist of depth profile, coastline positions, tide and wave data, size and position of structures on the coastline. The model is divided into definite number of grids and computation is performed for each individual grid. The integration of data over a period of time provides shoreline evolution over a period of time. For the shoreline evolution model, a shoreline of 10.1 km length was considered. The length was divided into 1010 grid points with a uniform grid size of 10 m. The

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Fig. 5 Shoreline evolution after second, fourth, sixth, eighth and tenth year

proposed location of the training walls was schematically located in the middle of the coastline. The transport rates were computed for the above-mentioned profile, which was used as input to the shoreline evolution model for LITLINE module of LITPACK software. As mentioned earlier, the Juvvaladinne fisheries harbour was proposed at the mouth of the creek, siltation due to littoral drift was expected. It was found from the field survey that creek mouth opens directly into the sea only in south-west monsoon. However, creek mouth gradually shifts to northern side due to deposition of silt in all other seasons. This indicates the dominance of northward drift in all the seasons. The model was used to simulate for the proposed condition in which the training walls were provided at the mouth of the creek. The model was run with the schematic layout of the training wall for a period of 10 years. The predicted shoreline change obtained from the model simulation is shown in Fig. 5. As the net transport is directed towards the north, the deposition on the south side of the southern training wall is noticed while on the north side of the northern, training wall erosion is observed. Further, the model was simulated subsequently for a period of 2, 4, 6, 8 and 10 years, and the maximum cross-shore advancement on the south side of the southern training wall for each period would be obtained as 60 m, 95 m, 125 m, 150 and 170 m, respectively, while maximum cross-shore recession on the north side of the northern training wall is 40 m, 70 m, 95 m, 115 m and 130 m from the prevailing

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coastline position. This is in line with the Kannan [5] observations based on 25 years remote sensing data. However, the quantum of both deposition and erosion is on the higher side in the present paper as the construction of training walls is likely to arrest more amount of sediment on the south side of southern training wall. It may be noted that during the LITPACK model simulation, it has been assumed that the shoreline consisted of erodible material. Further, the corresponding longshore effect of deposition was felt for a length of about 2000 m while the corresponding longshore effect of erosion was felt for a length of about 2500 m. The maximum cross-shore advancement and erosion of the shoreline in 10 years period would be of the order of 170 m and 130 m, respectively. Although accretion on the south side of the southern training wall is limited up to one-third of the proposed length (619 m) of the training wall, it would arrest only partial littoral drift as the surf zone extended up to 1.5 km during SW monsoon. It is recommended that sand bypassing arrangement may be made on the south side of southern training wall and beach nourishment measures should be made on the north side of the northern training wall.

5 Conclusions Mathematical model studies have been carried out to estimate littoral drift at the Juvvaladinne site at Andhra Pradesh and to assess the likely changes in the coastline due to the proposed northern training wall of length 835 m and southern training wall of length 619 m on either side of the Upputeru River. Following are the main conclusions of the model studies: 1. The annual northward and southward littoral transports are estimated to be 0.298 million cum and 0.001 million cum, respectively. The net longshore transport is towards the north, which mostly occurs during SW monsoon. 2. Based on the distribution of annual longshore transport, the sediment drift moves within a range of 1250 m from the shoreline and the peak of the littoral drift transport occurs at the depth of −3 m and about 75% transport occurs between 750 and 1250 m from shoreline, i.e. between −0.5 and −4.0 m depth contours. 3. As the net transport is directed towards the north, the deposition occurs on the south side of the proposed southern training wall. After a period of 2, 4, 6, 8 and 10 years, the maximum cross-shore advancement on the south side of the southern training wall for each period would be obtained as 60 m, 95 m, 125 m, 150 and 170 m, respectively, while maximum cross-shore recession on the north side of the northern training wall is 40 m, 70 m, 95 m, 115 m and 130 m from the prevailing coastline position. The corresponding longshore effect on the north side of the northern training wall would be felt up to 2500 m, while the corresponding longshore effect on southern side of the southern training wall would be felt up to 2000 m.

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4. In 10 years period, accretion on the southern side of the training wall is limited up to one-third of the training wall, but it would arrest only partial littoral drift as the surf zone would be extended up to 1.5 km especially during SW monsoon. Acknowledgements The authors are grateful to Dr. (Mrs.) V. V. Bhosekar, Director, CWPRS and Mrs. A.M. Vaidya, Scientist D for their guidance and constant encouragement during the course of study. The authors express their deep gratitude for granting permission to publish this paper.

References 1. Panigrahi JK, Sathish Kumar V, Tripathy JK (2012) Littoral drift by alongshore flow at Visakhapatnam–East Coast of India. J Hydro-environ Res 4(2010):317–327 2. Chandramohan P, Nayak BU, Raju VS (1990) Longshore sediment model for south Indian and Shri Lankan coasts. ASCE J Waterw Port Coast Ocean Eng 116:408–424 3. Sanil Kumar V, Pathak KC, Pednekar P, Raju NSN, Gowthaman R (2006) Coastal processes along the Indian coastline. Curr Sci 91(4):530–536 4. Vandana Devi V (2014) Integrated management of Kondurupalem lagoonal inlet on East Coast of India. PhD thesis, Anna University 5. Kannan R, Ramanamurthy MV, Kanungo A (2016) Shoreline change monitoring in Nellore Coast at East Coast Andhra Pradesh District using remote sensing and GIS. J Fish Livest Prod 4:161 6. MIKE 21 SW (2013) User manual, Danish Hydraulic Institute (DHI), Denmark 7. LITPACK (2013) An integrated modelling system for littoral processes and coastal kinetics, Danish Hydraulic Institute 8. CWPRS technical report no. 5496 (2017) Mathematical model studies to assess littoral drift distribution and shoreline changes due to development of fishery harbour at Juvvaladinne, A.P.

Impact of Flow-Driven Debris on Coastal Structure During Tsunami Bore S. Harish, V. Sriram, V. Sundar, S. A. Sannasiraj and I. Didenkulova

Abstract Tsunami impact on infrastructure along the coast causes severe destruction, loss of human lives and negative influence on the economy. When tsunami propagates towards the coastline, the flow often resembles a bore which propagates with a high velocity and takes everything on its way, including heavy objects. When reaching the structure, this water-driven debris induces a kind of impact force and magnifies the load on structures along the coast. The present study is aimed to measure the load of tsunami-borne debris on a building constructed near the shoreline. In many situations, tsunami or any flood nearshore resembles a surge caused by a dam-break event; therefore, to model this process, we conducted our experiments by setting up a dam-break arrangement in a wave flume of 72.5 m length, 2 m wide and 2.5 m deep at the Department of Ocean Engineering, IIT Madras, India. A Froude scale of 1:20 was adopted for modelling the coastal structure and the debris placed over a beach slope of 1:30. The hydraulic bore was generated by a sudden opening of the gate of the tank. We considered three water depths of 0.8, 0.9 and 1.0 m. The debris was modelled as a box-shaped structure weighing 4.2, 5.6 and 6.0 kg. A video camera was used to capture the surging of the hydraulic bore and to study the character of debris motion during impact. The impact forces acting on the structure due S. Harish (B) · V. Sriram · V. Sundar · S. A. Sannasiraj Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai 600036, India e-mail: [email protected] V. Sriram e-mail: [email protected] V. Sundar e-mail: [email protected] S. A. Sannasiraj e-mail: [email protected] I. Didenkulova Department of Marine Systems, Tallinn University of Technology, Tallinn, Estonia e-mail: [email protected] I. Didenkulova Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Nizhny Novgorod, Russia © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_24

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to debris were measured with a load cell. The acquired data were further analysed and discussed. Keywords Coastal structures · Tsunami bore · Dam-break set-up · Impact force Debris

1 Introduction Environmental impacts are significant in the areas nearer to the points of impact of the extreme scenarios like a tsunami. The stretch of the coast consists of houses, gas stations, important infrastructures, industrial areas and more importantly nuclear power plant facilities would be the most vulnerable due to potential contaminations from hazardous materials during extreme coastal calamity. Its post-event significantly affects the livelihood of the coastal community. Prior to the occurrence of tsunami in December 2004, the design of structures for such extreme calamity was considered as minor importance due to the fact that such occurrence has high return period. Improving the design guidelines for structures near coastline is brought to concern after the devastating effect of tsunami 2004. Further, tsunami or coastal flooding carry destructive debris that can have devastating impacts on all facets of the environment, as was observed and felt during 2011 Japan tsunami particularly its effect on Fukushima as well as during 2004 Indian Ocean tsunami. This debris carried by the extreme coastal events may collide with the nearshore structures leading to additional loading, the effect of which would not have been taken into account in the design. The debris-induced loading can be quite large which could often be one of the greatest causes for the damage of the structures. It is necessary to properly understand and to predict the impact loading due to debris on the structures that need to be incorporated in their design. A structure along the coastal turf can be torn down in a single natural calamity like tsunami if the loading of debris is not taken into account in the design. Available codes and design guidelines contain information for calculating the impact force of debris on the structure during floods but specifically not for violent energetic floods like tsunami. ASCE07 [3] provides a more general classical equation incorporating the effect of water depth, orientation of building to the direction of debris, blockage effect and the importance of the building for the impact load caused by debris during floods. FEMA P-646 [6] adopted the use of contact stiffness approach for finding the impact force of debris on structures due to tsunami. It describes debris as well as its type (like wooden logs, barges, shipping containers, etc.) to be chosen in evaluating the force due to its impact on a structure as a function of its location. It also provides formula for finding lower and upper bound values for design flood velocity. The current guidelines offer simple but not well-validated approaches to define the debris impact loads on structures.

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The present study will thus give an insight into the following aspects: • Incorporation of the debris impact on loadings in the design guidelines, currently, the existing ones lack the information on how to deal with such a wall of waterdriven debris. • Studies on impact effects of debris-laden flow with its complex interaction between loading and structural vibrations/resistance will be a vital contribution. • In the light of ageing infrastructure and hazards (such as breakage of ageing reservoir dam, storm surges or tsunami), it is important to increase the constructional safety of the structures near to the hazard-prone areas.

2 Physical Model Study 2.1 General Physical modelling of debris impact on structures during an extreme coastal event like tsunami is carried out in a 2 m shallow flume in the Department of Ocean Engineering, IIT Madras. The characteristics of tsunami can be approximated to that of solitary waves having very large time period propagating with high velocity in deep waters. However, on approaching the shoreline, the celerity decreases, whereas wave height increases resulting in breaking of waves. These broken tsunami waves inundate the low lying areas like the rapidly advancing hydraulic bore. This rapidly advancing tsunami bore resembles closely to the hydraulic bore generated during the dam-break wave [10]. Chanson [4, 5] demonstrated the analogy of using dambreak waves to quantify closer to the tsunami bore. Thus, the study is carried out by constructing a dam-break arrangement in the flume.

2.2 Dam-Break Set-up The dam-break arrangement was modelled as a tank of dimension 2 m × 2 m × 2 m in the flume. The tank was provided with a gate hinged on the front side of the tank from the water would be released. The swinging gate is rapidly opened manually by providing an additional pulling force to the door for generating the dam break bore.

2.3 Instrumentation and Model Details Three resistant type wave probes (W1-W3) with 2 mm accuracy were placed along the centre line of the flume. The first wave gauge, W1, was placed at 7.4 m from the opening door of the dam as shown in Fig. 1. The other two probes, W2 and W3,

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Fig. 1 Longitudinal sectional view and plan view of the experimental flume and experimental set-up (shown as WP1, WP2 and WP3 in the figure)

were fixed at 0.5 and 1 m from the first wave probe, respectively. This was used to register the bore velocity. The flume set-up showing the location of wave gauges, the structure, the dam break set-up and the debris is shown in Fig. 1.

2.4 Modelling of Debris The dimension of the debris of FRP was chosen as 30 cm × 15 cm × 20 cm which is comparable to the dimension of a conventional 20 feet shipping container with a scale of 1:20. A wooden box of the above-mentioned dimension was made with a thickness of approximately 6 mm. The draught was changed by adding steel plate of different weights inside the debris.

2.5 Structure Modelling The dimensions of the structure of steel considered were 70 cm × 30 cm × 30 cm to represent a four-storey structure in the coastal area with a model scale of 1:20 as shown in Fig. 2. The bottom face of the structure is closed in order to avoid the moon pool effect during the propagation of the bore. The provision was made for attaching a load cell at the top of the structure which in turn is rigidly fixed to a steel frame supported over the flume. The structure is mounted to a fixed steel frame through load cell. A small gap of 3–5 cm between the bottom floor and the structure base

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Fig. 2 Modelled structure and debris

facilitated the measurement of the total force on the structure without any disturbance to the vibration of structure [1]. Three types of bores were generated by varying the water depths in the experimental tank from 800 to 1000 mm in terms of 100 mm. The wave gauges registered the signatures of the approaching bore velocity and height. The average bore velocity was calculated by using the time the bore reached the wave gauges positioned at the known spacing of 500 mm. Prior to conducting the experiments, the debris was placed in its position at a distance of 2 m from the structure [11]. The 2 m distance was chosen such that debris does not miss the structure. The velocity of the debris was calculated during its movement in the surge from the video recorded during each test case. A minimum of two repetitions for each test case was carried out until the force recorded during the impact of debris was closer in the successive repetitions. The flume tests were carried out for each of the three water depths aforementioned and by varying the weights of the debris. The debris of smaller weight moved with a larger velocity comparable to the larger weight because of the bottom friction offered by the flume bottom initially as well as due to its own weight. In order to depict the real phenomenon of debris movement in the tsunami waves, the debris were not restricted in their movement in any of its six degrees of freedom, while floating in the water. The experiments were carried out for the dry bed condition which is the one in which there is no trace of water on the surface of the flume bed. Thus, when the dam is opened, the surging of the hydraulic bore exactly resembles the surging of the tsunami bore in the coastal area. An experiment would commence by impounding the water depth behind the swing gate in the experimental tank. The water would be filled inside the tank by pumping water inside the tank. The debris was placed in its position before starting the test. The gate was manually opened by the opening

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arrangement provided with the experimental tank. The signals from the load cell and wave probes were acquired simultaneously through separate data acquisition software.

3 Bore Velocity 3.1 Bore Velocity Formulas Several formulae were proposed by researchers for a rough estimation of the velocity of the surging hydraulic bore during tsunami. FEMA 55 [7] provides a formula for both lower and upper bound values of bore velocity during a riverine flooding. However, this manual does not provide any analytical formula for finding the velocity of the tsunami bore. Shen and Mayer [12] provided an analytical solution for the runup bore velocity given by Eq. 1, which is applicable to uniformly sloping bed: u



2g X tan α

(1)

where X is the distance from the maximum run-up location to the location of interest and α is the beach slope. According to Yeh [14], the above equation provides a maximum value for the run-up velocity, in which case the beach is not of uniform slope. Yeh [13] proposed the bore velocity based on the elevation of the land from the initial shoreline:   z (2) u  2g R 1 − R where R is the ground elevation at the maximum inland run-up of the bore and ‘z’ is the ground elevation at the point of interest for measurement of bore velocity. If z/R is set to zero, then the above equation gives the tsunami bore velocity at the point of interest. This equation is adopted by FEMA P646 [6] for evaluating the tsunami bore velocity at the point of interest on the shore. From the analytical formula proposed by FEMA P646 [6], the tsunami bore velocity was found to be 2.2 m/s at the point of location of debris from the gate of the dam.

4 Results and Discussions 4.1 Initial Bore Velocity Test In this first stage of the experiment, tests were initially conducted for determining the bore velocity and to obtain bore profile by the sudden opening of the gate for

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the impounding water depths of 800, 900 and 1000 mm. Since the wave probes were placed very near to the debris, the resulting velocity obtained from the wave probe reading will provide the instant bore velocity near the debris. Bore velocity is calculated using the time interval required for the bore to reach height of 50 mm in the successive probes [1, 9]. The averaged velocity measured using the wave probes are approximately found to be 3.2 m/s, 3.56 m/s and 3.8 m/s for the impounding water depth of 800 mm, 900 mm and 1000 mm, respectively. The bore velocity obtained is larger than the analytical bore velocity because the analytical formula does not account for the height of tsunami surge at the point on the shoreline, surge velocity at the point on the shoreline. These parameters depend on the distance of location of the origin point of tsunami and its intensity of tsunami.

4.2 Bore Profile and Bore Velocity The bore velocity was measured for each of the test conditions. Since three different masses of debris were used for a particular water depth test case for two repetitions, six bore profiles were obtained. The bore velocity for each of the case was measured. The results obtained shows that there was successful repetition in the bore profile (Fig. 3) and the bore velocities obtained with marginal variation (Table 1), although the experiment involves high non-linearity. From the test results, it was found that increasing the head of the water behind the swinging gate increased the bore velocity as observed by Arnason et al. [2]. Thus, the experiments were conducted with the velocity range of 3–4 m/s. 0.13

Trial1 Trial2 Trial3 Trial4 Trial5 Trial6

0.12

water level (m)

0.11 0.1 0.09 0.08 0.07 0.06 0.05 0

2

4

6

time (s)

8

10

12

Fig. 3 Repeatability of water level for different trials in 80 cm water depth condition measured at WP1

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Table 1 Bore velocity for three water depth conditions for different trials Trial 80 cm water depth 90 cm water depth 100 cm water depth condition (m/s) condition (m/s) condition (m/s) 1 2 3 4 5 6

3.33 3.12 3.33 3.33 2.94 3.33

3.57 3.57 3.57 3.12 3.50 3.57

3.68 3.82 4.16 4.00 3.62 3.80

4.3 Debris Velocity The impact loading of debris on the structure depends on the mass of the debris and the velocity with which the debris approaches the structure. The debris velocity is inversely related to the mass of the object. Tsunami entering the shore with high velocity is capable of carrying the debris and the debris also starts travelling with the same velocity as the bore velocity. However, if the density of the object is much higher, the debris will not float because of large draught. Most of the energy of the moving debris in tsunami bore is lost due to the friction with the bottom surface. This kind of debris thus hit the structure with lesser velocity in comparison with the debris mass. Also, this condition depends on the height of the hydraulic bore and its velocity. Thus, three different masses of debris were used for the experimental study to account for a more realistic phenomenon of debris motion that includes their draught conditions. Also, it was found from the experimental study that the debris having motion only in the surge direction travelled with a higher velocity in comparison with the debris motion coupled with surge and yaw motion in the surging tsunami bore. This depends on the angle of impact of surging bore on the debris and obstructions in the path of movement of debris. However, the motion of the debris is not controllable and can impact on structures from any direction in the real scenario. In the present study, the debris velocity is calculated as the averaged velocity with which it travels over distance of 2 m to hit the structure. The velocity of the debris is calculated from the video recordings of the movement of debris with the high-speed camera operating at 120 fps. The time required for the debris to travel for the distance of 2 m is found using the video recording for the particular test case. The travelling time is found by using open source software by analysing the recorded videos. The time is calculated from the initiation of debris motion from its rest for it to reaching the structure as shown in Fig. 4. Since the distance between structure and debris was maintained as 2 m, the averaged velocity was calculated. From Fig. 5, it is evident that the debris of lesser weight travels with a larger velocity compared to debris of larger weight. The velocity of the debris calculated was found to be in the range of 1.2–1.8 m/s. The debris velocity was found to be lesser than that of bore

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Fig. 4 Motion of debris in the surging tsunami bore Fig. 5 Comparison of velocity of debris for different masses in different water depths

velocity because the debris mass is large and also the debris need sufficient distance and time so as to reach the velocity of the bore.

4.4 Maximum Impact Force The local force–time history for the debris mass of 5.62 kg under three different water depths is shown in Fig. 6. It is observed from the results that an increase in the impounding water depth increases the force due to the debris on the structure [9]. In order to confirm the experimental results, two repetitions were carried out for each test condition and the variation was observed to be negligible. The variation in the maximum impact force obtained is due to the variation in the debris impact angle. Snapshots of debris at rest, moving in the surging bore at an oblique angle and while hitting the structure are depicted in Fig. 7. Debris hitting the structure with normal angle of incidence contributed to the largest force on structure compared to the debris hitting the structure from an oblique angle with respect to structure as shown in Fig. 7. In case of zero impact angles, the kinetic energy of the moving debris is transferred completely to the structure, thus inducing the largest force. However, in several cases, the debris is carried away by the bore, hitting the structure at an oblique angle imparting lesser impact force.

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Fig. 6 Local time history of the debris impact force of 5.6 kg mass at three different water depths

Structure

Debris

Fig. 7 Debris impact on structure at non-zero impact angle

From the force–time history, the maximum force acting on the structure was calculated for each of the test cases. By increasing the mass, the velocity of the debris was reduced inherently as stated earlier because of the inertia force of the body and the friction developed between the debris mass and the bottom of the flume. The variation of augmented velocity and the force measured from the load cell in Fig. 8. The force on the structure was for the augmented velocity range of 2–4.5(m/s kg0.5 ). The best fit gives the following expression: √ F  112u m.

(3)

The force expression for the best fit condition obtained is much lower compared to that proposed by Haehnel and Daly [8] because the debris is partially floating in the present study. Most of the energy imparted by the hydraulic bore on debris is lost in the form of friction and inertia component. Thus, the debris velocity is less and

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Fig. 8 Debris impact force with respect to augmented velocity

hence induces a lesser force on the structure compared to that of the formulation of Haehnel and Daly [8]. Thus, it was experimentally found out that increasing the debris mass need not necessarily increase the debris impact force. However, increasing the head of the water in the experimental dam causes a significant increase in the debris impact force on the structure. Thus, the experiment results prove that the force exerted on the structure due to debris is more likely dependent on the height and velocity of the tsunami bore at the shoreline irrespective of an increase in the mass and the distance of the debris from the structure.

5 Conclusion The present experimental study was conducted to have a better understanding of the behaviour of the debris in the partially floating condition which exactly resembles the debris motion in tsunami in the field. The experiments were conducted the bore velocity of 3–4 m/s resulted in the augmented velocity values ranging from 2 to 4.5 (m/s kg0.5 ). It was observed that the debris is the main source of impact force on structure during tsunami when compared to the force due to the tsunami bore during tsunami. Experimental results prove that varying the mass of the debris does not contribute much to the impact force as the debris velocity is reduced due to the inertia of the body and frictional force between debris and the floor. However, the variation in the impact force measured was observed by the variation in the water depth inside the experimental tank. This indirectly shows that the impact force on the structure is dependent on the speed of the surging tsunami bore in the beach, the height of the bore and the type of debris. Acknowledgements The paper was developed during the collaborative research project work Indian Institute of Technology, Madras and Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Russia on Impact of waterborne debris on the nearshore structures during extreme coastal

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floods funded by Department of Science and Technology, Government of India (Grant agreement no. INT/RUS/RFBR/P-203) and RFBR (15-55-45053). The author would like to thank Department of Ocean Engineering, IIT Madras for providing facilities for conducting the experiment.

References 1. Al-Faesly T, Nistor I, Palermo D, Cornett A (2012) Simulated tsunami bore impact on an onshore structure. In: 20th Canadian Hydrotechnical conference, pp HY-025-01–HY- 025-010 2. Arnason H, Petroff C, Yeh H (2009) Tsunami bore impingement onto a vertical column. J Disaster Res 4(6):391–402 3. ASCE (2005) Standard: minimum design loads for buildings and other structures. SEI/ASCE 7-05, 376 pp 4. Chanson H (2005) Analytical solution of dam-break wave with flow resistance: application to tsunami surges. Proceedings of 31st Biennial IAHR congress, Seoul, Korea, vol 0137, pp 3341–3353 5. Chanson H (2006) Tsunami surges on dry coastal plains: application of dam break wave equations. Coast Eng J 48(4):355–370 6. FEMA (2012) Guidelines for design for structures for vertical evacuation from Tsunamis. FEMA P646, Federal Emergency Management Agency, Wasington, USA 7. FEMA (2011) Coastal construction manual: principles and practices of planning, siting, designing, constructing, and maintaining residential buildings in coastal areas, 4th edn. FEMA P-55. Federal Emergency Management Agency 8. Haehnel RB, Daly SF (2004) Maximum impact force of woody debris on floodplain structures. J Hydraul Eng 130(2):112–120 9. Nouri Y, Nistor I, Palermo D, Cornett A (2010) Experimental investigation of tsunami impact on free standing structures. Coastal Eng J 52(1):43–70 10. Ramsden JD (1996) Forces on a vertical wall due to long waves, bores, and dry-bed surges. J Waterw Port Coasts Ocean Eng 122(3):134–141 11. Seyedreza S, Melville BW, Shamseldin AY, Adams. KN, Beskhyroun S (2016) Experimental investigation of tsunami-borne debris impact on structures: factors affecting impulsemomentum formula. J Ocean Eng 127:158–169 12. Shen MC, Meyer RE (1963) Climb of a bore on a beach Part 3. Run-up J Fluid Mech 16:113–125 13. Yeh H (2007) Design Tsunami forces for onshore structures. J Disaster Res 2(6):531–536 14. Yeh H (2006) Maximum fluid forces in the Tsunami Runup Zone. J Waterw Port Coastal Ocean Eng 132(6):496–500

Wave Transformation Around Submerged Breakwaters Made of Rubble Mound and Those Made of Geosynthetic Tubes—A Comparison Study for Kadalur Periyakuppam Coast M. Kalyani, A. S. Kiran, Vijaya Ravichandran, V. Suseentharan, Basanta Kumar Jena and M. V. Ramana Murthy

Abstract In the present paper, the hydrodynamic performance of two-segmented (200 m length, 60 m gap) submerged detached geosynthetic tube breakwaters has been compared with two-segmented traditional submerged detached rubble mound breakwaters under similar conditions, for Kadalur Periyakuppam (KPK) site. Bathymetry and wave conditions have been measured by NIOT. Tentative cost estimation of the superstructure shows that the cost of geosynthetic tube breakwaters is almost half of that of the rubble mound breakwaters and is preferred. Mike21 PMS and EMS modules have been used to simulate and compare the wave transformation under overtopping conditions for porous structures. PMS can predict diffraction accurately if wave action is perpendicular to structure, for an impermeable structure. EMS can simulate diffraction and can account for permeability and reflection characteristics, on a scale from (1, 0) to (0, 1) by externally feeding corresponding friction factor values into the numerical model. The amount of Kt or Kr cannot be predicted by the model itself as these are depth-averaged 2D models. Both the modules treat the structure as emerged only, and there is no direct provision for including the overtopping effects of submerged structures. In this paper, an attempt is also made to include overtopping effects externally (indirectly) into the model. The Kt values under different hydrodynamic conditions d’Angremond et al. (25th International Conference on Coastal Engineering, Orlando, Florida, 1996 [2]), Pilarczyk (Proceedings of 6th international conference on coastal and port engineering in developing countries, Colombo, Sri Lanka, 2003, [11]) have been fed appropriately, and the variation of leeside wave height with respect to water levels (CD vs. HWL) and type of structure (rubble vs. geosynthetic tube and impermeable-PMS) and the breaking characteristics are quantified.

M. Kalyani · A. S. Kiran (B) · V. Ravichandran · V. Suseentharan · B. K. Jena M. V. Ramana Murthy National Institute of Ocean Technology, Chennai 600100, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_25

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Keywords Kadalur periyakuppam · Geosynthetic tube · Submerged breakwater Rubble mound · MIKE21 PMS · MIKE21 EMS

1 Introduction The east coast of India is prone to cyclones during the North East monsoon season. These cyclones have caused large-scale erosion in the coastal areas. The cyclones have altered the sediment balance of the beaches resulting in a net erosion trend. Submerged breakwaters appear to be an ideal solution to prevent the beach erosion during cyclones as it reduces the impact of high energy waves on the coast. Wave transmission over submerged breakwaters can be studied by model studies—physical or numerical models. A large number of physical model studies are conducted by researchers all over the world. Based on these studies empirical relations are formulated to arrive at the wave transmission parameters. The primary variables which control shoreline response are distance offshore, length of the structure, transmission characteristics of the structure, beach slope and/or depth at the structure, mean wave height, mean wave period, orientation angle, predominant wave direction and gap in the case of segmented breakwaters [5–7]. The factors which control wave transmission include crest height and width, structure slope, permeability and roughness of structure, tidal and design level, wave height and period [11]. d’Angremond et al [2] provided a formula for wave transmission for exposed and submerged breakwater structure. Seabrook and Hall [12] conducted physical model studies to assess the performance of submerged rubble mound breakwaters. The study concludes that relative submergence, structure crest and incident wave height are the major design parameters. A design equation was proposed as a preliminary design tool for submerged rubble mound breakwater. Johnson et al. [8] compared the sediment transport fields computed behind a detached breakwater by use of three different wave models: MIKE 21 PMS, NSW and EMS. Wamsley et al [14] evaluated selected available formulas for predicting wave transmission at reef breakwaters and conventional structures. They have recommended appropriate formulas for shoreline response modelling. Based on the study, Ahrens formulation is proved to provide a reliable prediction for reef type structure. As part of the study, variable wave transmission was incorporated in the GENESIS shoreline change model. Van der Meer et al [13] has reanalysed the results of more than 2300 2D random wave tests, of wave transmission over low crested structures, available in the database as part of DELOS project funded by EU. The analysis proposed existing design formula for relatively small crest widths and new formula for very large crest width. For rubble mound structures, the transmitted wave angle is 80% of incident one. Reflection from low crested structures decreases with decreasing crest height. Makris and Memos [10] used existing formulae and wave models to study the wave transmission over submerged breakwaters. Recent semi-empirical formulas are found to perform satisfactorily as it takes into account crest width, wave breaking, breaker type, armour stone properties, etc. The parabolic mild slope model

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of MIKE 21 showed the most consistent and reliable performance. Wave breaking and structure porosity are the crucial factors which need further study for improvement. Blacka et al [1] studied the wave transmission for low crested geotextile breakwater structures. They used two-dimensional physical modelling to investigate various breakwater structures under monochromatic waves. The studies show increased wave transmission for longer wave period and higher submergence depth. For waves with shorter wave period, the wave transmission can be reduced by smaller crest width breakwaters while for larger wave periods, the reduction is less. From the above literature review, it is found that modelling the wave overtopping effects (for submerged BWs) as well as structure’s porosity characteristics is the need of the hour. Also, the latest trend is to design breakwaters using geosynthetics as against the traditional rubble mound breakwaters. Hence, their performance and cost-effectiveness are compared under similar conditions. The capabilities and effectiveness of Mike21 EMS as against the very computationally efficient but rather approximate PMS has also been compared.

2 Methodology National Institute of Ocean Technology (NIOT) has proposed to construct a sevensegmented submerged breakwater system to protect the coast of Kadalur Periyakuppam near Kalpakkam in Tamil Nadu. The project is being carried out on a pilot scheme to study its performance. Continuous monitoring is proposed to understand the shoreline behaviour. Two segments of breakwater (BW) system (100 m and 200 m) starting from the north side are constructed. The initially constructed 100 m segment could withstand Vardha cyclone (December 2016). In the present paper, two segments in the middle portion of the proposed seven-segmented BW system have been taken up, and numerical model studies are carried out to compare the performance of rubble mound BWs with that of geosynthetic tube BWs under different wave overtopping and transmission conditions using MIKE21. The bathymetry of the area has been carried out covering 17 km parallel to coast and 7 km normal to coast (Fig. 1a). It is then converted into MIKE 21 format with 2.5 m grid spacing to suit the criteria of representing the crest width with at least by 5–6 grids. The bathymetry for CD is shown in Fig. 1b. The coastline orientation in the chosen model domain is 32o N. The lateral boundaries are chosen such that they are more than six times the wavelength and five times the length of the BWs. The structure height (hs ) is 3.5 m and is kept around 4.0 m (w.r.t CD) water depth, beyond the breaking zone. With the changing tidal elevation, the heights above the structure’s crest (overtopping depth—RC ) are −0.5 m (CD), −1.1 m (MSL) -and −1.7 m (HWL), respectively. Considering the yearly climate, the maximum r.m.s. wave height at the structure is around 2.0 m. Therefore, rms wave heights of 1.0 and 2.0 m are tested. Wave period is kept constant (T  8.0 s), as this exercise is to bring out the comparison between

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Fig. 1 a Bathymetry survey coverage over entire model domain and b Mike21 bathymetry for CD

two different structures’ performance under different overtopping conditions. Wave direction is taken normal to structure to suit the PMS-diffraction capability to that of EMS. The MIKE21 bathymetry for both EMS and PMS are tilted such that wave direction is parallel to model west. In addition to bathymetry, sponge layer file and friction file were generated using MIKE 21 EMS toolbox to mimic absorption for nullifying numerical boundary effects and the partial reflection and transmission characteristics, respectively. The wave transmission characteristics for submerged breakwaters are obtained from the empirical formula deduced from experiments by Van der Meer and d’Angremond [11], which considers submergence depth, wave height, breaking characteristics, beach slope, crest width, etc. and is given by, The d’Angremond et al. formula reads: Rc B −0.31 +c (1 − e−0.5 ξ) Hi Hi  − 21 H0 ξ0  tan β L0

K t  0.4

(1) (2)

where Rc is freeboard, H0 = Hi —incident wave height, B is top width, ξ0 is surf similarity parameter, β is slope of the seabed and Kt is transmission coefficient. The c value is given as 0.64 for impermeable breakwaters and 0.8 for permeable breakwaters [11]. The top and bottom widths of geosynthetic tube BW are 8.0 m and 15.0 m in the field, respectively. A sensitivity study has been conducted, to check the effect of B on the Kt . In addition, for a particular water level condition, for varying incident wave heights, the varying crest width (exposed) during trough phase has been considered. The difference in Kt due to difference in B (8 and 15 m)

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Fig. 2 a Variation of KT with B and b variation of KT with changing B during trough phase

and varying B during trough phase are found to be in the order of less than 5% and 2%, respectively, as shown in Fig. (2a, b). Hence, in the present paper, the width of structure is fixed as 15.0 m to represent it in six grids to simulate its presence accurately in the numerical model. The friction factor (ff ) values corresponding to Kt (impermeable/permeable core) were calculated for d = 4.0 m and T = 8.0 s using DHI’s reflection/friction calculator (MIKE 21 EMS) as the case may be [3]. Geosynthetic tube breakwaters are treated as impermeable breakwaters and rubble mound breakwaters are treated as permeable ones. The Kt varies with both water level variation and wave height for a given structural dimensions (wave period and direction being constant). The appropriate ff values are fed into the numerical model for each case. The tidal variation changes the Rc , freeboard. The submergence depth (Rc ) increases from −0.5 to −1.7 m from CD to HWL. The bathymetry is changed according to water levels, and the appropriate Rc has been used to arrive at the Kt which is then fed in terms of corresponding friction factor in MIKE 21 EMS module. Throughout the study, the bottom roughness kN is kept constant at 0.0015. Different wave conditions tested were tabulated in Table 1. Simulations were carried out for beam sea (waves perpendicular to the structure, to suit diffraction for PMS) condition with monochromatic waves (to suit EMS) considering the effect of wave height (Hrms  1.0 m & 2.0 m) and breaking characteristics.

3 Results and Discussion For each scenario (I, II and III), all the eight cases specified in Table 1 are simulated. The wave height distribution from the structure to the coast in the vicinity of the structure for each case is shown in Fig. 3a–h for submerged impermeable breakwaters (PMS); in Fig. 3i–p for submerged rubble mound breakwaters (EMS) and Fig. 3q–x for submerged geosynthetic tube breakwaters (EMS), respectively.

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Table 1 Wave conditions simulated for the study Type of Water level Incident (rms) Breaking structure/module used wave height (m)

Simulation ID

I. Impermeable BWs (PMS) II. Rubble mound BWs (EMS) III. Geosynthetic tube BWS (EMS)

CD

1.0

Breaking

Case-1

CD

1.0

Non-breaking

Case-2

CD

2.0

Breaking

Case-3

CD

2.0

Non-breaking

Case-4

HWL

1.0

Breaking

Case-5

HWL

1.0

Non-breaking

Case-6

HWL

2.0

Breaking

Case-7

HWL

2.0

Non-breaking

Case-8

From these simulations, it is clearly understood that the submerged BW creates a shelter region behind the structure in its immediate vicinity (50–75 m). The effect of overtopping is to increase the water levels on the leeside as compared to the case of emerged structures. Its effect is supplemented by the dominant diffraction effects of the wave. The difference is clearly visible near the gap area which is not protected by any structure. The porosity of structure (rubble/geosynthetic tube) takes the third seat in making its impact felt. To bring out the variations in the sheltering effect due to various factors, three profiles have been taken along the centrelines of the top BW, gap area and bottom BW. The variation of leeside wave height along each profile for each case (1–8) has been plotted showing the difference between rubble (EMS), geosynthetic tube (EMS) and impermeable structures (PMS) in Fig. 4. The profile distance starts from 15 m to coast where 0 to 15 m represents structure’s width. For the profile along the centreline of the gap area between the two segments of BWs, the distance starts at −35 m as the unrestricted predominant wave heights are observed here. For the profiles along the centrelines of top and bottom BWs, as the diffracted wave heights were only 20% of the incident wave height, they are sustained during both low and high waters (weather breaking is enabled or not). The effect of shoaling is clearly visible as they approach shallow waters in this case. For the profile through the centreline of the gap area between the two breakwaters, the wave breaking was effective during low water for both the incident waves with Ho  1.0 & 2.0 m and a gradual reduction of wave height can be seen with decreasing water depths towards the coast. Same is true in the case of high waves with Ho  2.0 m during high waters. But low energy waves during high waters (Ho  1.0 m) did not break (even though breaking is enabled) as the depths available could sustain them. For non-breaking waves, shoaling was visible as they approach shallower depths which are comparable to the wave height. It is evident that, for either breaking/non-breaking waves, the reduction in wave height is more than 80% of the incident wave height (Ho  1.0 m or 2.0 m) and is apparent till the coast with slight variations in their pattern based on the porosity

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(a)

(b)

(c)

(d)

(e)

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(f)

(g)

(h)

Submerged-Impermeable Breakwaters

(i)

(j)

(k)

(l)

(m)

(n)

(o)

(p)

Submerged-Rubblemound Breakwaters

(q)

(r)

(s)

(t)

(u)

(v)

(w)

(x)

SubmergedGeosynthetictubeBreakwaters Fig. 3 Wave height distribution on the leeside of the BWs for eight cases as referred in Table 1 MIKE 21 PMS (top) and EMS (middle and bottom) simulations

of the structure. However, near the coast, EMS simulation has a wave absorber, and hence, drastic decrease in wave height is noticed whereas it is absent for PMS case. EMS and PMS results should not be compared in this area near the coast. PMS results showed an undulated wavy structure for all the three profiles along the centrelines of the two breakwaters and the gap area. PMS could capture the signatures of EMS on the leeside of the structures but these features are not profound and distinct as in the case of EMS which is obtained at the cost of computational effort. Hence, the trend line is drawn to understand the variation for PMS. The profile through the centreline of the gap area clearly shows the absence of any sheltering effect by the submerged BWs and naturally attenuated based on shoaling, refraction and depth breaking as the case may be.

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Fig. 4 Comparison of wave height profiles on the leeside of BWs for rubble mound BWs (EMS), geosynthetic tubes BWs (EMS) and impermeable BWs (PMS) (left: CL of top BW; middle; CL of gap and right; CL of bottom BW)

4 Cost Comparison The design and stability of the submerged breakwater made of geosynthetic tube is discussed in Kiran et al [9]. In order to compare the costing a submerged rubble mound breakwater of the same height is designed based on Coastal Engineering manual [4]. The crest width is slightly increased to accommodate the primary rock armour unit size required to withstand the storm wave (Fig. 6). The primary armour layer shall be made of tetrapods or other concrete units as the weight of armour unit required is too high for rock unit. The slope of the breakwater is taken as 1V:2H. The construction of the submerged breakwater (made of geosynthetic tubes) of 1400 m length is in progress (Fig. 5). The total cost of the project is Rs. 17 crores. The cost of a submerged rubble mound breakwater with tetrapod primary armour layer will cost around 35 crores for the same length (Fig. 6).

5 Conclusions In the present paper, the overtopping effects and the porosity characteristics of the submerged breakwaters used for coastal protection have been efficiently modelled by indirectly implementing them in the depth-averaged 2D model; MIKE 21 EMS. These effects are brought into transmission coefficient (Kt ) and then indirectly fed into the model using MIKE 21 friction factor for EMS corresponding to the desired Kt .

Wave Transformation Around Submerged Breakwaters …

Geosynthetic tube BWcross section

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Construction in progress

Fig. 5 Breakwater with geosynthetic tube

Fig. 6 Rubble mound breakwater cross section

The appropriate transmission characteristics are obtained from past research through the empirical formula for submerged breakwaters that consider various parameters of importance such as freeboard (negative), seabed slope, wave characteristics, breaking characteristics through surf similarity parameter and structural dimensions into account. Further, Mike21 PMS model is used under similar conditions which cannot consider the permeability/transmission characteristics, but around 50 times faster than the EMS computational efficiency. While the results for rubble and geosynthetic tube breakwaters (EMS) follow more or less similar trend with mild variation in their magnitude based on the degree of porosity, the PMS results showed a different trend compared to EMS results. This is attributed to the overtopping effects which are considered through Kt for EMS and could not be modelled in case of PMS. Still, as the diffraction (sheltering effect on the leeside of breakwaters) is the predominant phenomenon having maximum impact on the wave height on the leeside of the structure in the present case, all the significant features could be efficiently captured by PMS also, hence, it can be used as a first guess. While dealing with submerged structures, where overtopping and transmission characteristics are very important, and for structures where reflection is predominant (emerged structures, vertical walls), care should be taken while dealing with PMS. In such cases, EMS is preferred.

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The cost comparison of the rubble mound structures with that of geosynthetic tubes brought out the fact that, geosynthetic tubes are very economical (more than 50% cost savings) with equal hydrodynamic performance and being resilient structures they also appease to the aesthetics of the coastal environment. Hence, it is advised to go for submerged geosynthetic tube breakwaters and is being selected for construction.

References 1. Blacka MJ, Carley JT, Corbett BB, Jackson LA (2009) Wave transmission over low crested geotextile breakwater structures. In: 19th Australasian coastal and ocean engineering conference 2009 and the 12th Australasian Port and Harbour conference 2009, COASTS and PORTS 2009, pp 489–495 2. d’Angremond K, Van der Meer JW, de Jong RJ (1996) Wave transmission at low-crested structures. In: 25th International Conference on Coastal Engineering, Orlando, Florida 3. DHI (2005) MIKE21 user guide and reference manual. Danish Hydraulic Institute Water and Environment, Denmark 4. EM 1110-2-1100 (2006) Coastal engineering manual. US Army Corps of Engineers 5. Hanson H, Kraus NC (1989) GENESIS: generalised model for simulating shoreline change. Report 1: technical reference, Technical report CERC-89-19, US Army Engineer, WES, Vicksburg, MS 6. Hanson H, Kraus NC (1990) Shoreline response to a single transmissive detached breakwater. In: Proceedings of the 22nd coastal engineering conference. ASCE, The Hague 7. Hanson H, Kraus NC (1991) Numerical simulation of shoreline change at Lorain, Ohio. J Waterw Port Coast Ocean Eng 117(1). January/February 8. Johnson HK, Brøker I, Zyserman JA (1994) Identification of some relevant processes in coastal morphological modelling. In: Proceedings of the 24th international conference on coastal engineering, Kobe, Japan 9. Kiran AS, Vijaya R, Sivakholundu KM (2015) Stability analysis and design of offshore submerged breakwater constructed using sand filled geosynthetic tubes. Procedia Eng 116:310–319. 8th International conference on Asian and pacific coasts (APAC 2015). IIT Madras, Chennai 10. Makris CV, Memos CD (2007) Wave transmission over submerged breakwaters: performance of formula and models. In: Proceedings of 17th international offshore and polar engineering conference. ISOPE, pp 2613–2620 11. Pilarczyk KW (2003) Design of low-crested (submerged) structures: an overview. In: Proceedings of 6th international conference on coastal and port engineering in developing countries, Colombo, Sri Lanka 12. Seabrook SR, Hall KR (1998) Wave transmission at submerged rubble mound breakwaters. In: 26th International conference on coastal engineering, Copenhagen 13. Van der Meer JW, Briganti R, Zanuttigh B, Wang B (2005) Wave transmission and reflection at low-crested structures: design formulae, oblique wave attack and spectral change. Coast Eng 52:915–929 14. Wamsley T, Hanson H, Kraus NC (2002) Wave transmission at detached breakwaters for shoreline response modelling, ERDC/CHL CHETN-II-45, US Army Corps of Engineers

Study on Stability of Eden Navigational Channel in Hooghly River Estuary N. Saichenthur, K. Murali and V. Sundar

Abstract Hooghly estuary is a complex dynamic estuary facing dredging maintenance and navigation-related problems due to the high rate of sediment load brought by the Hooghly River. The present study is to investigate the hydrodynamics and morphodynamics of the Hooghly estuary, with specific reference to stability of Eden navigational fairway and permanent operation of the channel as a possible main navigational route to HDC in the place of Auckland channel from the Bay of Bengal. Impact of stoppage of dredging at Auckland bar on the other channels (Eden and the Rangafalla channel that connect to Kolkata Dock System, KDS) is investigated. Simulations involving different scenarios like Auckland channel dredged and nondredged conditions are considered to investigate the stability of the Eden channel and also to address the aspects relating to the maintenance of other channels. In the study, for the Auckland open condition, the predicted siltation levels are of about 8–12 cm over Auckland and about 4–8 cm over Eden bar, over 15 days of simulation. For Auckland closed condition and for Auckland with two tracks, the results indicate a marginal reduction in siltation over the entire Eden area, and it is also observed that the siltation in Jellingham and Haldi River confluence is significantly reduced. For the monsoon conditions in all the above scenarios, the results, as per the siltation patterns and as per the siltation levels on the edges of the channels, indicate that there will be a marginal increase in siltation, by about 20% when higher silt load is considered. The study suggests that Eden channel could continuously be used with little dredging in the longer term of more than 5 years with monitoring and realignment of the channel to cater for movement of sandbars. Further, non-dredging of Auckland channel may not have any bearing on the operation of Eden, Jellingham and Rangafalla channels. N. Saichenthur (B) · K. Murali · V. Sundar Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai 600036, India e-mail: [email protected] K. Murali e-mail: [email protected]; [email protected] V. Sundar e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_26

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Keywords Hydrodynamics · Tidal flux · Siltation · Navigation channels Dredging

1 Introduction The Hooghly estuary in the north-eastern part of India experiencing macromareal tidal range is complex in its dynamic behaviour. Two major ports, viz. Kolkata and Haldia are located along its course. Due to the massive sediment load brought by the Hooghly River, the aforementioned estuarine ports have been facing the perennial problem of siltation requiring continuous maintenance dredging. The navigation to Haldia Dock Complex (HDC) is through the Middleton–Auckland–Jellingham channels of Hooghly River and this channel to Haldia Port is maintained with 25 Mm3 per annum [4]. The estuarine islands emerge, accrete and dissipate due to sediment reworking in a high energy cyclone-dominated macro-tidal environment without any obvious relation to sea level change [7]. Kolkata Port estimated that 100 Mm3 of suspended sediment is transported per year into the Hooghly estuary downstream of Kukrahatti near the Hooghly point [5]. Freshwater flows during large runoff events can be greater than peak tidal flows. Thus, freshwater runoff can transport sediment downstream at very high rates, as evidenced by the unstable shallow sand shoals in Rangafalla channel [5]. The estimated loads vary in the order between 2.6 × 105 and 1.09 × 105 m3 s−1 during peak flood and ebb cycles at the estuarine mouth [7]. The wave activity in this region is less with significant wave heights less than 0.35 m. In the navigation channel, the significant wave heights are less during the winter months (6.6 m), and hence had not been considered for investigation. An initial survey from Diamond Harbour to Sagar Island was carried out to establish the baseline data and to identify the regions which require regular and high-resolution monitoring. Figure 3 shows bathymetry map of Diamond Harbour to Sagar Island surveyed in December 2015. Hence, the bathymetry surveys at regular time intervals, once a week during spring and neap tide has been carried out from HDC to Eden-LP (up to Lat 21° 41 00 N) along the navigation channel from 5 February ‘16 to 31 May ‘16 representing the–premonsoon period from 3 June to 30 September ‘16 being the monsoon period and from 1 October to 25 February 2017 being the post-monsoon period. The pre-monsoon, monsoon and post-monsoon bathymetry survey in the Eden bar constitutes 22 surveys for pre-monsoon, 19 for monsoon season and 17 monitoring surveys for the postmonsoon season, respectively. The surveys were carried out over each of the neap and spring tide. Figure 4 shows bathymetry map of Eden and Auckland bar. The total length and width of the channel are 15.75 km × 0.92 km, respectively. The channel has nine navigation tracks, each of which is 115 m wide. (The bathymetry survey was done along each of the navigation channels.) Single-beam, single-frequency echo sounder was used, the range of which is from 0.3 to 99.9 m with a frequency of 200 kHz. The calibration of the echo sounder was done using bar check plate and sound velocity probe. Finally, the sound velocity was fixed 1512 m/s. The depth under the vessel is then calculated from the two-way travel time of pulses and the mean speed of sound over the water column. Depth (D)  V ×

T 2

where D = Depth from reference water surface, V = Velocity of sound in the water column and T = Measured elapsed time from transducer to bottom and back to transducer. The HYPACK survey software was used for the data collection and postprocessing. This software allows importing of background maps and creating the planned line for navigating the survey vessel. It contains the post-processing module to analyse and prepare the bathymetry chart. This software is used to calculate the volume of siltation at different locations mentioned above.

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Fig. 3 Bathymetry chart from diamond Harbour to Sagar Island

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Fig. 4 Bathymetry chart Eden bar and Auckland bar

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5 Details of the Monitoring Survey

2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00

0.24 0.22 0.20 0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 N-S S-N N-S May-16

N-S S-N N-S Aug-16

Siltation Volume in Mm3 Fig. 5 Siltation depth at Eden bar for three seasons

N-S S-N N-S Dec-16 Change in depth in m

Siltation rate in m/7days

Deposition Volume in Mm3

Based on the survey during the above-mentioned periods, with CD as the base reference, the area of siltation, change in depth and volume of sediments in the vulnerable areas to be dredged in order to maintain the navigable depths is calculated. The siltation depth varies between the spring and neap tide periods due to the variation in the tidal flow velocities. The observations of the survey data are discussed below. All the depths dealt in the following sections are the ones measured from the reference line, i.e. below the CD at 2.82 m from MSL. Using the surveyed data, the volume of silt accreting and eroding can be calculated. As per the results shown in Fig. 5 and in Table 1, a clear general scenario can be observed, i.e. the Eden channel seems to be accreting during the spring-to-neap (S–N) period and eroding during the neap-to-spring (N–S) period. Though, the second neapto-spring time for pre-monsoon season shows an increased silting rate, it is observed that the erosion rate also increases considerably to counter the siltation. For the month of August, Table 1 shows the silting and scouring rate during the monsoon season which reflects a change in the natural setup, i.e. the silting volume increases linearly with time, irrespective of tidal time, but with slight reduction in silting rate during neap to spring. This aspect can be attributed to the excess silt load carried by the river during the monsoon time. Overall, it can be concluded that the Eden bar mostly erodes during neap to spring and accretes during spring to neap and this typical scenario is reflected in post-monsoon period. The influence of this setup on the stability of Eden channel is analysed and interpreted in the following section.

August 2016

2 3 4

8 9

December 2016

May 2016

1

5 6 7

Month

Sl. no

S-N N-S

S-N N-S N-S

S-N N-S N-S

N-S

Tidal time

9.32 11.17

11.90 10.22 9.31

12.67 12.66 11.90

12.67

8.71 5.28

4.85 6.36 0.41

5.85 3.47 5.15

9.74

Area (Mm2 )

1.78 0.43

0.69 1.03 0.05

0.59 0.48 0.37

0.96

Volume (Mm3 )

Total Depositing region surveyed area (Mm2 )

Table 1 Silting and eroding volume calculation in Eden bar for three seasons

0.20 0.08

0.14 0.16 0.12

0.10 0.14 0.07

0.10

(m/7 days)

Siltation rate

0.61 5.89

7.05 3.85 8.90

6.81 9.19 6.75

2.93

Area (Mm2 )

Eroding region

0.06 0.70

0.75 0.72 3.06

0.65 1.24 0.78

0.25

Volume (Mm3 )

0.10 0.12

0.11 0.19 0.34

0.10 0.13 0.12

0.08

(m/7 days)

Erosion rate

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6 Analysis of Bed Level Changes in Relation to Eden Stability In this activity, the Eden bar is divided into 10 sections as shown in Fig. 6. The minimum depth required for navigation in this channel is considered to be 4.6 m below the chart datum. From the results shown in Figs. 7, 8 and 9, it is seen that the depth changes in the tracks 3–7 during the different tidal times. Most of the tracks are experiencing erosion from neap to spring and depth is found to reduce in the springto-neap time due to siltation. In most cases, a minimum depth of 4.6 m is being maintained throughout the channel. So, whatever is accreting during the spring-toneap time is eroded during the neap-to-spring cycle. So, it can be predicted that this cycle will be repeated, and therefore the Eden is expected to be stable throughout the year. Reversal of scenarios only in few sections in the deeper part of the channel is observed. This can be due to other exceptions during monsoon and also due to some local sediment dynamics, caused by the presence of Kaukhali and Tigris sandbars on either side of the Eden channel as observed from Fig. 6. These exceptions can be catered with occasional dredging and realignment of channel. But, considering all the natural setup and few exceptions as observed in the results afore discussed, the dominant dynamics is more towards keeping the channel stable all throughout the year.

7 Interpretation on the Usage of Eden Channel as the Main Navigational Route to HDC It is observed that in Eden channel, the minimum depth required for the navigation is self-maintained in most of the tracks, during the entire survey period. It is also observed that significant silting occur only in the deeper parts of the Eden channel which can be maintained by dredging. The presence of shoal on either side of Eden bar is found to be interfering on the depths of some parts of the outer tracks. This can be addressed by the realignment of the channel once in a while if need arises. All the positive aspects on the stability of the Eden channel shall be attributed to the natural alignment of the channel in the direction of tidal flow. Since the channel is trying to self-maintain itself, it will be easy to maintain the minimum required depth in Eden channel through less quantity of dredging.

8 Conclusions The variation of bed level changes has been analysed for the Eden channel for three seasons, viz., pre-monsoon, monsoon and post-monsoon. Monitoring survey has been carried out using echo sounder to study the bed level change in the channel.

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Fig. 6 Cross section at Eden bar (upper, middle and lower part)

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Pre-Monsoon 3

4

5

6

7

4.5

Track No

Depth (m)

5

Minimum depth Neap-1

5.5

Spring-1

6

Neap-2

6.5

Spring-2

7 7.5

Monsoon 3

4

5

6

4.5

7 Track No

Depth (m)

5

Minimum depth Neap-1

5.5

Spring-1

6

Neap-2

6.5

Spring-2

7 7.5

Post-Monsoon 3 4.5

Depth (m)

5 5.5 6 6.5 7

4

5

6

7

Track No Minimum depth Neap-1 Spring-1 Neap-2 Spring-2

7.5 8 Fig. 7 Water depth of navigational channel at Cross Section-3 (C/S-3) for three seasons

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Pre-Monsoon 3

4

5

6

7 Track No

Depth (m)

4.5 4.7

Minimum depth

4.9

Neap-1

5.1

Spring-1

5.3

Neap-2

5.5

Spring-2

5.7 5.9

Monsoon 3

4

5

6

7 Track No

4.5

Depth (m)

4.7

Minimum depth Neap-1

4.9

Spring-1

5.1

Neap-2 Spring-2

5.3 5.5

Post-Monsoon 3 4.5

Depth (m)

4.7 4.9 5.1 5.3

4

5

6

7 Track No Minimum depth Neap-1 Spring-1 Neap-2 Spring-2

5.5 Fig. 8 Water depth of navigational channel at Cross Section-5 (C/S-5) for three seasons

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Pre-Monsoon 3

4

5

6

7 Track No

4.5 Minimum depth

Depth (m)

5

Neap-1

5.5

Spring-1

6

Neap-2 Spring-2

6.5 7 3

4

Monsoon 5

6

4.5

7 Track No

Depth (m)

5

Minimum depth Neap-1

5.5

Spring-1

6

Neap-2 Spring-2

6.5 7

Post-Monsoon 3 4.5

Depth (m)

5 5.5 6 6.5

4

5

6

7

Track No

Minimum depth Neap-1 Spring-1 Neap-2 Spring-2

7 Fig. 9 Water depth of navigational channel at Cross Section-8 (C/S-8) for three seasons

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Detailed analysis shows that, due to relative changes in the hydrodynamics, Eden channel mostly erodes during the neap-to-spring phase at a rate of 0.11 m/7 days and accretes in spring-to-neap phase of tidal cycle at a rate of 0.14 m/7 days on an average considering all three seasons. It is concluded that pre-monsoon and post-monsoon seasons depict a typical scenario in silting, i.e. alternate erosion and accretion corresponding to the tidal cycles. Though, the various seasons show dynamic changes in the bed levels which naturally maintains the channel depths, regular dredging in patches along the channel is to be carried out in order to maintain the minimum depth required for smooth manoeuvering of vehicles along the EDEN channel. Acknowledgements The authors wish to record their sincere thanks to the Authorities of Kolkata Port Trust for their valuable support during the survey and technical discussion.

References 1. Dalrymple RW, Zaitlin BA, Boyd R (1992) Estuarine facies models: conceptual basis and stratigraphic implications: perspective. J Sediment Res 62(6):1130–1146 2. Nandy Sreetapa, Bandyopadhyay Sunando (2011) Trend of sea level change in the Hugli Estuary India. Indian J Marine Sci 40(6):802–812 3. Dubey Rajesh P, Samarawickrama S, Gunaratna PP, Halgahawatta L, Pathirana KPP, Raveenthiran K, Subasingha K, Das B, Sugandika TAN (2013) Mathematical model studies for River regulatory measures for the improvement of draft in Hoogly Estuary, India. Evol Trends Eng Technol 2(84):1–12 4. Sanyal T, Chatterjee AK, Mandal GC (2000) Erosion—Deposition in Hooghly Estuary. Def Sci J 50(3):335–339 5. Bhaskaran PK, Mangalagiri S, Bonthu S (2014) Dredging maintenance plan for the Kolkata port India. Curr Sci 107(7):1125–1136 6. Rehitha TV, Ullas N, Vineetha G, Benny PY, Madhu NV, Revichandran C (2017) Impact of maintenance dredging on macrobenthic community structure of a tropical estuary. Ocean Coast Manag 144:71–82

Migration of Chilika Lake Mouth R. Sundaravadivelu, P. Shanmugam, A. K. Patnaik and P. K. Suresh

Abstract Chilika lake is the largest lagoon along the east coast of Indian state Odisha, situated between latitude 19° 28 and 19° 54 N and longitude 85° 05 and 85° 38 E. The place is known for rich biodiversity and is the largest wintering ground of migratory bird and largest population of Irrawaddy dolphin, habited by migratory birds and by a special type of dolphins. The highly productive ecosystem of the lake supports the livelihood for fishermen and also acts as drainage for Mahanadi River Basin. The estuary is very sensitive to the sediment dynamics. The closure of estuary mouth or shifting of Chilika Lake mouths tremendously changes salinity and ecology of the lake system. The east coast of India along this coast is having a net alongshore drift of about 0.7 × 106 m3 annually toward north direction. The inlets of Chilika Lake are under the influence of alongshore sediment transport from the coast. Apart from this, the rivers bring sediments during peak southwest monsoon season. Because of this the inlets are migrating, depending on the season. The details of migration of estuary opening were analyzed using satellite imageries. The analyses of watershed, coastal process, and configuration of estuary are detailed in this paper. Keywords Chilika lake · Ecosystem · Salinity · Coastal process

R. Sundaravadivelu (B) · P. Shanmugam · P. K. Suresh Indian Institute of Technology Madras, Chennai, India e-mail: [email protected] P. Shanmugam e-mail: [email protected] P. K. Suresh e-mail: [email protected] A. K. Patnaik Chilika Development Authority, Odisha, India © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_28

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1 Introduction Chilika Lagoon, the largest brackish water body of Asia, on the east coast of Odisha, India is 4000 years old [4]. The lagoon is separated from Bay of Bengal by a barrier spit shown in Fig. 1, 64.3 km long and connected to it by four tidal inlets of varying depth and size. All inlet activities occur on the onshore face of the lagoon. The brackish character of Chilika Lagoon was deteriorated during past three decades of the twentieth century. The hydrodynamic regime of the lagoon was affected during this period. Consequently, the ecology, biodiversity and economy of the area were also affected. The present study deals with the variation of geometry of mouth of estuary with time. The extreme meteorological events, hydrological aspects, tidal outlet (Fig. 2), and coastal process involved on the closure, migration, and opening of new tidal inlets in Chilika Lagoon at Arkhakuda, Gabakund, and Sipakuda are discussed. • Project location details Satapada and Magarmukh area of Chilika Lake are under Krushnaprasad and Brahmagiri block under Krushnaprasad Tahasil in Puri district. • Demographic details of the population Total fisherman population of peripheral villages of Chilika is more than 2 lakhs. Those are directly dependent on the lake fishery for their daily livelihood.

Fig. 1 Location of Chilika lake

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Fig. 2 Tidal outlets to Bay of Bengal

2 Geological Process Geological processes change the geomorphological landform features continuously. The study on the old topographical maps of 100 years indicates complete change of Chilika lagoon especially along the shore. The prevailing wind erodes transports and deposits sand from one place to another. These geodynamical actions may be due to several causes. However, identifying these causes, it is possible to make some sustainable development such as mouth stabilization.

3 Geological History Geological studies reveal that coastline along Chilika has shifted toward sea. The evidence is Konark temple is present now at 3 km from the shore since it was built on the shore. The causes of coastline shifting and growth of the spit are strong wind, absence of strong river and tidal current. Most of the lagoons were formed due to sea level rise over the last 6000–8000 years. The mouth of the Chilika Lake keeps on changing its position especially toward northeast. The width of the mouth was 1.5 km in 1780 and then reduced to half in 1820. The mouth is closed up frequently, so that it is necessary to dredge the silted sand for seawater entrance. Chilika Lake is being silted up and the depth is shallow.

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The coastline of the Odisha is being subjected to various environmental impacts which results in both accretion and erosion. The opening of the outer channel near Arkhakuda was reported during 1914 and was found ineffective in 2000. A new mouth was opened near Sipakuda in 2000. At present, Arkhakuda mouth is completely closed off and the artificially opened mouth near Sipakuda is enlarged. Satellite images indicate that 46 km2 areas have been silted up due to a constant inflow of 13 million tons of sediments per year due to erosion and transportation from the catchment area. Restoration plan for an integrated watershed management of the lagoon with active participation of local community and nongovernmental organizations on a micro-watershed basis, enhancement of welfare of local people, and communication and developments of various centers are required.

4 Hydrological Network Chilika is influenced mainly by the tributaries of Mahanadi River, namely, the Mahanadi River Delta and its branches which is shown in Fig. 2. The rainfall varies from 1000 mm to extreme values of 2500 mm. The southern distributaries, Daya and Bhargovi in Mahanadi delta join the sea via Chilika Lagoon. The abnormal rainfall has caused high floods during 2001, 2003, 2006, 2008, 2011, and 2014. Year 2000 was the minimum discharge year of the millennium. Chilika Lagoon, largest in Asia receives 61% of inland flow from Mahanadi system. As per studies of Mishra and Jena [3] major inflow to Chilika (60%) is from Mahanadi system. The number of rivers/rivulets draining into the lake is 52 and the catchment area is 3729 km2 .

5 Studies Using Satellite Imageries Preliminary studies were conducted on the migration of inlet of estuary adopting satellite imageries from Google Earth which is shown in Figs. 3, 4 and 5. The Chilika Lake mouth located originally near Sipakuda in 1800 has gradually shifted in the last 200 years toward the northern side to Arkhakuda. The sedimentation in the south and erosion in the north due to littoral drift is the major cause of continuous shift of the mouth toward north. The outer inlet channel of 18 km length was formed between Sipakuda and Arkhakuda and the tidal exchange through this channel was not sufficient to maintain the quality of brackish water and overall brackish ecosystem in the Chilika Lake. Because of low tidal prism, an intervention was made by cut opening a mouth of width 200 m near Sipakuda in September 2000 by the Chilika Development Authority (CDA) based on the numerical model study by CWPRS, Pune and implementation methodology by IIT, Madras. The opening of the new mouth at Sipakuda in the year 2000 improved the tidal and salinity flux to desired level in 2001. The satellite images of the mouths along the coasts in the years 1990 and 2000 are shown below.

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Fig. 3 Satellite view of mouths in year of 1990 and 2000

Fig. 4 Satellite view of mouths (extension) in year of 2008 and 2012

2016 Fig. 5 Recent satellite view of mouths in year of 2016

The Sipakuda mouth has gradually widened from 200 to 850 m toward NE and is now migrated from the original cut by about 2000 m. The widening of mouth is

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generally due to erosion of the northern spit and the sliding of sandbar embankment. The rates of tidal water flow and fresh water flow also play a critical role in widening of the mouth. Due to erosion of the spit on the north of Sipakuda mouth due to less supply of sediment and cyclone, another mouth was opened in August 2008, opposite to Gabakund at a distance of 1900 m from Sipakuda on the day of lunar eclipse. The Sipakuda mouth was consistently migrating toward north. The shifting of mouth is marginal and is only 300 m from 2000 to 2004. But from 2004 to 2016, the mouth has migrated by 3800 m with an average movement of about 300 m per year. In the process of migration, the Sipakuda mouth merged with Gabakund mouth in 2012 and the width was about 2700 m at the time of merging. However, the mouth opened at Sipakuda location has gradually closed and the Gabakund mouth stabilized with reduced width. Again in September 2012, a new mouth got opened by nature due to erosion of the northern spit, opposite to “Dhalabali”. Now the Chilika Lake has two mouths, viz., (i) Gabakund mouth on the southern side and (ii) Dhalabali mouth on the northern side of Gabakund mouth. The approximate distance between the centers of two mouths is around 2250 m. The length of the sand spit in between these two mouths is around 1850 m. The Gabakund mouth has the width of 800 m, whereas the Dhalabali mouth has the width of 300 m. Both Gabakund mouth and Dhalabali mouth are branching out into two major channels. The Gabakund mouth main channel leads toward main lake, i.e., toward south heading Satpada, whereas the Dhalabali mouth main channel leads toward north heading to Arkhakuda. The depth remains very shallow showing less than 1.6 m w.r.t. MSL in Dhalabali mouth. Gabakund mouth remains deeper than Dhalabali mouth with a maximum depth of 3.7 m w.r.t. MSL. Similarly, the quantity of flow through Gabakund mouth is very much higher compared to Dhalabali mouth and the required tidal prism is maintained.

6 Coastal Process The bathymetric details obtained from studies of [1] are provided which is shown in Fig. 6. The tide levels at Satapada before opening of the mouth (March 2000) was 10 cm, while this improved to 60 cm in March 2001 and the figures in March 2012 stood at 45 cm. The tidal chart is shown in Fig. 7. The tidal variations were observed and it was about 2 m.

7 Alongshore Sediment Transport The gross longshore sediment transport rate is about 1 × 106 m3 /year. The net sediment is toward north from May to October and is about 0.7 × 106 m3 /year as per studies and measurements by Chandramohan et al. [1]. The sediment transport is predominantly directed toward north direction. In a year, the alongshore sediment transport is directed toward north from May to October and toward south from

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Fig. 6 Bathymetric details of Bay of Bengal Fig. 7 Tidal chart for the site location

November to February. The southwest monsoon is active and during this period rivers carry large discharge and also bring enormous sediments. Hence, during monsoon, the estuary is flushed by flood waters. Considerable siltation is observed during fair weather period. Observation on sediments along Mahanadi was studied in detail by Central Water Commission [2] from 2002 to 2012. The average annual sediment is 4.44 million metric tons.

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Fig. 8 Rainfall pattern in the watershed of Daya river

8 Rainfall Details The details of rainfall are analyzed as per Mishra and Jena [3]. Chilika Lagoon receives flow from distributaries of Daya and Bhargovi in Mahanadi delta that joins the sea via Chilika Lagoon which is shown in Fig. 8. The variations of Chilika are in terms of geomorphology, ecology, and biodiversity for changes in precipitation and threshold flushing flow. Abnormal floods are observed because of rainfall during 2001, 2003, 2006, 2008, 2011, and 2014. Year 2000 was the minimum discharge year of the millennium. The tourist, flora, and aqua catch decreased remarkably during 1995–2000 for lagoon’s reduced salinity, siltation, and biodiversity. The anomaly in monsoon precipitation has trimmed down the threshold flushing flow to maintain salinity. The coast is vulnerable to cyclone during northeast monsoon. In the year 1999, it was subjected to a super cyclonic storm. Another very severe cyclonic storm Phailin crossed the coast in 2013.

9 Water Resources and Climate Changes Climate change is expected to have implications for several wetland features. The main diverse in Chilika is decrease in monsoon rainfall, increased temperature, sea level rise, and tropical cyclone events. It also has impacts on winter rainfall in India where drought and flood situation is quite normal. The storms, surcharges, and cyclones occurred frequently in coastal area of Odisha which has got bad impacts on the coastal lake ecosystem. During the heavy flood, the sediment along with the nutrient loads and debris enter to Chilika Lake and will cause siltation and eutrophication. Due to impact of climate change, the lake mouth was shifting at a faster rate and also Chilika catchment has been receiving erratic rainfall. When more precipitation

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Fig. 9 The area of waterlogging by flooding

will occur in the catchment area, the waterlogging will take place and the paddy field of the Kanas, Delanga and Brahmagiri blocks of the lake will get submerged. Figure 9 is showing the area of waterlogging by flood. The lake has faced two consecutive cyclones in the year 2013, the cyclone “Phailin” had the landfall in the close proximity in Chilika Lake on 12.10.2013 and another high impact cyclone also hit in the southern part of Chilika Lake called “Hud Hud” on the same day, next year, i.e., 12.10.2014 followed by a severe flood in the river system draining to Chilika lake. This has become a regular practice in these areas; a cyclone, drought, or flood is experienced every year. The occurred adverse climate phenomena are listed in Table 1.

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Table 1 List of occurrence of adverse climate phenomena S. no Category Year of occurrence 1

Flood

1956, 1959, 1969, 1970, 1986, 1987, 1988, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2001, 2003, 2005, 2006, 2008, 2011, 2014

2

Cyclone

1967, 1968, 1970, 1971, 1972, 1973, 1999, 2013, 2014

3

Drought

1956, 1970, 1987, 2000, 2002, 2010, 2015

4

Earthquake

2013, 2015

10 Desiltation of the Channel From the above observation, it has been felt that some further interventions inside the lake are essential like the desiltation in the main connecting channel from the mouth to lake, Balugaon channel and a ferry route is shown in Fig. 10. The ferry route will be maintained for years together as the propeller of the boats moving inside will make the channel free from siltation. The depth of ferry route with respect to mean sea level is shown in Fig. 11. The Balugaon channel is the interface between the main lake and also the outer channel of Chilika. The recruitment of fish and fish juveniles are taking place through Balugaon channel only and so the extension of the Balugaon channel is inevitable for maintaining the fish production of the lake.

Fig. 10 Ferry routes in Chilika lake

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Fig. 11 Depth of ferry route w.r.to MSL

By desiltation of the channels, the navigation in the lake will improve. The desiltation processes will also pave the way for the recruitment of juvenile from sea as 85% of the fish in Chilika Lake are migratory in nature. The lead dredged channel also facilitate in discharge of flood water from Delanga, Kansa, and Brahmagiri block, in the Mahanadi catchment (Chilika) in Puri district of Odisha which is more than 70,000 hectare of cultivable agriculture land.

11 Summary The opening of the mouth at Sipakuda in 2000 resulted in annual fish production from 2000 tons to 14,000 tons in 2003. The annual fish yield of Chilika has decreased from 14,000 tons (2003–04) to around 12,000 tons. The tide levels at Satapada before

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opening of the mouth (March 2000) was 10 cm, while this improved to 60 cm in March 2001 and the figures in March 2012 stood at 45 cm. Chilika as a brackish water lake is known for its substantial coverage of seagrass beds which acts as carbon sinks (blue carbon). Based on the outcome of this successful hydrological intervention, the Ramsar Wetland Conservation Award and Evian special prize 2002, which is the award of highest order by the Ramsar Bureau for outstanding achievement in the field of restoration of the wetlands is conferred on CDA. Chilika was also removed from threatened list of Wetlands, i.e., Montreux record in 2002. CDA is the first recipient of this prestigious award from Asiatic region. Chilika Estuary is mainly influenced by sediment transport by rivers into the lake and alongshore sediment transport along the coast toward north by wave action. The mouth is also migrating toward north due to deposition of sand in the south and erosion in the north of the mouth. The coast is also vulnerable to cyclone and this can also alter the mouth configuration. Substantial rainfall creates runoff into inlet and creates flushing of mouth. During below average rainfall, the mouth gets closed and there is no proper tidal prism action. If proper desiltation of channels inside the lake and lake to outer channel is carried out, the high siltation can be flushed out during substantial rainfall and the rate of migration of mouth can be reduced. Dredging of channels in the lake will also help movement and distribution of fishes, seaward breeding migration, etc.

References 1. Chandramohan PV, Sanil Kumar V, Naya BU (1993) Coastal process along shorefront of Chilika Lake east coast of India. Int J Mar Sci 22(3): 268–272 2. Government of India, Ministry of Water Resources, Central Water Commission (2015). Integrated hydrologic hand book. Non classified river basins 3. Mishra SP, Jena J (2015) Analytical study of monsoon rainfall south Mahanadhi delta and Chilika Lagoon Odisha. Int J Sci Technol 7(3):985–996 4. Venkataratnam K (1970) Formation of the barrier spit and other sand ridges near Lake Chilika on the east coast of India. Mar Geol 9(1970):101–116

Part II

Offshore Structures and Deepwater Technology

Coupled Dynamics of Deep Water Tension Leg Platforms Under Steep Regular Waves R. Jayalekshmi, R. Sundaravadivelu and V. G. Idichandy

Abstract The paper investigates the coupled dynamics of the hull–tether system of deep water TLPs under steep regular waves. The nonlinear finite element analysis program (NAOS) in time domain is used to include the wave frequency and highfrequency components. The first-order forces are calculated using relative velocity model of Morison. The second- and third-order force components are calculated using the FNV (Faltinsen, Newman and Vinjie, J Fluid Mech 289:179–198, 1995) [3] model. A hybrid model is developed combining all the force components. An incremental-iterative solution based on Newmark’s integration scheme is adopted. The TLPs are analyzed for regular waves of steepness values 0.025, 0.05, 0.075, and 0.1, at water depths 900, 1800 and 3000 m. Results are reported in the form of power spectral density functions as well as mean and dynamic responses. Maximum surge is found at 1800 m. To examine the participation of natural modes of vibration, the natural periods of vibration are also captured. The heave and tether tension are minimum at 1800 m water depth and increases with wave steepness. The study emphasizes the need for including the effect of higher order exciting forces for understanding the response behavior of deep and ultra-deep water TLPs. Keywords Hull–tether dynamics · Deep water TLPs · Higher order Hybrid wave force model · Morison’s equation · FNV model

1 Introduction Newly developed tension leg platforms are considered powerful structures for development of offshore oil fields in deep and ultra-deep seas. As the water depth increases, the natural frequencies are closer to the wave frequencies and hull–tether system R. Jayalekshmi (B) NSS College of Engineering, Palakkad, Kerala, India e-mail: [email protected] R. Sundaravadivelu · V. G. Idichandy Indian Institute of Technology Madras, Chennai, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_29

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dynamics become significant. An accurate analysis of the highly dynamic response of a TLP would generally require an elaborate time domain approach since this method can include all the nonlinearities in its full form. Reported results of model tests on large diameter surface-piercing cylinder due to steep waves show that wave loads are considerably larger than those estimated by classic analysis. The paper investigates the response characteristics of deep water TLPs considering higher order forces in addition to first-order forces using a newly developed hybrid model. Nonlinear analysis of offshore structures (NAOS), a versatile dynamic FE program [7] can treat nonlinear dynamic problems in time domain and the same is used based on an updated Lagrangian formulation. The incrementaliterative Newmark-beta algorithm is adopted. The tethers are modeled as structural beam elements using finite element method.

2 Nonlinear Finite Element Analysis The equations of motion of a TLP are highly nonlinear due to large displacements, large rotations, and hydrodynamic nonlinearities like drag force, etc. The versatility of the finite element method enables modeling of stiffness, hydrodynamic characteristics, and inertial characteristics of compliant offshore structures that exhibit nonlinear motion characteristics. The coupled dynamic analysis of TLPs is carried out in time domain using the modified code NAOS [7]. The hydrodynamic forces are estimated by the Hybrid wave force model which accounts the higher order wave force components. The updated Lagrangian formulation of the finite element equations has been adopted where the stresses, strains, displacements (including rotations), and loading are referred to the instantaneous or updated configuration of the structure at the current value of time. The analysis is performed with a variety of elements such as three-dimensional beam, bar, spring, and mass and damper elements. The columns, pontoons, and deck of the hull are modeled using rigid beam elements and the restoring force in heave, roll, and pitch by equivalent elastic spring elements, translational and rotational. The linear elastic stiffness matrix and the geometric stiffness matrix of the beam elements are used to model the tethers. The mass matrix of beam elements (M) includes consistent body mass matrix (Ms) as well as the added mass matrix (Ma) derived from the Morison model for fluid forces. Hydrodynamic damping is accounted by the drag term in the Morison equation. Structural damping is estimated as Rayleigh damping C  αRM + βRK, where “M” is the mass matrix, K is the stiffness matrix, and αR and βR are evaluated assuming modal damping in the first two modes of vibration of the system. Newmark-beta method is adopted for the solution of nonlinear equations of motion. The in-house computer program NAOS has been extensively validated for many benchmark problems found in the literature.

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3 Wave Force Models In this study, two wave force models are considered; the Morison model and a Hybrid model, which is a combination of the Morison model and the second- and third-order terms in the FNV model that was formulated by Faltinsen et al. [3] for regular waves and was developed further to include irregular waves by Newman [6].

3.1 Morison Model The Morison wave force model consists of two components; drag and inertia forces. Drag loads are developed by the relative velocity of the fluid, while the inertial loads due to the pressure gradient are associated with the relative acceleration of the ambient fluid. This method is valid for longer waves at lower frequencies. Since TLP is an inertia-dominated structure Airy’s theory can be used sufficiently accurately for deriving the hydrodynamics of the wave field. Stoke’s higher order theories may also be used. However, it is unlikely to considerably improve results for inertia-dominated structures like TLPs since only the predicted velocities (and not accelerations) of fluid particles differ appreciably between linear and higher order wave theories. Chakrabarti’s approach is adopted to incorporate the effect of variable submergence, which is an important aspect of hydrodynamic loading on TLPs. Wave force, buoyant force, and self-weight are combined together and converted into equivalent nodal loads by Simpson’s numerical integration method.

3.2 Hybrid Model For TLPs, typical diameter of vertical columns is such that in severe sea states, characteristic wavelengths are about 200–400 m with kR < π/10. Hence, the TLP columns come under the long-wavelength regime, i.e., the wavelength “L” is more, compared to characteristic dimension kR  1. But for steep waves, the amplitude “a” is of the order of R and there will be significant nonlinear effects in the near field close to the cylinder, which cannot be neglected. These nonlinear effects due to steep waves are accounted for the long wave formulations of second- and third-order wave forces by FNV method in a simplified way as given in [4]. By FNV model, the force on a surface-piercing vertical cylinder is given by FFNV  F1 + F2 + F3 where F1 and F2 are the long wave approximation of the first- and second-order force components represented by the linear and quadratic transfer functions (LTF

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and QTF). F3 is a third-order force obtained from the nonlinear potential and approximated using the assumptions regarding wavelength and wave amplitude [4]. Here, F1 is nothing but the inertia term of the Morison equation. The FNV method does not consider the relative velocity of the cylinder which is important for a compliant platform like the TLP. In deeper water depths, the drag loads significantly increase due to larger influence of tethers. A Hybrid wave force model is developed including all the three force components, i.e., the first-order wave force by the relative velocity form of Morison equation, accounting viscous effects by the drag term and second- and third-order forces by the FNV method. The FNV model is valid for surface-piercing vertical cylinders only. Moreover, at the depth of submergence of pontoons, wave effects are negligible because wave kinematics are not felt beyond a depth of about half the wavelength in the fluid. Hence, the hybrid model is used for computing the wave forces on vertical column members and only the Morison model is used for the estimation of wave forces on pontoons and tethers. In the finite element formulation, the second-order forces are integrated up to the free-surface level and the third-order force is added as a horizontal force at the free-surface nodes of the beam element of columns [4]. The Hybrid model has been validated by the experimental studies done on a single-column, single-tether TLP by Sundaravadivelu et al. [8].

4 Parametric Studies The higher order effects due to nonlinear steep waves are investigated by conducting parametric studies of TLPs in three water depths, i.e., 900, 1800 and 3000 m, under regular waves of steepness; H/L  0.025, 0.05, 0.075, and 0.1. The wave forces are computed by both wave force models and comparisons are made between the dynamic responses and tether tensions. The geometrical configurations of the deep water TLPs used for the study are selected from the “Deep Star Theme Structure Studies” [1, 5, 9, 10] in the Gulf of Mexico region. The platform details are given in Table 1. The pretension in tethers is assumed as a constant percentage of displacement of the platform (22%). The tethers are assumed hinged at the hull and seabed template. The tether group per corner is replaced by a hydrodynamically equivalent tether with same stiffness and pretension. Cd  0.7 for pontoons, 1.2 for columns, and 1.0 for tethers and Cm  2.2 for pontoons, 2.3 for columns, and 2.0 for tethers are adopted in the study and these values follow those used in the DeepStar studies and conform to the API RP 2T recommendations

Coupled Dynamics of Deep Water Tension Leg Platforms … Table 1 Geometric details of the TLPs Case description 900 m

1800 m

387

3000 m

Draft (m)

24

30.9

33

Displacement (t)

32,667

52,205

86,888

No. of columns Column diameter (OD) (m)

4 16.2

4 19.2

4 23.4

Column height (m)

44.1

52.5

54

Column spacing (m)

60

60

72

Pontoon width (m)

8.1

9.6

10.8

Pontoon depth (m)

7.2

8.4

9.6

Deck dimension Deck post height (m)

72 × 72 2.4

78 × 78 2.4

90 × 90 2.4

Total weight (kN)

240,770

346,656

606,770

No. of tethers Length (m)

8 812.8

12 1769.1

16 2970.75

Diameter (OD) (mm)

878.4

1117.6

864

Thickness (mm)

33

47

48

(N/m3 )

77,000

77,000

16,500

Tether pretension (kN)

71,868

114,851

191,154

T/

0.22

0.22

0.22

Density

5 Natural Periods and Coupled Dynamics of the Hull–Tether System For a TLP, translational and rotational modes in the vertical direction are in the highfrequency region, while its corresponding modes in the horizontal direction are in the low-frequency region. The natural frequencies of tethers decrease with increasing water depth as the tether mass become comparable to the platform weight. In deeper regions, the frequencies of higher tether modes may fall within the wave frequency range. The six rigid body modes of the platform influence the higher tether modes, and thus coupled mode vibration occurs depending upon the wave frequency [2]. The present work uses a formulation accounting for this coupling wherein the tethers are modeled by bar elements or beam elements with small bending rigidity. The elastic modes of vibration are captured. The coupled analysis yields tether response simultaneously with platform response. The undamped natural periods of TLPs have been estimated and are presented in Table 2. The surge (or sway) and yaw periods are the highest and both these periods are well above the range of ocean wave periods (4–25 s). The next higher frequencies are tether modes, clearly the first three modes lie within the wave frequency range of 4–25 s for d  900 m, whereas for d  1800 m, 7 modes are there and for d  3000 m more than 7 modes are within this range. However, wave periods in the range of

388 Table 2 Natural periods of deep water TLPs

R. Jayalekshmi et al. Water depth (m)

900

1800

3000

Surge

117.48

174.2

224.6

Heave Pitch I tether mode II tether mode III tether mode IV tether mode V tether mode VI tether mode VII tether mode VIII tether mode

2.873 1.094 14.24 7.21 4.79 3.57 2.89

3.15 1.11 39.2 19.3 12.9 9.7 7.7 6.4 5.4 4.7

4.167 1.2 52.93 26.4 17.58 13.2 10.59 8.8 7.55 6.8

4–6 s are associated with smaller wave heights and may be significant from fatigue point of view, due to their high percentage of occurrences. The larger period waves (6–25 s) are the ones associated with wave heights of practical significance for which the dynamic response is of concern. For d  900 m, first two modes; for d  1800 m, 5 modes and for, d  3000 m, 6 modes lie in this range. These tether modes will be excited by the waves and the dynamic problem becomes coupled. For 3000 m deep TLP, the heave period is 4.17 s and gets coupled with higher tether modes which are in the range of ocean wave periods and will effectively participate in the platform responses. For 900 m and 1800 m TLPs also, the heave mode gets coupled with higher tether modes but lies below the wave period range and will not effectively participate in the platform response.

6 Response Analysis Numerical simulation of the TLPs in deep water (≥900 m) and ultra-deep water (1800–3000 m) under regular wave conditions has been carried out. The platforms being symmetrical, the response in surge, heave, pitch, and tether tension is investigated for beam sea conditions for wave steepness values; H/L  0.025, 0.05, 0.075, and 0.1 corresponding to regular waves of heights H  7.85, 15.3, 22.94 and 30.58 m with a wave period T  14 s. The program gives time histories of surge, heave, pitch, and tether tension using both wave force models. Certain parameters are defined with respect to the time series to analyze the responses. Mean drift is the time average of the steady-state surge response and dynamic surge is the amplitude of surge motion. Set down in the present study is the time average of steady-state heave oscillation and dynamic heave is the amplitude of heave motion. The results corresponding to influence of parameters; water depth “d” and wave steepness “H/L” are presented in the following sections.

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Fig. 1 Variation of dynamic surge and dynamic heave (M-Morison, H-Hybrid)

Fig. 2 Variation of dynamic tension (M-Morison, H-Hybrid)

Fig. 3 Variation of mean drift surge and set down (M-Morison, H-Hybrid)

The variation of first-order responses, i.e., the dynamic surge, dynamic heave and dynamic tension, and second-order responses, i.e., the mean drift and set down for different wave steepness values are compared in Figs. 1, 2 and 3. Though the geometrical details differ for the three water depths, the pretension levels and wave forces are kept same for comparison. Figure 1 depicts that dynamic surge is maximum at d  1800 m for both models and increases with wave steepness. The Hybrid model predicts about 12% increase in dynamic surge from Morison model. For 900 and 3000 m, the difference is minimal.

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The dynamic heave shows a reverse behavior. It is reduced to almost 50% as d is increased from 900 to 1800 m and increases 5.8 times for H/L  0.05, 3.7 times for H/L  0.075 and 3.4 times for H/L  0.1, in Morison model. The hybrid model shows similar behavior for dynamic heave and the variation is significant for H/L  0.1. The dynamic tension closely follows the pattern of dynamic heave (Fig. 2). The mean drift presented in Fig. 3 varies linearly with water depth for low steepness; H/L  0.025 for both models and the platform moves opposite to the direction of wave action for d  900 m; along with the waves for d  1800 m and again moves opposite to wave direction for d  3000 m. The drift by Hybrid model is less when the platform moves in the same direction and higher as it moves in the opposite direction. Lower values predicted by the Hybrid model may be due to the phase difference of first-order and higher order forces. Set down is maximum for d  1800 m and the increment increases with wave steepness as d increases from 900 to 1800 m. For d  900 m, both models show negligible variation in set down for H/L  0.025 and 0.05. The set down is reduced by 7–8% for d  1800 m and increased by 10–20% for d  3000 m in Hybrid model when H/L  0.075 and 0.1. To highlight the effect of higher order wave forces due to steep waves, the PSDs of dynamic responses and tether tension for H/L  0.1 are examined. The PSD of surge compared in Fig. 4 does not vary with water depth and higher values are predicted by Hybrid model. This may be due to the inclusion of higher order forces. The firstorder heave spectral density (Fig. 5) decrease with water depth and second-order spectral density is not so predominant in Morison model, while in Hybrid model, the first-order PSD increases with water depth and the second harmonic spectral peak is comparable for d  3000 m. The spectral density plots of pitch (Fig. 6) shows the second-order effect of force in Hybrid model. The third-order force is included as a point force at the surface level in the Hybrid model which will induce additional pitching moment on the platform. The maximum pitch PSD is almost doubled in Hybrid model. Tension in tethers is due to the combined effect of surge, heave, and

Fig. 4 PSD of surge

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Fig. 5 PSD of heave

Fig. 6 PSD of pitch

Fig. 7 PSD of dynamic tension

pitch oscillations. Spectral density of tension increases with water depth for both models and for d  3000 m, the first-order maximum tension PSD and the secondorder maximum tension PSD are almost equal in Hybrid model as given in Fig. 7.

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7 Summary and Conclusions The dynamic behavior of TLPs are investigated under regular waves at three water depths; 900, 1800 and 3000 m. A versatile, dynamic finite element program developed for nonlinear analysis of offshore structures in time domain is used for the analysis of TLPs. A Hybrid wave force model is introduced to investigate the relative importance of the nonlinearity associated with the interaction of the tether with its surrounding fluid, as the platform is excited by higher order forces up to third-order. Regular waves with wave steepness values H/L  0.025, 0.05 0.075, and 0.1 are considered. The present study of the nonlinear dynamics of the TLPs has provided some insight into the effects of the hull–tether interaction in deep water and ultra-deep water under steep regular waves. Some of the principal conclusions obtained on the basis of numerical investigations are as follows: • The number of tether modes and coupled modes that come under the range of ocean wave periods (4–25 s) increase with water depth and makes the dynamics of TLPs coupled. • The Morison model and Hybrid model predict similar behavior of first-order responses in surge, heave, pitch, and tether tension for all water depths and wave steepness and both the models can be used. It is recommended to use Hybrid model for predicting the higher order response for all water depths and wave steepness. • The higher order spectral density peaks of high-frequency responses; heave, pitch, and tether tension for H/L  0.1 as indicated by the Hybrid model highlight the importance of including higher order forces. • The motions and tether tension are almost linear with water depth for steepness up to H/L  0.075 and significant increase in the response is observed for high steep waves (H/L  0.1) in ultra-deep water (d  3000 m). • The variation of the response parameters is similar for all steepness values and the response increases with wave steepness.

References 1. Bhat SU, Greiner WL, Barton D (2003) Deep star 10,000-ft water depth study. In: Proceedings of offshore technology conference, OTC15102 2. Bhattacharyya SK, Sreekumar S, Idichandy VG (2003) Coupled dynamics of SeaStar mini tension leg platform. Ocean Eng 30:709–737 3. Faltinsen OM, Newman JN, Vinje T (1995) Nonlinear wave loads on a slender vertical cylinder. J Fluid Mech 289:179–198 4. Krokstad JR, Marthinsen T, Nestegard A, Stansberg CT (1996) A new non-slender ringing load approach verified against experiments. In: Proceedings of the international offshore mechanics and artic engineering conference, pp 371–387 5. Ma W, Lee MY, Zou J, Huang EW (2000) Deepwater nonlinear coupled analysis tool. In: Proceedings of offshore technology conference, OTC12085

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6. Newman JN (1996) The second-order wave force on a vertical cylinder, J. Fluid mechanics, 320, pp. 417–443 7. Sreekumar R (2001) Analytical and experimental investigations on the dynamics of deep water mini tension leg platform. PhD thesis, Dept. of Ocean Engineering, IIT Madras 8. Sundaravadivelu R, Idichandy VG, Jayalekshmi R (2007) Deep water TLP—tether coupled dynamics in regular waves. In: ECOR workshop engineering committee on oceanic resources, UK 9. Wichers J, Devlin PV (2004) Benchmark model tests on the deep star theme structures FPSO, SPAR and TLP. In: Proceedings of offshore technology conference, OTC 16582 10. Zou J, Ormberg H, Stansberg CT (2004) Prediction of TLP responses: model tests vs. analysis. In: Proceedings of offshore technology conference, OTC 16584

Residual Strength of Cracked Tubular Joint Using Nonlinear Finite Element Analysis Natarajan Vignesh Chellappan and Seeninaidu Nallayarasu

Abstract Fixed offshore platforms have been used for extraction of oil and gas. These platforms were primarily constructed using steel frames made of tubular members welded at joint or specially fabricated joints. The tubular joints are vulnerable to fatigue-induced cracks which initiate at joints and may propagate through its design life. If the platform life is extended depending upon oil and gas availability, the initial cracks may extend beyond acceptable limits. In recent times, the research on evaluation of residual strength of cracked tubular connection has been considerably increasing since the platforms in various oil and gas fields are ageing. To determine the residual capacity of cracked T-tubular joints, a nonlinear finite element analysis has been carried out. The FEM model of uncracked T joint was validated with experimental result available in literature. The benchmark study has also been made on uncracked T-joints with a specific d/D, t/T and D/2T and compared with the results obtained from empirical equations (API RP 2A). The possible crack locations have been identified using the maximum SCF at crown and saddle points for axial loads. The cracks are introduced in the maximum SCF locations of tubular joint. The study has been extended to range of d/D and D/2T . A correlation has been established between lengths of crack to the residual strength for various crack locations investigated. The residual strength obtained has been compared with reduction factor (BS 7910). It was also found that the residual strength of joints decreases with increase in D/2T . Keywords T-tubular joints · Crack · Residual strength · SCF Extended finite element (XFEM) analysis

N. Vignesh Chellappan (B) · S. Nallayarasu Department of Ocean Engineering, IIT Madras, 600036 Chennai, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_30

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1 Introduction Fixed offshore platforms have been used for extraction of oil and gas. These platforms were primarily constructed using steel frames made of tubular members welded at joints or specially fabricated joints. The tubular joints and members of the steel structures are subjected to cyclic loading due to wave and wind during its design life. Further, in some cases, the design life may also be extended due to prolonged period of production of oil and gas depending on the availability of oil and gas, which also increases the period of cyclic loading. The tubular joints are vulnerable to fatigueinduced cracks which may propagate during the lifetime. The joint strength capacity reduces as the crack length/depth increase in its size and it eventually fails by brittle fracture or ductile deformation, if repair of the cracks is not carried out on time. The estimation of residual strength of cracked tubular joints is a subject matter of interest for decades; two methods are widely accepted as approaches relevant and appropriate. The first method is based on reduction factor FAR applied to the ultimate strength and the reduction factor is calculated based on method described by BS 7910 [1]. The second method is developed based on failure assessment diagram (FAD) as described by BS 7910 [1]. The reduction factor approach focuses only on ultimate strength of cracked tubular joints, whereas the FAD approach focuses on ductile tearing effect of crack. Earlier investigations have focused on reduction in joint strength for part through thickness cracks in T, DT and K joints under axial tension. This resulted in reduction factor FAR proposed by Burdkein [2], and subsequently the reduction factor F AR had undergone further modifications by BS 7910 [1]. The plastic collapse capacity (Pu−c ) of cracked tubular joint is predicted by applying this reduction factor F AR to ultimate capacity of uncracked tubular joint (Pu ). In these investigations, the crack locations were arbitrarily chosen at crown or saddle points of weld toe in the tubular joint and which extends up to 33% of perimeter of chord brace intersection. In reality, the crack initiates at the hotspot location of tubular joint and not always at crown or saddle location. There seems to be some degree of variation in the conservativeness of the reduction factor, so a penalty factor has been proposed by Lie et al. [3, 4] for residual static capacity of pre-cracked square hollow section (SHS) joints and tubular joints, respectively. The difficulties involved in numerical modelling of cracked tubular joints are modelling of weld at tubular joint, crack geometry and crack tip singularity [3, 4]. The T-tubular joints have been considered as specially fabricated joints without welding as stated by Lee [5]. Generally, the cracks are irregular in shape and vary up to any length [6]. In numerical analysis, the crack tip is considered as sharp [6] and a regular crack shape needs to be assumed. In order to capture the effects of crack and crack deformation, appropriate element type and mesh is required [7–9]. There have been extensive studies on element type and mesh techniques to capture crack tip singularity and crack effects. Previously, the programs like PATRAN, NASTRAN, ANSYS, PRETUBE and PMBSHELL were used for mesh generation of cracked tubular joints. Even though automatic mesh generation capabilities are

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397

available, the necessity of an upgraded mesh generation has been addressed by Lie et al. [7–9] to capture crack tip singularity and crack effects. To implement upgraded mesh, improved skill over meshing strategy is required. The crack problems have been solved using virtual crack extension or closure technique [3, 4, 7–9]. The shortcomings of FEM formulation for numerical modelling of crack is overcome by extended finite element method (XFEM) [10–12]. The XFEM technique uses enrichment functions for crack modelling. This enrichment function ensures for crack tip singularity in this analysis. Since XFEM modelling is available in ABAQUS [12] package, this software package was used for the present study. The residual static strength of cracked tubular joints has been estimated using nonlinear XFEM and compared with codal provision of BS 7910 [1].

2 Methodology 2.1 Numerical Modelling of Uncracked Tubular Joints A typical cross-sectional view of the T-tubular joint is shown in Fig. 1a. The geometrical dimensions of tubular joints are expressed as non-dimensional parameters, such as diameter ratio β  d/D, thickness ratio τ  t/T and chord slenderness ratio γ = D/ 2T, where D is the chord diameter, d is the brace diameter, t is the thickness of brace and T is the thickness of chord, respectively. The corresponding non-dimensional parameters used for the simulation are β  0.3–0.9, τ  0.3, 0.5 and 0.7 and γ  10, 20, 30 and 40. The chord diameter (D) of the tubular joint is 750 mm. The chord ends are fixed and the brace end is restrained except in axial direction to allow the axial loads as shown in Fig. 1b. The actual boundary conditions for the chord ends are partially fixed as the ends may rotate due to joint flexibility. In order to avoid short chord effects and stiff joint, the length of chord is assumed as L c  5D and the length of brace was taken as L b  3d. Thus, the non-dimensional chord length parameter α  2L c /D becomes 10, which falls within the applicability range of 4–40 as per API RP 2A [13]. The steel material properties used for the simulation is summarised in Table 1. The material selected is in accordance with the recommendations of API RP 2A [13]. The nonlinear finite element analysis method is based on arc length (RIKS) as proposed in reference [14] which is used in the present study and the solution procedure is available in ABAQUS [12]. This method has been used to determine the ultimate capacity and deformation of tubular joints. The eight-node brick elements are used as it will have facility to simulate through thickness crack. To obtain the hotspot stress around the joint intersection, procedure from DNV-RP-C203 [15] has been adopted, which requires small element sizes around the joints. In order to reduce the number of elements, coarse mesh was used away from the joint and denser mesh around the joint as suggested by Lee [5] and Lie et al. [7–9].

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Fig. 1 a Cross-section view of tubular joints, b boundary conditions of tubular joint Table 1 Material properties E (MPa) μ

σ y (MPa)

σ u (MPa)

Elongation (%)

200 × 103

0.3

240

410

20

200 × 103

0.3

345

490

25

The generated mesh is shown in Fig. 2. This varying mesh was surrounded by the same size of elements around the joint which extends up to 0.8D from the centre of intersection in chord and up to 0.4D in brace from the chord surface. The limits used in varying mesh were arbitrary and it was sufficient to cover the length required to obtain SCF. The numerical model proposed in this paper to evaluate the static strength of cracked and uncracked joints has been validated using experimental data

Residual Strength of Cracked Tubular Joint …

399

Fig. 2 Meshed geometry of tubular joint with varying element sizes

published in Lie et al. [4] for uncracked tubular joint. Hence, the same numerical modelling technique has been adopted for both uncracked and cracked tubular joints, so that the results can be compared.

2.2 Numerical Modelling of Crack in Tubular Joints The location of pre-crack for simulation has been selected based on the stress concentration factor (SCF) obtained from uncracked tubular joints. The hotspot location was observed in and around saddle position as expected and extends up to 20 mm for β < 0.6. This was due to punching action and ovalizing flexibility of the chord, the brace member transfers most of the load at saddle position. As the diameter ratio (β ≥ 0.6) approaches unity, the brace transfers the load tangentially on to the chord, thus hotspot location can be observed in crown and saddle with slight deviations. This can be substantiated by dramatic increase in the ultimate capacity of joints. The present study focuses on residual strength of small crack length in hotspot and non-hotspot regions. The crack length used for analysis is summarised in Table 2a, b for part through and through thickness crack. Since the T-tubular joint is symmetry in two planes the crack length was considered up to 25% of brace circumference. As stated earlier, cracks can be modelled in XFEM independent of mesh [10–12]. The in-built level set method automatically generates the position of crack with respect to model when the shell is used for representation of crack. It can also be written in the input file using signed distance (F, ) value for respective nodes. The signed distance is the distance between the discontinuity (crack) and the nearest nodes. For example, in a 2D mesh layout (see Fig. 3a), the signed distance value shall be (0.5,

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Table 2 a. Part through thickness crack geometry and crack locations. b. Through thickness crack geometry and crack locations Case β γ 2c (mm) a (mm) Cracked % of crack Crack tip area (mm2 ) length =2c/π d (a) TN12

0.5

20

5

5

19.64

0.4

Crown QP

TN1 TN5a TN8a1 TN8a2 TN4 TN6a TN6a1 TN6a2 TN2a TN3a1 TN10a1 TN8a3 TN8a4 TN16a TN2a1 TN6a3 TN6a4 TN9a1 TN8a5 TN8a6 TN3a2 TN7

0.3 0.5 0.8 0.8 0.5 0.6 0.6 0.6 0.3 0.4 0.4 0.8 0.8 0.3 0.3 0.6 0.6 0.3 0.8 0.8 0.4 0.7

10 10 10 10 10 10 10 10 10 10 20 10 10 30 10 10 10 20 10 10 10 10

5 13.13 30 30 20 24 30 30 20 28 30 60 60 30 30 60 60 30 90 90 54 100

5 10 18 18 10 10 18 18 10 18 10 18 18 7 18 18 18 10 18 18 18 10

19.64 103.12 424.15 424.15 187.5 188.5 424.15 424.15 157.09 424.15 235.62 848.23 848.23 164.93 424.15 848.23 848.23 235.62 1272.34 1272.34 848.23 785.4

0.7 1.1 1.6 1.6 1.7 1.7 2.1 2.1 2.8 3.0 3.2 3.2 3.2 4.2 4.2 4.2 4.2 4.2 4.8 4.8 6.0 6.1

Crown Saddle Saddle Crown Crown Crown Saddle Crown Saddle Saddle Saddle Saddle Crown Saddle Saddle Saddle Crown Saddle Saddle Crown Saddle Saddle QP

TN10a2 TN6a5 TN6a6 TN16a2 TN2a2 TN9a2 TN3a3 TN10a3 TN16a3 TN2a3 TN9a3

0.4 0.6 0.6 0.3 0.3 0.3 0.4 0.4 0.3 0.3 0.3

20 10 10 30 10 20 10 20 30 10 20

60 90 90 60 60 60 84 90 90 90 90

10 18 18 7 18 10 18 10 7 18 10

471.23 1272.34 1272.34 326.84 848.32 471.23 1272.34 766.85 494.8 1272.34 766.85

6.4 6.4 6.4 8.5 8.5 8.5 9.0 9.5 12.7 12.7 12.7

Saddle Saddle Crown Saddle Saddle Saddle Saddle Saddle Saddle Saddle Saddle (continued)

Residual Strength of Cracked Tubular Joint … Table 2 (continued) Case β γ

401

2a (mm) b (mm)

Cracked area (mm2 )

% of crack Crack tip length =2a/π d

(b) TN15 TN8b TN6b

0.9 0.5 0.6

20 10 10

14.2 20 211.5

37.5 37.5 37.5

532.5 750 7931.3

0.7 1.1 12.8

Saddle Saddle Crown QP

TN3b

0.4

10

141.3

37.5

5298.8

15

Crown QP

TN2b TN5b

0.3 0.5

10 10

176.5 294.4

37.5 37.5

6618.5 11038.8

25 25

Saddle Saddle QP

Fig. 3 a Typical 2D Mesh showing nodal distance and crack location, b meshed joint with crack pre-set location for XFEM analysis

−1.5) at node 1, similarly it can be written for other nodes. The level set method is to track discontinuity using signed distance function. This was incorporated in XFEM [12] to track the crack tip with respect to nearby nodes. The jump (Heaviside) and asymptotic function [12] are used to capture the discontinuity at prescribed nodes

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and crack tip singularities, respectively. These functions are enriched for a radius equal to 3 times the characteristic element length from the crack tip by default [12]. The complexity of crack is limited by the given three-dimensional shell in XFEM. Based on SCF, the crack has been assigned at position using three-dimensional shell, as shown in Fig. 3b. Then, the XFEM method was applied to estimate the residual static strength and predict the failure using J-integral from elastic and elastic-plastic analysis.

3 Results and Discussion 3.1 Validation of Numerical Model The geometric and material properties of joint UT5 used for the validation have been taken from Lie et al. [4] and the same is summarised in Table 3. The validation study has been carried out using varying mesh with finer mesh near the footprint of the brace brick elements. Mesh details and the ultimate capacity obtained from the simulation are summarised in Table 4 and shown in Fig. 4a, b. The sizes of elements were varied from 20 to 1.75 mm. This resulted in total number of elements ranging from 20,000 to 112,290. The ultimate capacity is defined as the maximum peak load in the load–deformation diagram, i.e. when joint is loaded in compression from brace end which may show a maximum peak load before the load carrying capacity reduces for further deformation. In contrast, there may not be any distinct maximum peak load when joints are subjected to brace end tension. This was evident from the experiment and numerical investigation carried out by Lie et al. [4]. Thus, it is necessary to use

Table 3 Joint parameters used for validation Specimen Brace Chord d (mm) t (mm) D (mm) T (mm) UT5

108

6

219

6

σy (MPa)

σu (MPa)

E (MPa) Elongation

290.5

585.8

161.0

Table 4 Summary of ultimate strength of uncracked tubular joint (T5) Joint ID Size of element No. of Numerical Simulation Pu (kN) (mm) elements Around Away δ/D  12.5% 2 TES joint from joint 0.03

25.5%

Experiment (Lie et al.) Pu (kN)

UV1

4

20

20,268

197.1

199.2

380

UV2

3

20

28,348

196.5

207.4

–

174 174

UV3

2

20

83,010

204.7

210.0

380

174

UV4

1.75

20

1,12,290

204.7

210.0

380

174

Residual Strength of Cracked Tubular Joint …

403

Fig. 4 a Load (P)—displacement( ) response, b load (P)—chord deformation (δ/D) response

an appropriate criterion to estimate the ultimate capacity for tensile loaded joints. Several methods exist in literature for the evaluation of ultimate capacity of tubular joints. The noted one commonly used are listed below: (a) Twice Elastic Slope (TES) method, (b) 12.5% maximum principal strain method, (c) 3% chord displacement method. TES method uses the intersection of a straight line from origin to the load–deflection curve, and the slope of the line is taken as twice the elastic slope (F) taken clockwise from vertical axis (i.e. load axis). The 12.5% maximum principal strain method uses the load at 12.5% strain as the ultimate capacity. The strain is taken as a peak strain at the chord–brace interface locations. The 3% chord displacement (ovalisation) method uses the load at which the chord displacement becomes 3% of chord diameter. Lie et al. [4] have used Twice Elastic Slope (TES) criterion to determine the ultimate capacity of tensile loaded joints. The ultimate capacity obtained using this method by Lie et al. [4] for the uncracked tubular joint (UT5) in experiment was 174 kN. The ultimate capacity obtained from numerical simulation by applying TES criteria was 380 kN in all cases, except in one case. Lee and Dexter [16] predicted the ultimate capacity for T- and Y-tubular joints (γ > 10) using TES. The determined ultimate capacity using TES was widespread when compared with the values obtained from characteristic equations of codal provisions under brace end tension loads. Hence, this method seems to be not recommended for the present investigation of uncracked joints. The chord ovalisation and first crack were observed by Lee and Dexter [16] on comparing the BOMEL database at an assumed 12.5% maximum principal strain. This criterion was consistent and has some physical significance with ISO characteristic equations. Thus, the 12.5% maximum principal strain criterion has been employed to determine the ultimate capacity in the present study. The ultimate capacity obtained using 12.5% maximum principal strain is varying from 199.2 to 210 kN

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for various simulation IDs (UV1, UV2, UV3 and UV4) with different mesh sizes as summarised in Table 4. The other alternative was to use the serviceability criterion based on chord ovality expressed as δ/D. The serviceability criterion of tubular joints [17] was specified as 3% deformation limit of chord wall as shown in Fig. 1a. The 3% chord deformation limit could be obtained by normalising the chord wall displacement (δ) at joint with respect to the diameter of chord (D) and excluding chord beam bending due to axial load [16, 17]. This 3% deformation limit is represented in Fig. 4b by drawing solid straight line at (δ/D  0.03) by excluding chord beam bending. The 3% deformation limit could be used only for uncracked joints as cracks should not occur at serviceability load. The ultimate capacity estimated using 3% deformation limit varies between 197.1 and 204.7 kN for various cases investigated for the validation study. The brace end displacement ( b ) of 12.07 mm is noted at the ultimate capacity as observed from Fig. 4a. The brace displacement ( b ) was noted as 21 mm at ultimate capacity from experiments conducted by Lie et al. [5]. The 3% deformation limit (see Fig. 1a) was calculated by subtracting chord beam bending displacement of ( c  c1 + c2 ) 5.5 mm. Yura limit [13] was not considered additionally as it was nearby 3% deformation limit. It can be observed from Table 4 that the values estimated using 12.5% strain and 3% chord deformation limit are reasonably closer to that estimated from experiments though the difference between them varies 20% to 16.5%, respectively. However, 12.5% strain limit gave consistent results than the 3% deformation limit, and hence 12.5% strain limit is used in the present study for estimating the ultimate strength of uncracked joints loaded under tension. It is further noted from Table 4 that the mesh convergence has been noted between UV3 and UV4 that the ultimate strength of joint has not changed even though the number of elements has been increased considerably between UV3 and UV4. Hence, the mesh size for all the cases in this study is adopted similar to UV3.

3.2 Ultimate Strength Assessment of Uncracked Tubular Joint The ultimate capacity of uncracked T-tubular joints for brace end compression and tension load has been summarised in Table 5 and 6, respectively. The von Mises stress distribution on uncracked tubular joint under tension and compression loading is shown in Fig. 5a, b. The brace punch through was observed for tubular joints loaded under brace end compression as shown in Fig. 5b, whereas the brace pullout was observed for tubular joints loaded under brace end tension as shown in Fig. 5a. The non-dimensional parameter Qu has been obtained by dividing the estimated ultimate capacity with yield stress and square of thickness of chord, as shown in Eq. 1. This non-dimensional capacity has been compared with that obtained from

Residual Strength of Cracked Tubular Joint …

405

Table 5 Ultimate capacities of uncracked joints loaded under compression Joint 8 β γ Fy Peak δ/D  FE Qu API Qu ID load 0.03 (Mpa) = Pu /F y * (kN) (kN) T2 TN2 90 0.3 TN3 90 0.4 TN5 90 0.5 TN6 90 0.6 TN7 90 0.7 TN8 90 0.8 TN9 90 0.3 TN10 90 0.4 TN11 90 0.5 TN13 90 0.6 TN14 90 0.8 TN16 90 0.3 TN17 90 0.5 TN18 90 0.6 TN19 90 0.8 TN20 90 0.3 TN21 90 0.5 TN22 90 0.6 TN23 90 0.8 Mean Standard deviation CoV (%)

10 10 10 10 10 10 20 20 20 20 20 30 30 30 30 40 40 40 40

240 240 240 240 240 240 240 240 240 240 240 345 345 345 345 345 345 345 345

2810 3895 5076 6649 7602 8848 993.4 1210 1620 2088 3065 780 926 1110 2021 215 524 667 1096

2810 3882 4921 6392 7435 8599 820.4 1140 1536 2015 3064 581.4 909 1097 1684 210 496 658 1080

8.33 11.50 14.58 18.94 22.03 25.48 9.47 13.16 17.73 23.26 35.36 10.79 17.18 20.59 37.49 6.91 16.34 21.67 35.58

6.88 9.26 12.04 15.16 18.62 22.41 8.13 11.06 18.61 23.02 33.04 8.04 14.67 18.69 33.22 8.04 14.67 18.69 33.22

FE/API

1.21 1.24 1.21 1.25 1.18 1.14 1.16 1.19 0.95 1.01 1.07 1.34 1.17 1.10 1.13 0.86 1.11 1.16 1.07 1.12 0.14 12.80

empirical equations based on recommendations of API RP 2A for tubular joints. The non-dimensional capacity for axial load can be expressed as Qu 

Pu sin θ Fy T 2

(1)

where Pu is the estimated ultimate capacity of joint against the axial load. The ultimate simulated capacities (Pu ) of joints loaded under compression were determined using 3% chord displacement in order to limit the deformation. Moreover, the ultimate capacities estimated using 3% chord displacement limit were similar to maximum peak load, except in few cases. The effect of thickness ratio (τ) on ultimate strength was less as expected, for a common chord slenderness ratio (γ) and diameter ratio (β), as shown in Fig. 6a. The non-dimensionalised load–deformation response for compression loaded joints is shown in Fig. 6b, which are typical for other compression loaded joints.

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Table 6 Ultimate capacities of uncracked joints loaded under tension Joint ID 8 β γ Fy δ/D  12.5% 2 TES FE Qu 0.03 (Mpa) load = Pu /F y (kN) (kN) * T2 TN2 90 0.3 TN3 90 0.4 TN5 90 0.5 TN6 90 0.6 TN7 90 0.7 TN8 90 0.8 TN9 90 0.3 TN10 90 0.4 TN13 90 0.6 TN14 90 0.7 TN16 90 0.3 TN17 90 0.5 TN18 90 0.6 TN19 90 0.8 TN20 90 0.3 TN21 90 0.5 TN22 90 0.6 TN23 90 0.8 Mean Standard deviation CoV (%)

10 10 10 10 10 10 20 20 20 20 30 30 30 30 40 40 40 40

240 240 240 240 240 240 345 345 345 240 345 345 345 345 345 345 345 345

3095 4158 5291 6370 7398 8496 2070 3140 3930 3348 1080 1845 1910 3660 728 1228 1450 2412

3052 4075 5100 6200 7185 8247 1563 2597 3488 2700 780 1579 1900 2190 300 750 1080 1300

2900 3880 4800 6100 6980 8100 1968 2980 4272 3000 1520 – 1954 3770 680 – – 2596

9.04 12.07 15.11 18.37 21.29 24.44 12.55 16.50 28.01 31.16 14.48 29.29 35.25 40.63 9.84 27.88 35.43 42.65

API Qu

FE/API

9 12 15 18 21 24 9 12 18 21 9 15 18 24 9 15 18 24

1.00 1.01 1.01 1.02 1.01 1.02 1.39 1.38 1.56 1.48 1.61 1.95 1.96 1.69 1.09 1.64 1.97 1.78 1.41 0.37 25.9

The variation of Qu with thickness ratio obtained from simulation has been compared with that estimated using API RP 2A [13] as shown Fig. 6a for γ  10 and 20. The simulated/estimated codal API RP 2A [13] ultimate capacity statistics has been summarised in Table 5, which show a mean of 1.12 and coefficient of variation of 12.8% for T-joints loaded under compression. This indicates overall good correlation between simulated and predicted results. Thus, ultimate capacities are safely underpredicted by the empirical equations of API RP 2A [13] for joints loaded under compression. As stated earlier, there is no distinct peak for joints loaded in tension which is shown in Figs. 7a, b. The load–deformation response for the τ  0.5 and γ  10 joints is shown in Fig. 7a, which is typical for other tension loaded joints. In this plot, the applied load has not been non-dimensionalised in order to compare with TES and 3% chord displacement limit. So, the relative proximity of all the failure criteria can be compared. The residual γ effects are overpredicted after non-dimensionalisation of ultimate capacities as shown in Fig. 7b. The ultimate simulated capacities for joints loaded under tension were determined using 12.5% maximum principal strain criteria. The simulated/codal API RP 2A [13] ultimate capacity statistics has been

Residual Strength of Cracked Tubular Joint …

407

Fig. 5 a Stress distribution of tubular joint under tensile load, b stress distribution of tubular joint under compressive load

summarised in Table 6, show a mean of 1.41 and coefficient of variation of 27% for T-joints under tensile loading. This indicates that the ultimate capacities are safely much underpredicted by the empirical equations of API RP 2A [13] for joints loaded under tension.

3.3 Residual Strength Assessment of Cracked Tubular Joint The 12.5% maximum principal strain is a first crack failure criterion [16]. According to serviceability criteria (3% deformation limit), there should be no visible crack in the tubular joints [17]. As the joints are pre-cracked, the criteria such as 12.5% principal strain and 3% deformation limit are not considered for the residual capacity of cracked tubular joints. Hence, the residual strength for cracked tubular joint was estimated using twice elastic slope criterion. This criterion is well established for residual strength of cracked tubular joints [3, 4, 18]. Figure 8a, b represent the

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Fig. 6 a Comparison of FE results for compression loaded joints (β  0.3) with API, b load–deformation responses for compression loaded joints (τ  0.5)

typical deformation of part through thickness crack and through thickness crack, respectively. From the plots Fig. 9a, b, it can be inferred that the initial stiffness slope of cracked remains the same with respect to uncracked tubular joints. The residual strength of cracked tubular joint can be estimated by applying the reduction factor FAR to the respective characteristic strength of uncracked tubular joint. The FAR used for evaluation is as per BS 7910 [1], which is shown in Eq. 2.   mq 1 Ac (2) Reduction factor FAR  1 − * T lw Qβ Qβ  1 for β ≤ 0.6

Qβ 

0.3 for β > 0.6 β(1 − 0.833)

Residual Strength of Cracked Tubular Joint …

409

Fig. 7 a Load (P)–deformation (δ) responses for tension loaded joints (τ  0.5, γ  10), b load (P)–deformation (δ) responses for tension loaded joints (τ  0.5, β  0.3)

where Ac = area of crack, Ac = 0.5πac and 2ab for part through thickness crack and through thickness, respectively, lw  2π rK a as per AWS [19], r  effective radius of intersection, K a  1 for axial load, mq  0 for part through thickness crack. mq = 1 and 0 as per HSE characteristic design strength and API RP 2A [13] design tension strength for through thickness crack. The non-dimensional parameter (Quc ) is obtained in similar as of Eq. (1), expect the ultimate capacity (Pu ) that is replaced by (Pu−c ). Then, the actual F AR is obtained by dividing Quc /Qu . The residual strength estimated using BS 7910 [1] method based on FAR compares reasonably well with that obtained from present numerical simulations as shown in Table 7a. A maximum decrease in estimated residual static strength of cracked is observed to be 8.1% when compared to corresponding ultimate strength of uncracked, in case of TN6a. The residual strength of TN3a was only 0.625 times of TN6a, even though the crack length of TN3a was 10 times of TN6a. This shows that the influence of crack length is not much in the reduction of residual strength. The reduction in residual strength is significant for joints with smaller diameter ratio (β) which can be seen in Fig. 10. The residual strength for joints with small

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Fig. 8 a Deformation of through, b deformation of part through thickness crack

Fig. 9 a Load–deformation response through thickness crack, b load–deformation for response for part through thickness crack

Residual Strength of Cracked Tubular Joint …

411

Table 7 a. Residual strength of joints with part through thickness crack under tension. b. Residual strength of joints with through thickness crack under tension Case

Pu (kN) {1}

F AR {2}

Pc−p (kN) = Pu × F AR {3}  {1} * {2}

Pu−c (kN) {4}

Actual F AR (Quc/ Qu ) {4}/{1}

Pu−c /Pc−p {4}/{3}

TN12 TN1 TN5a TN6a TN4 TN2a TN7 TN3a TN2a1 TN2a2 TN2a3 TN3a1 TN3a2 TN3a3 TN6a1 TN6a3 TN6a5 TN6a2 TN6a4 TN6a6 TN8a1

1272 1980 4800 6100 5046 2970 7282 4036 3052 3052 3052 4075 4075 4075 6100 6100 6100 6100 6100 6100 12,000

0.999 0.999 0.998 0.996 0.996 0.994 0.987 0.969 0.984 0.968 0.952 0.989 0.977 0.966 0.992 0.984 0.976 0.992 0.984 0.976 0.994

1266.0 1998.5 4788.8 6167.7 5028.0 2952.2 7189.6 3827.1 3003.2 2954.3 2905.5 4030.2 3981.3 3936.5 6051.2 6002.4 5953.6 6051.2 6002.4 5953.6 11928.0

1269.0 1978.0 4790.0 5600.0 5030.0 2800.0 7100.0 3820.0 2995.2 2894.1 2841.5 3964.9 3915.3 3904.3 5983 5969 5955 5963 5952 5992 11,920

0.998 0.999 0.998 0.918 0.997 0.943 0.975 0.946 0.981 0.948 0.931 0.973 0.961 0.958 0.981 0.979 0.976 0.977 0.975 0.982 0.993

1.002 0.990 1.000 0.908 1.000 0.948 0.988 0.998 0.997 0.980 0.978 0.984 0.983 0.992 0.989 0.994 1.000 0.984 0.990 1.006 0.999

TN8a3

12,000

0.988

11856.0

11,900

0.992

1.004

TN8a5

12,000

0.982

11784.0

11,860

0.988

1.006

TN8a2

12,000

0.994

11928.0

11,915

0.993

0.998

TN8a4

12,000

0.988

11856.0

11,900

0.992

1.004

TN8a6

12,000

0.982

11784.0

11,885

0.990

1.008

1563 1563 1563 780 780 780

0.982 0.964 0.947 0.981 0.963 0.944

1534.9 1506.7 1480.2 765.2 751.1 736.3

1475.0 1445.0 1425.0 704.8 693.3 686.1

0.944 0.925 0.912 0.904 0.889 0.880

0.961 0.959 0.963 0.921 0.923 0.932 0.963 0.93

4800 6090 2970 4036 8363

0.750 0.858 0.750 0.850 0.989

3600.0 5314.3 2227.5 3430.9 8112.9

4539 5762 2210 3785 8248

0.945 0.931 0.744 0.938 0.986

1.260 1.100 0.992 1.080 1.017 1.090 9.63

(a)

TN9a1 TN9a2 TN9a3 T16a1 T16a2 T16a3 Mean CoV (%) (b) TN5b TN6b TN2b TN3b TN8b Mean CoV (%)

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Fig. 10 Comparison of reduction in strength with crack length at saddle location for different diameter ratios β and γ  10, τ  0.5

Fig. 11 Comparison of reduction in strength with crack length for different crack locations and γ  10, τ  0.5

diameter ratio (β  0.3, 0.4) decreased by an average of 1.3% in addition to the existing reduction factor (FAR ). The residual strength is higher for the same crack length present on increasing diameter ratio. The reduction in residual strength is of similar manner irrespective of hotspot position, i.e. crown or saddle at higher diameter ratio (β > 0.6), which can be seen from Fig. 11. The residual strength decreases on increasing the chord slenderness ratio for a common crack length and diameter ratio, which can be seen in Fig. 12. The residual strength for joints with increasing chord slenderness ratio γ  10–30 decreased by an average 3% in addition to the existing reduction factor (FAR ). It is known that the

Residual Strength of Cracked Tubular Joint …

413

Fig. 12 Comparison of reduction in strength with crack length at saddle location for different chord slenderness ratios γ and β  0.3, τ  0.5

reduction factor as per BS 7910 [1] is based on β, T and l w . In general, the strength of joint reduces as the chord slenderness ratio increases. So, this chord slenderness factor needs to be considered. The residual strength of joints with through thickness crack loaded under tension has been summarised in Table 7b. The maximum reduction in strength for through thickness crack was 26%, in case of TN2b. This shows that the joint has residual capacity even when the crack length was 25% of brace circumference. The reduction in residual strength varies based on crack type which can be seen on comparing cases TN5a (part through thickness crack) and TN8b (through thickness crack). These two joints have crack tip at hotspot (saddle) and the same percentage of crack length (1.1%). The reduction in strength is higher for TN8b (β = 0.8) compared to TN5a (β = 0.5), even though β is higher compared to TN5a. This shows that through thickness crack results in higher reduction of residual strength. The residual static strength for brace end compression load cases is summarised in Table 8a, b for part through and through thickness crack, respectively. The reduction in residual static strength was less irrespective of crack type, under brace end compression load which can be noted from Table 8a, b. The influence of brace end loading on residual strength has been examined under both load cases. It has been noticed that reduction in residual strength was higher in case of brace end tensile load rather than compressive load which can be seen in cases of TN1 and TN2a. Thus, an overall reduction of 5% was estimated in addition to the existing reduction factor as per BS 7910 [1] for joints with part through thickness crack loaded under tension. The reduction factor as per BS 7910 [1] was satisfactory for through thickness crack under tension loading.

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Table 8 a. Residual strength of joints with part through thickness crack under compression. b. Residual strength of joints with through thickness crack under compression Case Pu (kN) F AR Pc−p (kN) Pu−c (kN) Pu−c /Pc−p Actual F AR d{1} = Pu × F AR {4} {2} {4}/{3} (Quc /Qu ) {4}/{1} {3}={1}*{2} (a) TN1 TN2a (b)

1971 2977

0.999 0.994

1969.0 2959.5

1962 2957

0.996 0.999

0.995 0.993

TN15

3353

0.990

3319.2

3293

0.992

0.982

4 Summary and Conclusion 4.1 Summary The FE simulations were carried out for uncracked and cracked T-tubular joints under axial compressive and tensile loading. On comparing, the simulated ultimate capacities of uncracked tubular joints with codal provisions (API RP 2A [13]), a good correlation was obtained, even though there are some deviations due to γ effect. This demonstrates the validity of numerical procedure. The hotspot location was observed in and around saddle position as expected and extends up to 20 mm for β < 0.6. As the diameter ratio (β ≥ 0.6) approaches unity, the hotspot location can be observed in crown and saddle with slight deviations. The residual strength was obtained using twice elastic slope criterion for cracked tubular joints.

4.2 Conclusion The residual strength depends upon crack location, crack type, crack shape, load applied and also geometric parameters of tubular joints such as β and γ ratio. From simulations, the following were observed: • If the crack is present at the saddle location (hotspot), the reduction in residual strength is higher at smaller diameter ratio β < 0.6 compared to β ≥ 0.6. • The reduction in residual strength is in similar manner irrespective of hotspot location, i.e. crown or saddle, when β ≥ 0.6. • In the existing reduction factor (BS 7910 [1]) an additional 5% deduction is suggested, while estimating the residual strength, for part through thickness crack in tubular joints (β ≤ 0.6, γ > 10) loaded under tension. • The existing reduction factor (BS 7910 [1]) is conservative for through thickness crack in tubular joints loaded under tension.

Residual Strength of Cracked Tubular Joint …

415

• The through thickness crack results in much reduction of strength compared to part through thickness crack. The joint has residual capacity even when the crack length was up to 25% of brace circumference. • The residual strength reduction was less for tubular joints under compression loading as expected. The residual strength has been obtained by considering tubular joints as specially fabricated. A weld correction factor is needed to be used in order to employ these residual strengths to tubular joints with weld.

References 1. British Standards 7910 (2005) Guide to methods for assessing the acceptability of flaws in metallic structures, vol 3 2. Burdekin FM (2001) The static strength of cracked joints in tubular members. Offshore technology report OTO-2001/080, Healthy and Safety Executive, London, UK 3. Lie ST, Li T, Shao YB (2017) Fatigue and fracture strength of a multi-planar circular hollow section TT-joint. 129:101–110. https://doi.org/10.1016/j.jcsr.2016.11.001 4. Lie ST, Li T, Shao YB (2014) Plastic collapse load prediction and failure assessment diagram analysis of cracked circular hollow section T-joint and Y-joint. Fatigue Fract Mater Struct 314–324. https://doi.org/10.1111/ffe.12115 5. Lee MMK (1999) Strength of ring-stiffened tubular T-joints in offshore structures—a numerical parametric study. 51:239–264 6. Anderson TL (1995) Fracture mechanics. CRC press 7. Lie ST, Lee CK, Chiew SP, Shao YB (2005) Mesh modelling and analysis of cracked uni-planar tubular K-joints. J Constr Steel Res 61:235–264. https://doi.org/10.1016/j.jcsr.2004.05.006 8. Lie ST, Lee CK, Wong SM (2003) Model and mesh generation of cracked tubular Y-joints 70:161–184 9. Lie S, Lee C, Chiew S (2006) Static strength of cracked square hollow section T joints under axial loads II: numerical. J Struc Eng 132:378–386 10. Dolbow J, Belytschko T (1996) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46(1):131–150 11. Jitpairod K (2015) Fatigue behavior and xfem based life prediction of tubular x-joints with concrete filled chord. PhD thesis submitted to National University of Singapore 12. ABAQUS (2012) ABAQUS theory manual, Version 6.12. Hibbitt, Karlsson and Sorensen Inc, Pawtucket, Rhode Island 13. American Petroleum Institute (2014) Recommended practice for planning, designing and constructing fixed offshore platforms—working stress design 14. Riks E (1979) An incremental approach to the solution of buckling and snapping problems. Int J Solids Struct 15:524–551 15. Det NorskeVeritas (2011) Recommended practice—C203. Fatigue design of offshore steel structures 16. Lee MMK, Dexter EM (2004) Finite element modelling of multi-planar offshore tubular joints. ASME 126:120–128 17. Wardenier J Hollow sections in structural applications. Comite International pour la’ Development et Etude de la construction tubulaire

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18. Taliie-Faz B, Dover WD, Brenan FP (2000) Static strength of cracked high strength steel tubular joints. Health and Safety Executive 78:1–53 19. American Welding Society (2006) D.1.1.-1 Structural welding code—steel

Wave Transformation Due to Floating Elastic Thick Plate over Changing Bottom Topography K. M. Praveen and D. Karmakar

Abstract In the present study, the wave interaction with floating thick elastic plate is studied over changing bottom topography. The effect of flexible floating plates is studied based on Timoshenko–Mindlin’s theory in finite water depth and shallow water approximations. The hydroelastic analysis is performed at varying water depths and plate sizes to get the behaviour of elastic plate under the action of ocean wave. Different bottom topography cases are considered in the analysis of wave interaction with floating thick elastic plate. A mathematical model considering the modecoupling relation along with the orthogonality condition is formulated to analyse the wave scattering due to floating thick elastic plate with varying bottom topography. The numerical results for the hydroelastic behaviour are obtained for wave interaction with floating plate with free-edge condition in varying bottom topography. The present analysis helps to understand the significance of rotary inertia and transverse shear deformation for the floating elastic plates. The study provides an insight into the effect of seabed profile over the wave interaction with floating thick elastic plate in finite water depth. Keywords Hydroelasticity · Timoshenko–Mindlin’s plate theory Bottom topography · VLFS

1 Introduction There has been increasing demand for the exploration of the sea along the coastal areas for land and energy. The construction of VLFS has been advantageous as compared to traditional sea reclamation and bottom supported offshore structures. These structures are huge in length as compared with the wavelength of the ocean waves, and hence wave-induced rigid body motions are negligible. These structures are considered to be flexible, and hence the study of hydroelastic behaviour becomes more K. M. Praveen · D. Karmakar (B) Department of Applied Mechanics and Hydraulics, National Institute of Technology Karnataka, Surathkal, Mangalore 575025, Karnataka, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_31

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important than their rigid body motions. These structures are usually constructed near shore, and hence the effect of sea bottom profile becomes significant. The sea bottom is not flat throughout; there are various kinds of undulation which give rise to wave refraction, shoaling and wave breaking. Most of the studies performed by researchers have considered the structure to be thin for the hydroelastic analysis of VLFS based on Euler–Bernoulli beam theory but these structures have an accountable thickness, and hence Timoshenko–Mindlin’s plate theory is more realistic for the analysis as formulated by Mindlin [16]. A significant study using the Timoshenko–Mindlin’s thick plate theory was carried out by researchers [2, 9, 11, 17] for wave interaction with sea ice and wave interaction with offshore floating structure. The scattering of waves for varying water depth was analysed by Evans and Linton [8] transforming the problem into a uniform strip resulting in a variable free-surface boundary condition. Athanassoulis and Belibassakis [1] derived a consistent coupled-mode theory for the propagation of small amplitude water waves over variable bathymetry regions. Kyoung et al. [15] considered an influence of sea bottom topography on the hydroelastic response of a very large floating structure (VLFS). The finite element method based on the variational formulation is used to calculate the sea bottom effects in the fluid domain. Karmakar and Sahoo [12] analysed the scattering of surface water waves by a semiinfinite floating membrane due to an abrupt change in bottom topography. Further, Karmakar et al. [13] studied the oblique flexural gravity-wave scattering by multiple step bottom topography in finite water depth and shallow water approximations. The energy relation is derived for the oblique flexural gravity-wave scattering due to a change in bottom topography using the argument of wave energy flux. Bhattacharjee and Soares [5] investigated diffraction of obliquely incident waves by a floating structure near a wall with step-type bottom topography in finite water depth and shallow water approximations. Eigenfunction expansion method was used to obtain the solution of the problem under the potential flow approach. Karmakar and Soares [14] performed the study on the interaction of oblique incident wave with a moored floating membrane for both the cases of finite water depth and shallow water approximation with changes in bottom topography. The energy relation was also derived for the oblique gravity wave in the presence of floating membrane due to an abrupt change in bottom topography for various cases using the law of conservation of energy flux and alternately by the direct application of Green’s second identity. The studies on the wave interaction with floating structures with change in bathymetry were performed by researchers to analyse the effect of bottom topography in the wave transformation. Belibassakis and Athanassoulis [3, 4] and Belibassakis et al. [6] extended the coupled-mode model applied to the hydroelastic analysis of three-dimensional large floating bodies of shallow draft or ice sheets of small thickness, lying over variable bathymetry regions. The hydroelastic mode series expansion of the wave field is adopted, enhanced by an appropriate sloping bottom mode to treat the wave field beneath the elastic floating plate, down to the sloping bottom boundary. Rezanejad et al. [18] analysed the effect on the efficiency by implementing a dualchamber oscillating water column (OWC) placed over the stepped bottom. Matched eigenfunction expansion and boundary integral equation method (BIEM) was used

Wave Transformation Due to Floating Elastic Thick Plate …

419

to analyse the change in the topography on the power generation. Choudhary and Martha [7] examined the diffraction of surface water waves by an undulating bed in the presence of different kinds of thin vertical barriers. Gerostathis et al. [10] extended the coupled-mode model applied to the hydroelastic analysis of three-dimensional large floating bodies of shallow draft lying over variable bathymetry regions. A general bathymetry is assumed, characterised by a continuous depth function joining two regions of different depths. In the present study, the wave scattering by a floating elastic plate is analysed based on Timoshenko–Mindlin’s thick plate theory in finite water depth with varying bottom topography. The eigenfunction expansion method with mode-coupling relation is applied to obtain the solution for the case of wave interaction with freely floating articulated elastic plate. The free-free edge of the floating elastic plate is considered in the analysis. The bottom topography is considered to be stepped type topography and the effect of stepped bottom topography is analysed by varying the water depth in wave transmitted region. The numerical computation is performed to analyse the wave reflection, wave transmission and hydroelastic behaviour of an elastic plate under the action of the incident wave with varying bottom topography.

2 Mathematical Formulation The scattering of waves due to finite floating elastic plate based on Timoshenko –Mindlin’s thick plate theory with changing bottom topography is analysed under the assumption of linearised wave theory. The monochromatic wave is incident on the thick floating elastic plate along the positive x-direction. A two-dimensional coordinate system is considered in the analysis with x-axis being the horizontal and the y-axis considered vertically downward positive as shown in Fig. 1. The fluid domain in finite water depth is divided into three regions, upstream open water region at 0 < x < ∞, 0 < y < h1 as region 1, the finite thick floating elastic plate covering the free surface of the fluid at −a < x < 0, 0 < y < h2 as region 2 and downstream open water domain at −∞ < x < −a, 0 < y < h3 as region 3. The two edges of the plate at x  0 and x  −a are considered to satisfy free-free edge boundary condition. The floating elastic plate is considered to be having considerable thickness and modelled under the assumption of Timoshenko–Mindlin plate theory. Under the assumption of linearized wave theory, the velocity potential, j (x, y) for j  1, 2, 3 satisfies the Laplace’s equation given by ∇ 2 j (x, y)  0 at − ∞ < x < ∞, 0 < y < hj , j  1, 2, 3.

(1)

The linearised kinematic boundary condition at the mean free surface is of the form ζjt  jy , at y  0.

(2a)

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K. M. Praveen and D. Karmakar

Free surface

Incident wave

Thick elastic plate

y=0 x=0

x=-a Region 2 h3

Region 3

h2

Region 1

x h1 y y=h

Fig. 1 Schematic diagram for thick floating elastic plate in changing bottom topography

The dynamic free-surface boundary condition is given by ρjt − ρgζj  patm at y  0,

(2b)

where patm is the atmospheric pressure. The bottom boundary condition is given by jy  0, at y  hj , j  1, 2, 3.

(3)

In the plate-covered region, it is assumed that the plate satisfies the Timoshenko –Mindlin’s equation [9] which includes the effect of rotary inertia and transverse shear deformation is of the form      ρp 2 ρp d 3 2 EI 2 ρp d 2 2 ∂x2 − EI ∂x2 − ∂t ∂t ζ2 + ρp d ∂t2 ζ2  − 1 − ∂x + ∂t p. μGd 12 μGd 12μG

(4)

 where d is the plate thickness, ρp is the plate density, EI  Ed 3 12(1 −ν 2 ) is the plate rigidity, E is the Young’s modulus, ν is the Poisson’s ratio, G  E 2(1 + μ) is the shear modulus of the plate, p is the pressure and μ is the transverse shear coefficient of the plate. Assuming that the wave elevation and the plate deflection are t) simple harmonic motion in time with frequency ω, the velocity potential  j (x,  y, −iωt t) can be written as  y, t)  Re φ y) e and the surface deflection ζ (x, (x, (x, j j   j and ζj (x, t)  Re ηj (x) e−iωt , where Re denotes the real part. In the open water region j  1, 3, the linearized free-surface boundary condition is given by  2 ω φj  0, for x < −a and x > 0, (5) ∂y φj − g The plate-covered boundary condition is obtained by combining the linearised kinematic condition at the surface and Timoshenko–Mindlin’s equation as

Wave Transformation Due to Floating Elastic Thick Plate …



    ms ω2 I EI ms ω2 IS 4 2

∂ +

 − S ∂x + 1 − φ2y EI ρg − ms ω2 x ρg − ms ω2 

ms ω2 IS ρω2 2  1− − S∂x φ2  0, for − a < x < 0, +

EI ρg − ms ω2

421

(6)

 where ρ is the density of water, ms is the mass of the plate, I  d 2 12 is the rotary inertia and S  EI /μGd is the shear deformation for the Timoshenko–Mindlin’s equation. The continuity of velocity and pressure at the interface x  −a and x  0, 0 < y < hj , j  1, 2 is given by φjx  φ(j+1)x and φj  φ(j+1) at x  −a and x  0, 0 < y < hj .

(7)

The floating elastic plate is considered to be freely floating, so the bending moment and the shear force at the edges x  −a and x  0, 0 < y < h2 satisfies the relation 4 2 ∂y3 φ2 (x, y)  0 and ∂xy 3 φ2 (x, y)  ℘∂xy φ2 (x, y) for x  −a and x  0 at y  0, (8)

with ℘ 



 . The far-field radiation condition is given by ⎧

 ⎨ e−ik10 x + R0 eik10 x f10 (y) as x → ∞, φj (x) 

 ⎩ T0 e−ik30 x f30 (y) as x → −∞,

mω2 (S+I ) EI

(9)

with R0 and T0 are the complex amplitudes of the reflected and transmitted waves and kj0 for j  1, 3 are the positive real roots that satisfy the dispersion relation given by  kj0 tanh kj0 hj − ω2 g  0.

(10)

In the next section, the solution procedure of the wave interaction with finite floating elastic plate with changing bottom topography is presented and discussed in detail.

3 Method of Solution In this section, the scattering of waves due to the finite floating elastic plate over varying bottom topography is analysed based on Timoshenko–Mindlin plate theory. The boundary value problem for the scattering of wave by a finite floating elastic plate over varying bottom topography with free-free edge condition is formulated. The velocity potentials φj (x, y) for j  1, 2, 3 satisfy the governing Eq. (1) along

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K. M. Praveen and D. Karmakar

with the boundary condition (3), (5), (6) and (9) as defined in Sect. 2. The velocity potentials φj (x, y) for j  1, 2, 3 at the free surface and the plate-covered regions are of the form ∞ 

 φ1 (x, y)  I0 e−ik10 x + R0 eik10 x f10 (y) + Rn e−κ1n x f1n (y) for x > 0, 0 < y < h1 n1

φ2 (x, y) 

⎧ II    ⎪ ⎪ ⎪ An e−ik2n x + Bn eik2n x f2n (y) ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩

n0,I

+

⎫ ⎪ ⎪ ⎪ ⎪ ⎬

∞ ⎪ 

 ⎪ ⎪ An eκ2n x + Bn e−κ2n x f2n (y)⎪ ⎭

for − a < x < 0, 0 < y < h2

n1

φ3 (x, y)  T0 e−ik30 x f30 (y) +

∞ 

Tn eκ3n x f3n (y)

for x < −a, 0 < y < h3

n1

(11) where Rn , n  0, 1, 2 . . . , An , Bn , n  0, I , II , 1, 2 . . . and Tn , n  0, 1, 2 . . . are the unknown constants to be determined. The eigenfunctions fjn (y)’s are given by



  cosh kjn hj − y cos kjn hj − y fjn (y)  for n  0, I , II and fjn (y)  for n  1, 2, .. (12) cosh kjn hj cos kjn hj

where kjn for j  1, 3 and n  0 are the eigenvalues. These eigenvalues satisfy the dispersion relation in the open water region given by  kj0 tanh kj0 hj − ω2 g  0.

(13)

with kjn  iκjn for n  1, 2 . . . and the dispersion relation has one real root kj0 and an infinite number of purely imaginary roots κjn for n  1, 2 . . . In the plate-covered region, the kjn for j  2 satisfies the dispersion relation given by     α0 − α1 kjn2 + α2 kjn4 kjn tanh kjn hj − β0 − β1 kjn2  0. (14)  

IS   ms ω2 I EI where α0  1 − ms ω2 EI − S , α2  ρg−m , α1  2 2 , β0  (ρg−ms ω ) ( sω )

 2 2 ρω ρω S IS 2 1 − ms ω2 EI , β1  − ρg−m 2 , I  d /12 is the rotary inertia. The (ρg−ms ω2 ) ( sω ) dispersion relation as in Eq. (14) has one real root kj0 and four complex roots kjn for n  I , II , III , I V of the form ±α ± iβ. In addition, there are an infinite numbers of purely imaginary roots κjn for n  1, 2 . . . It may be noted that the eigenfunctions fjn (y)’s in the open water and plate-covered region satisfy the orthogonality relation as given by 0 for m  n,     0 for m  n, fjm , fjn j1,3   and fjm , fjn j2  (15) Cn for m  n, C  for m  n, with respect to the orthogonal mode-coupling relation defined by

Wave Transformation Due to Floating Elastic Thick Plate …



fjm , fjn

423

hj

 j1,3



fjm (y)fjn (y)dy,

(16a)

0

hj f2m , f2n 

f2m (y)f2n (y)dy − 0

+ where Cn  Cn 

 α1   f2m (0)f2n (0) Q(k2n )

 α2   β1  f (0)f  (0) + f2m f2m (0)f2n (0), (0)f2n (0) + Q(k2n ) 2m 2n P(k2n )

2kjn hj +sinh 2kjn hj ,j 4kjn cosh2 kjn hj

(16b)

 1, 3.

2 + α k 4 )2k h + (α − 3α k 2 + 5α k 4 ) sinh 2k h + (4β k cosh2 k h ) (α0 − α1 kjn 2 jn jn j 0 1 jn 2 jn jn j 1 jn jn j 2 + α k4 ) (4kjn cosh2 kjn hj )(α0 − α1 kjn 2 jn

.

 



2 4 2 P(k2n )  α0 − α1 k2n + α2 k2n and Q(k2n )  β0 − β1 k2n . The constant term Cn , Cn , P(k2n ) and Q(k2n ) for n  1, 2, . . . are obtained by substituting kjn  iκjn for j  1, 2, 3. In order to determine the unknown coefficients, the mode-coupling relation (16b) is applied on the velocity potentials φ2 (0, y) and φ2 (−a, y) with the eigenfunction f2m (y). Using the orthogonal property of the eigenfunction f2m (y) as in Eq. (15) and the expressions of velocity potentials as in Eq. (11) along with the continuity of pressure as in Eq. (7) across the vertical interface x  0, −a, 0 < y < h2 and also applying the edge condition as in Eq. (8) yields hj R0

f10 (y)f2m (y)dy + 0

+

⎧ II ⎨ ⎩

(An + Bn ) +



f10 (y)f2m (y)dy + 0

Rn

N  n1

f1n (y)f2m (y)dy 0

⎫ ⎬ α α1 2   (An + Bn ) (0) − (0) f  (0)f2m f  (0)f2m ⎭ Q(k2n ) 2n Q(k2n ) 2n

β1 f2n (0)f2m (0) − δmn f2n , f2m  −I0 P(k2n )

hj T0 eik30 a

hj

n1

n0,I

+

N +2 

N +2  n1

Tn e−κ3n a

hj

(17)

f10 (y)f2m (y) dy. 0

hj f1n (y)f2m (y)dy +

N  

An e−ik2n a + Bn eik2n a



n0,I ,II

0

α2 α1 β1   (0) − (0) + f  (0)f2m f  (0)f2m f2n (0)f2m (0) − δmn f2n , f2m  0. (18) Q(k2n ) 2n Q(k2n ) 2n P(k2n )



1 for m  n, 0 for m  n. Again, applying the mode-coupling relation (16b) on φ2x (0, y) and φ2x (−a, y) with the eigenfunction f2m (y) and using the orthogonal property of the eigenfunction f2m (y) as in Eq. (15) and the expressions of velocity potentials as in Eq. (11) along where kjm  iκjm for m  1, 2, . . . and δmn 

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K. M. Praveen and D. Karmakar

with continuity of velocity across the vertical interface x  0, −a, 0 < y < h2 as in Eq. (7) and the edge condition as in Eq. (8) yields hj f10 (y)f2m (y)dy − κ1n

ik10 R0 +

N +2 

hj Rn

n1

0

ik2n

II 

(An − Bn ) − κ2n

0

N 



(An − Bn )

n1

n0,I



f1n (y)f2m (y)dy

 α2   α1   ℘f2n (0)f2m f  (0)f  (0) (0) + f2n (0)f2m (0) − Q(k2n ) Q(k2n ) 2n 2m hi β1 f2n (0)f2m (0) − δmn f2n , f2m  −ik10 I0 f10 (y)f2m (y) dy. + P(k2n )

(19)

0

hj − ik30 T0 e

ik2n 

II 

N +2 

Tn e

−κ3n a

n1

0

+

f30 (y)f2m (y)dy + κ3n

ik30 a

(An e

−ik2n a

− Bn e

ik2n a

) − κ2n

ht f3n (y)f2m (y)dy 0

N 

(An e

κ2n a

− Bn e

−κ2n a

)

n1

n0,I

 α2     ℘f2n (0)f2m (0) + f2n (0)f2m (0) Q(k2n ) β1 α1  f2n (0)f2m f2n (0)f2m (0) − δmn f2n , f2m  0. (0) + − Q(k2n ) P(k2n ) ×

(20)

for kjm  iκjm for m  1, 2, . . . The infinite series sums of the algebraic equations as in (17), (18), (19) and (20) are obtained and the linear equations are truncated up to a finite number of N terms in order to solve the system of (4N + 12) equations. The expansion formulae for each of the three regions as in Eq. (11) consists of (4N + 12) unknown coefficients such as Rn , Tn , n  0, 1, 2, . . . N , N + 1, N + 2, An , Bn , n  0, I , II , 1, 2, . . . , N . On solving the system of algebraic equation, the full solution is obtained in terms of the potential functions with the reflection and transmission coefficients is given by ! ! ! k30 tanh k30 h3 ! ! (21) T0 !. Kr  |R0 | and Kr  ! k10 tanh k10 h1 ! The reflection and transmission coefficients are observed to satisfy the energy  2 k30 k10 sinh 2k10 h1 2k30 h3 +sinh 2k30 h3 2 2 balance relation Kr + χ Kt  1 where χ  k k 2 sinh 2k h 2k10 h1 +sinh 2k10 h1 . 10 30

30 3

Wave Transformation Due to Floating Elastic Thick Plate …

425

4 Numerical Results and Discussions The hydroelastic behaviour of the floating thick elastic plate under the action of incident wave is analysed based on Timoshenko–Mindlin theory in finite water depth. The study is performed to analyse the reflection coefficient Kr , plate deflection ζj , bending moment |M (x)|, shear force |W (x)| and strain on the plate |ε| for floating elastic plate with varying bottom topography. The numerical computations are carried out for different values of water depth hj /L, plate thickness d /L, Young’s modulus E and wave frequency ω considering E  5 GPa, ρp /ρw  0.9, ν  0.3 and g  9.8 ms−2 . In this analysis, the parameters such as plate length L  500 m and wave frequency ω  3 s−1 are considered to be fixed unless otherwise mentioned. The water depths in reflected and transmitted regions are considered to be h1  100 m and h3  100 m, respectively. The accuracy of the computed numerical results are checked with the energy relation which satisfies Kr2 + χ Kt2  1.

4.1 Reflection and Transmission Coefficients

(a)

(b)

1.0

1.0

Transmission Coefficient, K t

Refelection Coefficient, K r

The reflection and transmission coefficients are plotted at varying wave frequency. The study shows the variations in reflected and transmitted waves due to the changes in bottom topography with varying wave frequency at varying water depths over plate-covered region as shown in Fig. 2a, b. The zeros in the reflection coefficient indicate complete transmission of waves through the plate. The reflection and transmission coefficients value equal to unity implies that complete reflection or transmission of waves. It is observed that there is an increase in wave with the decrease in water depth which may be due to the increase

0.8

0.6

0.4

0.2 h=90m h=80m h=70m

h=90m h=80m h=70m

0.8

0.6

0.4

0.2

0.0

0.0 0

1

2

3

4

5

Wave frequency, ω(sec ) -1

6

0

1

2

3

4

5

6

Wave frequency, ω(sec-1)

Fig. 2 a Reflection and b transmission coefficient versus wave frequency for different values of water depths

426

K. M. Praveen and D. Karmakar

(a)

0.03

(b)

d=3m d=4m d=5m

0.10

h=70m h=80m h=90m

0.02

Deflection, ζ(m)

Deflection, ζ(m)

0.05 0.01

0.00

-0.01

0.00

-0.05

-0.02 -0.10

-0.03 -500

-450

-400

-350

-300

-250

-200

-150

-100

-50

0

-500

-450

-400

Distance, x(m)

-350

-300

-250

-200

-150

-100

-50

0

Distance, x(m)

Fig. 3 Plate deflection along the plate length at varying a plate thickness and b water depths with changing bottom topography

in wave height at lower water depths. At lower frequencies, there is an increase in reflected waves, whereas at higher frequencies, transmission of waves is found to be higher.

4.2 Surface Deflection The surface deflection along the length of the plate for varying plate thickness and varying water depths over plate-covered region are shown in Fig. 3a, b. It is clearly seen that the deflection increases at the edges of the plate and the deflection decreases with increase in plate thickness. This is due to the fact that with the increase in the plate thickness, the plate rigidity increases and as a result the deflection decreases. It is also observed that there is an increase in deflection with the decrease in water depth at 70 m and it is mainly due to the rise in wave height and reduction in wavelength as the waves approach shallower water depth.

4.3 Wave-Induced Strain on Floating Plate The strain induced in the floating elastic plate due to the action of ocean waves are analysed for varying plate thickness and water depth along plate-covered region in Fig. 4a, b. The wave-induced strain decreases with the increase in plate thickness which is mainly due to an increase in the plate rigidity. The increase in the strain with the decrease in water depth at 70 m may be due to rise in wave height and reduction in wavelength as the waves approach shallow water depth.

Wave Transformation Due to Floating Elastic Thick Plate …

(a)

(b)

-5

4.0x10

d=3m d=4m d=5m

-5

3.0x10

427

-4

6.0x10

h2=70m h2=80m h2=90m

-4

4.0x10 -5

2.0x10

-4

2.0x10 -5

Strain,

Strain,

1.0x10

0.0

0.0

-5

-1.0x10

-4

-2.0x10 -5

-2.0x10

-4

-4.0x10 -5

-3.0x10

-5

-4

-4.0x10

-500

-6.0x10 -450

-400

-350

-300

-250

-200

-150

-100

-50

0

-500

-450

-400

-350

Distance, x(m)

-300

-250

-200

-150

-100

-50

0

Distance, x(m)

Fig. 4 Wave-induced strain versus plate length at varying a plate thickness and b water depths with changing bottom topography

(b)

6

4.0x10

d=3m d=4m d=5m

7

2.0x10

h2=70m h2=80m

7

1.5x10

6

Bending Moment (N-m)

Bending Moment (N-m)

(a)

2.0x10

0.0

6

h2=90m

7

1.0x10

6

5.0x10

0.0

6

-5.0x10

7

-2.0x10

-1.0x10

7

-1.5x10

6

7

-4.0x10

-500

-2.0x10 -450

-400

-350

-300

-250

-200

-150

-100

-50

0

-500

Distance, x(m)

-450

-400

-350

-300

-250

-200

-150

-100

-50

0

Distance, x(m)

Fig. 5 Bending moment along the length of the plate at varying a plate thickness and b water depths with changing bottom topography

4.4 Bending Moment of Floating Plate The bending moment resultants due to the wave interaction with the floating elastic plate are plotted at varying plate thickness and water depth in plate-covered region along the plate length in Fig. 5a, b. The bending moment resultant decreases with an increase in plate thickness mainly due to an increase in plate rigidity. It is found that bending moment increases with the decrease in water depth at 70 m due to rise in wave height and reduction of wavelength as the wave approaches shallow water depth.

428

(a)

K. M. Praveen and D. Karmakar

(b)

5

2.0x10

d=3m d=4m d=5m

5

1.5x10

5

Shear Force (N)

Shear Force (N)

1.0x10

4

5.0x10

0.0

4

8.0x10

5

6.0x10

5

4.0x10

5

2.0x10

5

0.0

-2.0x10

5

5

-4.0x10

5

5

-6.0x10

5

5

-8.0x10

5

-5.0x10

-1.0x10

-1.5x10

h2=70m h2=80m h2=90m

-2.0x10

-500

-450

-400

-350

-300

-250

-200

-150

-100

-50

0

Distance, x(m)

-500

-450

-400

-350

-300

-250

-200

-150

-100

-50

0

Distance, x(m)

Fig. 6 Shear force along the length of the plate at varying a plate thickness and b water depths with changing bottom topography

4.5 Shear Force on Floating Plate The shear force resultants due to the wave interaction with the floating elastic plate are plotted at varying plate thickness and water depth along the plate length in Fig. 6a, b. The shear force resultants decrease with an increase in plate thickness mainly due to the increase in plate rigidity. The shear force is found to increase with the decrease in water depth and may be due to rise in wave height as wave’s approaches shallow water depth.

5 Conclusion The hydroelastic behaviour of floating elastic plate based on Timoshenko–Mindlin’s plate theory under the action of ocean waves in finite water depths is analysed for changing bottom topography. The mathematical model using eigenfunction expansion method is developed for the freely floating elastic plate over changing bottom topography. The conclusions drawn from the present study are as follows: • The increase in the wave transmission is observed in the case of finite water depth for higher wave frequency. • Complete wave transmissions are observed at certain values of wave frequency and significant effect due to the change in water depth in the hydroelastic behaviour of floating elastic plate is observed which is mainly due to rise in wave height and reduction in wavelength. • A steep increase in hydroelastic behaviour is observed at lower water depths in plate-covered region may be mainly due to higher difference in water depth between the mediums of interaction. • The plate rigidity and plate thickness play an important role in the reduction of the hydroelastic behaviour of the plate.

Wave Transformation Due to Floating Elastic Thick Plate …

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• At lower wave frequency, there is an increase in the hydroelastic behaviour of the plate, whereas no significant hydroelastic behaviour is observed at higher wave frequencies. Acknowledgements The authors are thankful to National Institute of Technology Karnataka Surathkal and MHRD for providing necessary support. The authors also acknowledge Science and Engineering Research Board (SERB), Department of Science & Technology (DST), Government of India for supporting financially under the Young Scientist research grant no. YSS/2014/000812.

References 1. Athanassoulis GA, Belibassakis KA (1999) A consistent coupled-mode theory for the propagation of small-amplitude water waves over variable bathymetry regions. J Fluid Mech 389:275–301. https://doi.org/10.1017/s0022112099004978 2. Balmforth NJ, Craster RV (1999) Ocean waves and ice sheets. J Fluid Mech 395:89–124. https://doi.org/10.1017/s0022112099005145 3. Belibassakis KA, Athanassoulis GA (2005) A coupled-mode model for the hydroelastic analysis of large floating bodies over variable bathymetry regions. J Fluid Mech 531:221–249. https://doi.org/10.1017/s0022112005004003 4. Belibassakis KA, Athanassoulis GA (2004) Hydroelastic responses of very large floating structures lying over variable bathymetry regions. In: Proceedings of 14th international offshore and polar engineering conference, Toulon, France, 23–28 May 2004, pp 584–591 5. Bhattacharjee J, Guedes Soares C (2011) Oblique wave interaction with a floating structure near a wall with stepped bottom. Ocean Eng 38(13):1528–1544. https://doi.org/10.1016/j.oceaneng. 2011.07.011 6. Belibassakis KA, Athanassoulis GA, Gerostathis Th (2013) Hydroelastic analysis of very large floating structures in variable bathymetry regions. In: Proceedings of 10th HSTAM international congress on mechanics. Chania, Crete, Greece, 25–27 May 2013 7. Choudhary A, Martha SC (2016) Diffraction of surface water waves by an undulating bed topography in the presence of vertical barrier. Ocean Eng 122:32–43. https://doi.org/10.1016/ j.oceaneng.2016.06.013 8. Evans DV, Linton CM (1994) On step approximations for water-wave problems. J Fluid Mech 278(1):229–249. https://doi.org/10.1017/s002211209400368x 9. Fox C, Squire VA (1991) Coupling between the ocean and an ice shelf. Ann Glaciol 101–108. https://doi.org/10.3189/1991AoG15-1-101-108 10. Gerostathis TP, Belibassakis KA, Athanassoulis GA (2016) 3D hydroelastic analysis of very large floating bodies over variable bathymetry regions. J Ocean Eng Marine Energy 2(2):159–175. https://doi.org/10.1007/s40722-016-0046-6 11. Karmakar D, Sahoo T (2006) Flexural gravity wavemaker problem-revisited. In: Dandapat BS, Majumder BS (eds) Fluid mechanics in industry and environment. Research Publishing Services, Singapore, pp 285–291 12. Karmakar D, Sahoo T (2008) Gravity wave interaction with floating membrane due to abrupt change in water depth. Ocean Eng 35(7):598–615. https://doi.org/10.1016/j.oceaneng.2008. 01.009 13. Karmakar D, Bhattacharjee J, Sahoo T (2010) Oblique flexural gravity-wave scattering due to changes in bottom topography. J Eng Math 66(4):325–341. https://doi.org/10.1007/s10665009-9297-8 14. Karmakar D, Guedes Soares C (2012) Oblique scattering of gravity waves by moored floating membrane with changes in bottom topography. Ocean Eng 54:87–100. https://doi.org/10.1016/ j.oceaneng.2012.07.005

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15. Kyoung JH, Hong SY, Kim BW, Cho SK (2005) Hydroelastic response of a very large floating structure over a variable bottom topography. Ocean Eng 32(17–18):2040–2052. https://doi.org/ 10.1016/j.oceaneng.2005.03.003 16. Mindlin RD (1951) Influence of rotary inertia and shear on flexural motion of isotropic elastic plates. J Appl Mech (ASME) 18:31–38 17. Praveen KM., Karmakar D, Nasar T (2016) Hydroelastic analysis of floating elastic thick plate in shallow water depth. Perspect Sci 8:770–772. https://doi.org/10.1016/j.pisc.2016.06.084 18. Rezanejad K, Bhattacharjee J, Guedes Soares C (2015) Analytical and numerical study of dualchamber oscillating water columns on stepped bottom. Renew Energy 75:272–282. https://doi. org/10.1016/j.renene.2014.09.050

Installation Analysis of Monopile for Offshore Wind Data Collection Platform in High Tidal Environment Devender Gujjula, Satya Kiran Raju Alluri, G. Dhinesh, R. Panneer Selvam and M. V. Ramana Murthy

Abstract India has one of the fastest growing economies in the world and has an increasing energy demand, which is expected to double in 2020 compared to the present demand. Wind energy has gained wide acceptance across the globe and presently the focus is toward development of offshore wind farms. The offshore wind farm technology faces a number of technical challenges due to the harsh installation and operation conditions. Foundations supporting offshore wind turbines/wind data collection platforms are subject to constant wave loads. Offshore work involves increased risks of strong winds which affect the amount of time available for installation and maintenance which in turn influence capital and operation costs. Hence, this work is focused on development and analysis of economic and safe installation methodology in high tidal and current environment. A monopile has been designed suitable for high tidal environment at Gulf of Khambhat and Gulf of Kutch, Gujarat. Monopile static analysis, pile–soil interaction studies, and free vibration analyses have been carried out using finite element method. Developed safe and economic installation methodology through detailed lowering analysis for monopile in regular and irregular wave conditions and recommended appropriate vessel with hydraulic gripper as attachment to restrict the lateral displacements. Keywords Monopile · Design · Lowering analysis · Installation Pile driving analysis D. Gujjula (B) · S. K. R. Alluri · G. Dhinesh · M. V. Ramana Murthy National Institute of Ocean Technology, Chennai 600100, TN, India e-mail: [email protected] S. K. R. Alluri e-mail: [email protected] G. Dhinesh e-mail: [email protected] M. V. Ramana Murthy e-mail: [email protected] R. Panneer Selvam Indian Institute of Technology Madras, Chennai 600036, TN, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_32

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1 Introduction The clean energy cooperation initiative has the purpose to assist India to meet the future energy demand by utilizing sustainable energy generation technologies. Wind energy has gained wide acceptance across the globe and presently the focus is toward development of offshore wind farms. The offshore wind farm technology faces a number of technical challenges due to the harsh installation and operation conditions. India is in the process of developing offshore wind energy in the direct and focused manner for optimum exploitation of offshore wind energy. Significant offshore wind potential has been identified by various technological institutes using satellite and onshore measured winds along Gujarat and Tamil Nadu coasts [1]. For the development and establishment of offshore wind farm, it is required to obtain bankable wind data and check commercial viability of offshore wind project to ensure the financial stability of the project as part of feasibility studies. To obtain the bankable wind data continuously for 2–3 years, a reliable data collection system is required either by utilizing conventional method of wind mast systems or by using any advanced technology options. The conventional offshore met masts are used for data collection but they are costly and require sophisticated marine spread for installation. Presently, due to the advancements in technology, remote controlled Light Detection And Ranging (LiDAR) data collection platforms are being used across the world for ease of installations in offshore locations. To house the data collection equipment, a suitable and reliable supporting structure is required for withstanding the hydrodynamic loads in high tidal range with complex wave-structure environment. This paper focuses on development and analysis of economic and safe installation methodology in high tidal and current environment for selected monopile structure. A monopile is considered as foundation structure to support the wind data collection platform to record the wind behavior continuously for minimum of 2 years to check the commercial feasibility for investors. These structures are subjected to incessant environmental loads such as waves, currents, etc., which are highly nonlinear in nature and may cause failure of structures. Hence, suitable design and installation methods are required to support the platforms without damage during the life span of substructure. Substructure is fabricated as cylindrical hollow structure using the flat steel plates and one end of cylindrical portion will be embedded into seabed during the installation of structure. Large cyclic, lateral loads and bending moments due to the wave, wind loads in addition to axial loads will act on the monopile structures and its design will be governed by these environmental loads. The design limits used for monopile are its lateral deflection and natural frequencies. This type of structures is relatively easy to install in shallow to medium water depths and well suited for sites with water depth ranging from 0 to 40 m. The typical diameter ranges from 1 to 8 m depending on the capacity of turbines. Installation involves hammering the monopile into the seabed, then attaching a platform on its top for housing the data collection equipment.

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As the water depths increase, diameter of pile required to resist static and dynamic forces increases due to high hydrodynamic loads. The wind turbine capacity also increases along with the water depths. Therefore, transportation and installation of monopiles in open sea environment is a challenging task. Hence, this work is focused on development and analysis of economic and safe installation methodology of monopile in high tidal and current environment.

2 Design of Monopile The offshore wind data collection platform has two components, superstructure (support platform) and substructure (monopile). These two components are separately analyzed for appropriate loads and designed as per relevant standards. The superstructure of the platform was designed for self-weight and these loads are transferred to design monopile. In this study, only the design of monopile has been carried out and reported. Various analyses (static, dynamic, free vibration, pile–soil interaction, etc.) were carried out with water depth of 15 and 20 m, considering the wind loads, top equipment loads, and hydrodynamic loads under regular and irregular waves and arrived the monopile diameter as 1 m for 15 m water depth and 1.2 m for 20 m water depth. However, in this paper, detailed analyses and results are reported for 20 m water depth. Monopile of 1.2 m diameter and thickness of 25 mm is considered as substructure for data collection platform. It is embedded to a depth of 15 m below seabed, in a maximum water depth of 20 m and a clearance of 7.5 m (above maximum tide level) to avoid splashing of water on support platform under extreme events. The governing serviceability criterion for design of support platform for LiDAR is limited in maximum rotation at platform level (0.20) under extreme events for flawless operation of LiDAR. The tidal range of 5–7 m and the weight on the top of monopile including platform is 6 tons considered for design. The loads considered for this design are wind loads, hydrodynamic loads, and dead loads on the platform. Wind loads: Extreme wind loads as per IS 875 part-3, with survival (extreme) and operational basic wind speeds at reference height of 10 m above SWL were 50 m/s and 12 m/s, respectively, considered for design and analysis. Appropriate factors are applied to these wind speeds due to probability risk, terrain, structural size, and topography. The drag forces due to corrected wind speeds are obtained as per IS 875 part-3. Hydrodynamic loads: Two critical conditions considered for estimation of hydrodynamic loads due to waves and currents were considered. They are survival (extreme cyclonic event) and operational conditions. It is assumed that waves and currents act in the same direction and site-specific parameters considered for wave and current. Wave kinematics are estimated using appropriate wave theory based on height, period, and water depth as per API RP 2A WSD. The wave and current forces are estimated using Morison’s equation which is semi-empirical formula assuming total

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Fig. 1 Modeling methodology for Pile–soil interaction

forces as sum of inertia and drag forces. The force on the structure depends on ratio of wavelength to diameter. For the present structure with wave diameter to length is less than 0.2 for both the wave climates, and hence falls under Morison’s regime. Static analysis: The monopile is modeled as beam element in Finite Element Software, SACS and analyzed for two extreme cases for two end conditions. First one is bottom fixed condition and second one is considering the pile–soil interaction. The loads for two extreme cases are applied and the deflection profiles are obtained. The utilization of various members is estimated as per API RP 2A WSD. Platform and equipment loads are modeled as lumped mass on top of the monopile. Pile–soil interaction was modeled using three nonlinear springs for each soil layer (two horizontal and one vertical spring—Fig. 1). The nonlinear properties for all horizontal springs are governed by p–y curve (i.e., lateral load versus deflection of the pile), vertical springs for all layers except bottommost layer by t–z curves (i.e., skin frictional resistance versus deflection along pile), and vertical spring for bottommost layer by Q–z curve (i.e., tip resistance versus pile tip deflection). These curves are generated using API RP 2A-WSD and determined the deflection, utilization factor, and rotation. Free vibration analysis: Natural periods and corresponding mode shapes are important properties of any offshore structure. Free vibration analysis is done to find the natural periods and mode shapes of a structure. It is one of the most important factors to check before the dynamic analysis that the natural periods of the structure should be away from the periods of environmental excitation forces. Monopile is modeled as equivalent stub in finite element code.

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3 Lowering Analysis of Monopile Lowering process of a monopile through open ocean attracts more attention due to variable submergence, which in turn results in hydrodynamic property (axial added mass and inertial loads) variations continuously. It is important for the quality of the simulation to select proper time-variant system properties, e.g., added mass, damping, wire stiffness etc., for the response analysis of the system. This needs a nonstationary load and response analysis, normally carried out in time domain. The capital costs of offshore systems are significantly higher than land-based systems because of the higher cost in foundations, installation, and complex logistics. Offshore work involves increased risks of harsh ocean environment which affect the amount of time available for installation and maintenance which in turn influence capital and operation costs. Hence, this work is focused on development and analysis of economic and safe installation methodology in high tidal and current environment. The operational procedure of monopile in the field is reviewed prior to the installation in high tidal ocean environment which is very expensive and identified the critical events that could occur during the installation. Qualitative risk analysis has been carried out to identify these critical events. Following are the identified critical events for lowering operation: (i) lift wire breakage, (ii) failure of hydraulic system in the gripper, (iii) monopile displacement due to wave forces, and (iv) excessive hammer force. All these events are the probable failure systems during the installation operation. Out of all these events, monopile displacement is the most critical event as it affects remaining operations and hinders entire operation. Hence, to determine the maximum lateral displacement of monopile, lowering operation is analyzed. Modeling and lowering analysis of monopile has been carried out using finite element software package, ORCAFLEX program, which gives options for modeling of vessels, different structures, and connection elements. As no Response Amplitude Operator (RAO) data is known for any specific installation vessel, the value for each cylinder method is used for the analysis. The line function is used to model lowering/lifting line, and the 6 Degree (6D) buoy function is used to model the monopile as shown in Fig. 2. Time-domain simulations of the entire lowering operation were performed. The winch was started at 50 s with a constant speed of 0.05 m/s and was stopped at 500 s. The analyses were performed for regular wave and irregular waves to study the behavior of monopile during lowering process. The environmental conditions Hs and Tp were used as per published site conditions and irregular waves were modeled using JONSWAP spectrum.

4 Results The results of static analysis and free vibration analysis include deflections, utilization factors, and rotations for both load cases and natural periods along with its mode

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Fig. 2 Monopile model attached to barge through steel wire and winch

Table 1 Deflections, utilization factors, and rotations Sl. no Parameter Extreme case

Limiting value

1

Deflection at platform 0.166 (m)

0.21 (Span/150-IS:800)

2

Rotation at platform (°)

0.19

0.2° (meteopole)

3

Utilization of monopile

0.16

1

shapes. The critical values of deflections, utilization factors, and rotations for both load cases are provided in Table 1 and the lateral deflection from the pile–soil interaction is shown in Fig. 3. The deflections, rotation of platform, and utilization factors of monopile are within the limits. The obtained natural periods for first five modes are 0.873 s, 0.873 s, 0.148 s, 0.148 s, and 0.029 s, respectively, and the corresponding mode shapes are shown in Fig. 4. The natural periods of system are far away from the regular wave periods (6–30 s). So, it can be concluded that the substructure concept is safe against resonance due to waves. Figure 5 shows the response time history of the monopile during lowering for regular wave using stokes fifth-order conditions. The responses in figures include the forces and motions of the monopile in lateral direction. Similarly, the behavior of monopile subjected to irregular waves has been studied using JONSWAP spectrum. Figures 6 and 7 show the response time history of the monopile and FFT during lowering operation subjected to irregular wave conditions. FFT is plotted for obtained results of lateral force and displacement and compared with input spectrum. It is observed that, in addition to input peak, there is one smaller peak which may belong to the frequency of winch system.

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Fig. 3 Lateral displacement of monopile

Preliminary pile driving analysis has been carried out by estimating the ultimate capacity of substructure as sum of skin friction over the entire pile surface and end bearing using suitable standards. The number of blows required for achieving designed capacity of the pile is obtained by calculating the ultimate capacity of the pile through skin friction and end bearing conditions. Clay soil is used for calculations on the basis of existing geotechnical data at specified location. Figure 8 shows number of blows required for specified depth of penetration of the pile with respect to the ultimate capacity using modified Engineering News Record (ENR) formula. Results show that the major contribution of ultimate capacity is through skin friction than end bearing.

5 Summary and Conclusions In this work, a monopile has been designed for high tidal range with strong tidal currents for water depth of 15 m and 20 m at Gulf of Khambhat location. The design includes static analysis, pile–soil interaction, and free vibration analysis specific to the Gulf of Khambhat using finite element code. The deflection, rotation of platform,

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Fig. 4 Mode shapes of substructure

Fig. 5 Lateral force and motion on the monopile (extreme event Hs  3 m and Tp  12 s)

and utilization factors of monopile are within the limits, and hence the design is safe. Pile–soil interaction analysis showed that the lateral deflection of pile at the seabed surface is 0.0065 m, which met the expected capacity. Monopile installation methods/processes are critically reviewed and developed safe and economic installation methodology through detailed lowering analysis in regular and irregular wave conditions. Lowering analysis indicated larger lateral displacement of monopile which helped to identify the appropriate vessel with hydraulic gripper as attachment to it to restrict the lateral displacements. Preliminary pile driving analysis indicated that

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Fig. 6 Lateral force on the monopile and FFT (Irregular wave Hs  1.5 m and Tp  7 s)

Fig. 7 Lateral motion on the monopile and FFT (Irregular wave Hs  1.5 m and Tp  7 s)

Fig. 8 Number of blows required w.r.t. ultimate capacity

a number of blows are in the range of 40–50 to achieve the design capacity, contribution from skin friction, and end bearing. When the monopile is erected vertically on the seabed, a hydraulic hammer is placed on top of it and pile is driven into the seabed. To ensure an exact pile positioning a pile gripper is recommended. Acknowledgements The authors wish to express their sincere thanks to Dr. S. C. Shenoi, Director, NIOT, and Dr. S. A. Sannasiraj, Professor and Head Ocean Engineering Department, Indian Institute

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of Technology Madras, Chennai for their keen interest and encouragement for successful completion of the work. The authors thankfully acknowledge the support extended by MoES in funding the project.

References Alluri SKR, Shit T, Dhinesh G, Gujjula D, Kumar SVS, Murthy MV (2017) Offshore wind to meet increasing energy demands in India. Curr Sci 113(4):00113891

Analysis and Design of Guyed 120 m-Long Offshore Met Mast Supported on Suction Piles Mallela Mounika , C. R. Suribabu, Satya Kiran Raju Alluri and M. V. Ramana Murthy

Abstract Development of modern technology has increased thrust for renewable energy. The land-based resources were used to its maximum potential. India with a coastline of 7,517 km is seeking to meet its demand from offshore resources like offshore wind energy through installation of offshore wind turbines. Ministry of New and Renewable Energy (MNRE) has identified the coasts of Gujarat and Tamil Nadu as potential sites. The wind potential was assessed either using satellite winds or extrapolated onshore winds, which include considerable uncertainties. Before setting up an offshore wind farm, it is mandatory to collect bankable wind data for a couple of years at potential location. In the present study, an initiative has been taken to come up with a low-cost and feasible structure for the collection of wind data considering financial constraints in prefeasibility stages. Feasibility of using conventional onshore-based-guyed met mast in offshore environment by replacing the anchorage with suction pile foundation was studied. The structure was modeled using beam elements and analyzed for environmental loads using finite element method. The deflected profiles of the structure were arrived and are in acceptable limits. Free vibration analysis was performed to study the resonance of the structure due to wave loads. Earthquake analysis was performed using spectral and time history methods and the utilization factors are in acceptable limits. A nonlinear static pushover analysis was carried out and results indicate reserve strength ratio of 2.2. An installation methodology was developed for the proposed structure considering available marine spread in Indian waters. Preliminary cost estimates indicated the cost of proposed M. Mounika (B) · C. R. Suribabu SASTRA University, Thanjavur, India e-mail: [email protected] C. R. Suribabu e-mail: [email protected] S. K. R. Alluri · M. V. Ramana Murthy National Institute of Ocean Technology Pallikaranai, Chennai 600100, TN, India e-mail: [email protected] M. V. Ramana Murthy e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_33

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structure to be less than conventional offshore self-standing mast and LiDAR-based platform. Keywords Offshore renewable energy · Offshore wind farms Wind collection platform · Guy wires · Suction pile Dynamic analysis of offshore structures

1 Introduction The demand for energy is rapidly growing due to advancement in technology, industrialization, and modernization. In the initial stages of industrialization, nonrenewable sources like coal, oil, and gas played crucial role. But, these sources of energy increased the emission of greenhouse gases that result in global warming and other environmental damages. So, awareness was implanted across the globe to move toward green and sustainable sources of energy. Wind is one of the popular, widely accepted, and economical forms of renewable energy. Now, the countries with long coastlines are focusing on offshore wind due to many promising factors like consistent winds, zero sound pollution, less transportation charges for coastal areas, etc. In the prefeasibility stage, the location for establishing offshore wind farms is identified using wind potential maps. These maps are derived using secondary data like satellite winds or extrapolated onshore winds. The rate of power generation is proportional to cube of wind speed. So, the uncertainty in wind speeds from secondary data may lead to wrong selection of site for wind farm. To avoid these issues and increase viability of project, it is mandatory to collect site-specific wind profiles at least for a year. Conventionally, offshore wind profiles are collected using freestanding met mast. In this method, the structure requires large sections for resisting lateral loads. For installation of these towers, sophisticated marine spread will be required increasing the cost of the project. Recently, due to advancement in laserbased technology instruments are being used for measurement of wind profiles such as LiDAR. But, the cost of these instruments is high as they are in very early stages of development. The collection of wind data is part of a feasibility study and investment of huge capitals at this phase of project is difficult. So, in this study, an initiative is taken to optimize the structure for collection of wind profiles. To achieve this, free-standing masts will be provided with guy wires for lateral stability of the structure which reduces the section size and minimizes marine spread. In this method, suction piles are used instead of conventional piles to reduce the marine operations. A new initiative has also been proposed for the method of installation of the mast to reduce the installation cost. Location and environmental conditions: The wind potential map for Indian coast is shown in Fig. 1. These maps show significant potential along Tamil Nadu coast. Preliminary survey by Ministry of New and Renewable Energy also indi-

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Fig. 1 Offshore wind potential maps for Indian Coast by ESSO–INCOIS (Source Data from the Ministry of New and Renewable Energy)

cates significant wind potential along the coast of Kanyakumari and Rameshwaram, Tamil Nadu. So, the proposed location for the present study is along the coast of Kanyakumari in Tamil Nadu, Indian coast. As per the data from wave atlas of Indian Ocean, prepared by National Institute of Ocean Technology, Chennai, [1] (https:// searchworks.stanford.edu/view/11382270) the water depth at the proposed location is about 15 m (MSL). This region is subjected to high tidal currents of about 1 m/s, extreme wave height of about 4 m, and cyclonic wind speed of 39 m/s. The soil at proposed location is medium dense silty sand.

2 Design Methodology The design methodology adopted is shown in Fig. 2 in the form of a line diagram and the details of loads, parameters, and relevant standards considered in estimating loads are summarized in Table 1. Wave and wind currents are assumed to act in the same direction. So, two load combinations (from extreme conditions) are adopted by taking one combination with wind and wave in 0° direction and other by taking wind and wave in 45° direction. For earthquake analysis, the load combinations are made by taking the normal environmental conditions in 0° and 45° direction.

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Fig. 2 Design methodology Table 1 Estimation of loads and relevant standards Load Parameter

Relevant standards used to analyze the loads

Equipment weight

Self-weight of mast, monopole, anemometer

From the structure

Wind load—Mast

Survival wind speed  39 m/s

IS 875 - 3 [2]

Hydrodynamic load

Operational wind speed  12 m/s Wave height (Severe)  4 m

Stokes fifth-order wave theory to simulate wave kinematics

Wave height (Normal)  2 m Wave period (Severe)  12 s Wave period (Normal)  8 s Current speed (Severe)  1 m/s

Earthquake load

Current speed (Normal)  0.5 m/s Earthquake zone  0.1

IS 1893 - 2 [3]

Importance factor  1.5 Reduction factor  2

3 Finite Element Modeling The structure is modeled in Structural Analysis Computer System (SACS), which is a design and analysis software for offshore structures and uses the concept of finite element analysis, where the entire structure is discretized into many number of beam

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Outer diameter (mm)

Wall thickness (mm)

Vertical legs (VER)

35

4.5

Horizontal bracings near guy wires (HOR)

20

2.5

Horizontal bracings (HBR)

10

0.8

Diagonal bracings (DBR)

16

2

elements [4]. The loads are distributed uniformly over the beam elements. The cross section of the members is taken as tubular which results in decreased axial loads in the members [5]. The proper dimensions of the tubular members required to take the loads acting on it are arrived by trial and error method. The final dimensions of the members are shown in Table 2. The support structure for the mast is a monopole of diameter 0.4 m, which is attached to the mast using links of high stiffness. Guy wires are galvanized wires with a diameter of 9.5 mm. Various types of analyses have been performed to assess the behavior of structure under action of slow moving loads (Static analysis), loads such as earthquake loads, which will have dynamic impact (Response spectrum and Time history analysis), nonlinear behavior of structure under static loads (pushover analysis).

4 Results and Discussions The deflection obtained from static analysis is of magnitude 0.27 m, which is within the acceptable limits of L/100 with critical load as total load acting on to the corner of the structure. The design of the members was done based on the specifications of API RP 2A in load resistance factor method and the utilization factors obtained were about 0.95, which is less than 1 [6]. The deflected profile is shown in Fig. 3. The guy wires were checked for end forces which should be less than the ASTM B498-78 specified ultimate tensile strength of 62.52 KN, in order to maintain the lateral stability of the structure [7–9]. From the joint reactions of the support structure and the guy wires, the pile design was made considering the soil as granular soil and the obtained dimensions are 2.8 m length and 1 m diameter for guy wires, 4.8 m length and 2.5 m diameter for monopole [10]. Free vibration analysis of the structure was carried out to find the natural periods of vibration of the structure and the corresponding mode shapes. The natural periods were maintained so as not to match with the natural wave periods of 5–30 s, to avoid resonance effect. The mode shapes are shown in Fig. 4 and the corresponding wave periods obtained range between 0.688 and 1.42 s, which is well below the natural wave period range [11].

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Fig. 3 Deflected profile

Fig. 4 Mode shapes

Earthquake analysis was done using response spectrum method by assuming a damping ratio of 2% as the material is steel. The utilization factors obtained from the code check were well below the acceptable limits. For earthquake analysis, normal wind and wave parameters were considered. The plot of acceleration versus time obtained from the analysis shows a peak acceleration of 1.5 m/s2 at a time period of 2 s which is shown in Fig. 5. Time history analysis has been done by taking the time history data from El Centro earthquake and the analysis was performed. The base shear versus time plot obtained shows a peak base shear of 45 KN at a time instant of 2.5 s which is shown in Fig. 6.

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Fig. 5 Acceleration versus time graph

Fig. 6 Base shear versus time graph

Pushover analysis was performed to study the nonlinear behavior of the structure and formation of plastic hinges. Reserve strength of 2.2 was observed for cyclonic event using pushover analysis. When the applied load reaches a magnitude which is of 2.2 times the original value, collapse of structure takes place.

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5 Installation Methodology In order to avoid the use of costly heavy machineries like high-capacity cranes, a simple methodology as shown in the above figure is adopted (Fig. 7). The total mast length is made up of a number of bays. During installation more than one bay will be connected to form a module. The number of bays that make up a module may depend on the site conditions and should be flexible. The modules may be preassembled onshore or can be assembled offshore just before installation depending on the site conditions and the kind of vessel available for installation. Once the first module is installed, a pulley mechanism will be fitted on top of the module to raise the next module on to place which can then be connected manually to the underlying module. The pulley mechanism will then be shifted to the topmost module and the process will be repeated till the mast is completed. The guyed wires will be connected as and when the mast reaches the design levels for guyed wires. Suction piles replaced the use of driven piles in deep water because of technical challenges and costs associated with the installation equipment like heavy-lift vessels which can be avoided. The installation of suction piles can be achieved mostly under its own weight and can be positioned at the desired depth by pumping out the water inside the caisson, and thereby creating suction by making use of suction pumps. The installation procedure is simplifying and shortening. Through this simple procedure, the cost of the project can be greatly reduced.

5.1 Costing For cost estimation, the quantity of steel for mast, monopole, and guy wires were considered and the total cost was estimated by taking the unit weight of steel as 140,000 and for galvanized steel wire as 30,000. The cost of installation was also included to get the overall installation cost which was 3.9 crores, which is less than the cost of a free-standing mast that is very much less than the cost of installation of monopole-supported LiDAR.

6 Conclusions A guy-wire-based offshore met mast is designed for wind potential sites along Tamil Nadu coast. The design is governed by deflections and material utilization factors. Suitable configuration of suction piles was arrived to support the structure and anchor the guy wires. Free vibration analysis indicates the fundamental frequency of structure far away from exciting wave frequencies. The dynamic behavior of the structure under earthquake analysis using spectral and time history analyses methods and the structural dimensions are optimized. A nonlinear static analysis (pushover analysis)

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Fig. 7 Installation of the mast offshore. a Lifting a segment of the mast through pulley. b Lifted segment of the mast at its highest position to be connected manually

was carried out to estimate the reserve strength of the structure (2.2). A simplified technique was proposed for installation of the designed structure with available marine spread in India to minimize the project cost. Detailed cost estimation indicates that the overall cost of the project will be less than the cost of offshore self-standing mast and LiDAR-based platforms. It can be concluded that the proposed concept is economical in Indian waters along the coasts of Rameshwaram and Kanyakumari, Tamil Nadu.

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References 1. Sivakholundu KM et al (2014) Wave atlas of Indian Coast. National Institute of Ocean Technology, Chennai 2. IS: 875 (Part 3) (1987) Indian Standard Code of practice for design loads (other than earthquake) for buildings and structures. Bureau of Indian Standards, New Delhi 3. Bureau of Indian Standards (BIS) (2002) Criteria for earthquake resistant de-sign of structures. IS 1893 Part-IV 4. Bentley Systems (2015) Structural analysis computer software (SACS)—manual, United State 5. de la Cruz A (2015) Structural behavior of a guyed mast. In: Proceeding of 14th international conference on wind engineering 6. API RP 2A WSD (2007) Recommended practice for planning, designing and constructing fixed offshore platforms—Working Stress Design (RP 2A-WSD) 7. Pezo M et al (2012) Stability analysis of a guyed mast subjected to wind action by using finite element method. University of Belgrade, Faculty of Transport and Traffic Engineering 8. Gantes C et al (1993) Modelling, loading, and preliminary design considerations for tall guyed towers. J Comput Struct 49(5):797–805 9. Ballaben JS, Rosales MB (2012) Parametric study of the dynamic along-wind response of a guyed tower 10. Tomlinson MJ, Woodward J (2007) Pile design and construction practice, 1995. E & FN Spon publisher, London SE1 8HN, UK 11. Bihst RS, Jain AK (1989) Wind and wave induced behavior of offshore guyed tower platform. J Ocean Eng 25:501–519

Reliability-Based Multi-objective Optimization of Offshore Jacket Structures Vishnu Murali

Abstract In the light of the ever-growing requirements in ecological concerns, government legislations, and consumer demanding, this paper focuses on the structural design of lightweight offshore structures with acceptable levels of reliability. The conflict in these two parameter figures a multi-objective problem with minimizing jacket mass and maximizing reliability as objective functions with member group dimensions as design variables. A Multi-Objective Particle Swarm Optimization (MOPSO) algorithm is selected to solve the problem to obtain the Pareto optimal frontier. The Radial Basis Function (RBF) coupled with Monte Carlo Simulation (MCS) is used to approximate the response of objectives and evaluate reliability in the context of optimization. The study aims to provide multiple solutions for the structural design considering economic cost and structural integrity. Although a Pareto frontier provides multiple solutions, we use the knee point by minimum distance method to decide the most acceptable arrangement from Pareto set. Keywords Multi-objective optimization · Offshore jacket · Reliability

1 Introduction Fixed offshore structures are one of the most commonly used offshore structures. These are technically feasible and economically viable but are highly complex in design. This possesses many challenges in designing. Offshore structures are designed to resist extreme wave loading which may lead to collapse of individual components or the entire structure. The life cycle cost of the structures is influenced by capital operational and risk costs. Capital cost or CAPEX is mainly influenced by the material volume, fabrication, and labor cost. Any design solution that can reduce the material volume without compromising the structural integrity can provide many cost savings. During the design stages, structures undergo plastic analysis to predict V. Murali (B) Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_34

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their ultimate load carrying ability, which is often evaluated by the collapse of load factor [1]. The incremental elasto-plastic method [1] is conventionally used for the calculation of the collapse load factor of a frame structure. Static nonlinear analysis is widely utilized in current offshore standards, such as API, ISO, and DNV [2, 3] to evaluate nonlinear behavior and ultimate capacity of offshore platforms against environmental loads. The present study aims to optimize the capital cost of fixed jacket structure by evolutionary-based multi-objective optimization. The objective is to minimize structural mass and maximize reliability of structure under extreme environmental loading. Here, static nonlinear analysis (pushover) is used to find ultimate collapse load factor or Reserve Strength Ration (RSR). The annual reliability or probability of failure can be evaluated using First-Order Reliability Method (FORM). The probability density functions for the limit state variables that are evaluated from integrating Radial Basis Function (RBF) and Monte Carlo Simulation (MCS). In this approach, the variables of the failure function are defined as stochastic in nature. This helps to provide more accurate and precise estimation of the reliability values. The stochastic-based design also takes account of the inherent nonlinearity present in the structure and environmental loading. Solimon et al. [4] studied the probabilistic inspection and monitoring of ship structure using multi-objective models to minimize the life cycle cost. Based on the stress profile inspection planning has been documented to increase the service life of the structure. Heredia-Zavoni et al. [5] provided a design methodology to find the target reliability under various environmental loads. The paper also signifies the importance of considering site characteristics and structural characteristics in selecting optimal reliability. Karadeniz et al. [6] studied the reliability-based design optimization of offshore jacket structure using FORM. The paper explains the complicated and difficult process to carry out optimization of such large structural systems. Chew et al. [7] studied the optimization of wind turbine support structure under combined fatigue and extreme loading conditions. In this paper, the mass of the steel structure is considered proportional to the CAPEX cost of the structure. The reliability of the structure depends on the design parameters and wave loading. For having a realistic quantification of safety, stochastic nature of material and geometric properties has been considered. The study incorporates nonlinear finite element analysis tool USFOS [8] to evaluate the global response of the structure. Here, integrating Radial Basis Function (RBF) and Monte Carlo Simulation (MCS) [9] is used to investigate the reliability of the jacket structure [10]. The proposed evolutionary algorithm based on multi-objective Particle Swarm Optimization (PSO) provides Pareto frontier and optimal solutions. Even if the Pareto provides numerous design solutions, a selection has to be made for the most acceptable solution (named as “knee point”) from Pareto set finally [11].

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2 Structural Model The jacket structure used here was designed to support an offshore wind turbine. The height of the jacket structure is 66 m and is placed at a water depth of 45 m. The structure consists of 56 nodes, 104 beams of steel tubular cross section and weighs 673 ton. The jacket structure is modeled using Sesam Genie as shown in Fig. 1. For simplifying the structure, the tubular members of the jacket are categorized into two groups for the purpose of structural optimization and the cross-sectional details of the groups are given in Table 1.

Fig. 1 Jacket model

454 Table 1 Jacket dimensions

V. Murali Member groups

Groups

(Diameter, thickness) in mm

Legs

1

(1200, 50)

Braces

2, 3, 4, 5, 6

(800, 20)

3 Nonlinear FEA The collapse analysis requires a nonlinear finite element analysis tool [12]. This should be robust enough to handle both material and geometric nonlinearities. USFOS is useful for nonlinear static and dynamic analyses of space frame structures. It simulates the collapse process accurately from initial yielding to the formation of complete collapse mechanism and even the post-collapse behavior [13]. USFOS makes use of the “Idealized Structural Unit Method” (ISUM) proposed by Ueda and Rasheed [14]. Material nonlinearity is modeled using plastic hinges. Plastic hinges can be inserted at element ends and mid-span of the elements. The basic element formulation is based on exact solution of the differential equation for a beam subjected to end forces. The stiffness formulation is derived from potential energy consideration. The influence of axial force on bending stiffness is accounted for the nonlinear terms in Green strain formulation. The beam column behavior of slender members is taken care using an element stiffness formulation by stability functions. These stiffness terms are nonlinear functions of axial force. Figure 1 depicts the USFOS-based jacket model used in the study. From the load–displacement curve, collapse load factor can be found directly. The ultimate collapse load factor can also be denoted as Reserve Strength Ratio (RSR) RSR 

Fcollapse Freturn period

(1)

Here, Fcollapse is the ultimate load at which structure collapses and Freturn period is the applied environment load with respect to the chosen return period (100 years). Hence, pushover analysis can be used as a measure of reserve strength in the determination of the probability of failure and the reliability index of a platform. When designing the structure against extreme events, safety of structure can be ensured explicitly by selecting a certain RSR value and associated reliability level.

4 Wave Loading For the static pushover analysis, regular wave is used with extreme wave conditions. Morison’s formula is used in USFOS code for calculation of hydrodynamic forces which are suitable for slender structures such as jackets. In the code, regular wave theories are used for wave force calculation which are based on water depth, wave

Reliability-Based Multi-objective Optimization … Table 2 Wave properties

455

Parameter

Values

Wave height

12 m

Time period

10 s

Wave order Water depth

Stokes fifth order 45 m

height, and wave velocity and wave period. Stokes fifth-order wave theory is used for water particle kinematics. Morison’s formula is usually calculated per unit length of the monopile/jacket based on Morison’s equation [15]. The equation is also given in Sect. 2.3.1b-10 of the API recommended practice [2]. In Eq. (1), D is the cylinder diameter, ρw refers to the mass density of seawater and (CD, CM ) are drag and added mass coefficients. CD and CM are empirical hydrodynamic coefficients depending on Keulegan–Carpenter number and V is the horizontal wave particle velocity. Fw  Cd ρDV |V | +

π D2 Cm ρw A 4

(2)

At each time step based on the linear wave theory, the wave kinematics is obtained and used for calculating the hydrodynamic forces for each section (Table 2).

5 Multi-objective Optimization In addition to the nonlinear analysis of the jacket structure, we developed a design optimization framework, which is integrated with the finite element analysis and PSO algorithms using metamodel [16]. The neural-network-based metamodel used here is Radial Basis Function (RBF) [9]. In this section, we explain the framework of optimization. We also introduce a fully automated design optimization framework that integrates the geometry space, finite element analysis, and optimization algorithm by MATLAB.

5.1 Radial Basis Function Metamodel is an optimization method for combining design values and statistics. The global approximation is obtained by regression analysis. The original response characteristics are metamodeled with least error possible. RBF is one of these approximations. If the problem has known values of responses from design space, a metamodel can be created using this method. The optimization can be based on this network of nodes without losing much accuracy. The Latin hypercube sampling method is

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Table 3 Stochastic variables Stochastic variable Mean

Distribution

Cov.

Leg diameter

Varying

Lognormal

0.03

Leg thickness

Varying

Lognormal

0.03

Brace diameter

Varying

Lognormal

0.03

Brace thickness

Varying

Lognormal

0.03

Young’s modulus E

2.1e5 MPa

Lognormal

0.06

used here with total of 200 design combinations to create approximate model for the global response (RSR) (Table 3).

5.2 Particle Swarm Optimization Meta-heuristic or Evolutionary Algorithms (EA) are inspired by the processes involved in the natural evolution. Since gradient information is not required, they are used widely for many problems in which gradient information is very difficult to compute [17]. Perez and Behdiman [20] reported the robustness of PSO algorithm for truss optimization. Initially, the design variable and objective functions are defined. Fitness values for each design are evaluated by integrating finite element analysis code with PSO algorithm.

5.3 Optimization Methodology Figure 2 depicts the flowchart of structural optimization model of jacket structures, which combines the FE model, RBF-MCS, and PSO algorithm. Each step of the flowchart is defined as follows and illustrated in Fig. 2. Step 1. Step 2. Step 3. Step 4.

Define objective function, variables, and problem constraints. Generate initial design points based on population from LHS. Run nonlinear static pushover analysis for the initial design space. Perform metamodeling to approximate design variables and global response. Step 5. Find Pareto optimal front. Step 6. If final design point (knee point) is within bounds, accept solution.

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Fig. 2 Flowchart of design methodology

5.4 Reliability Index The limit state function can be formulated in terms of base shear strength of the jacket structure from 100-year maximum wave loading. The ratio of ultimate strength of the structure to the design wave load can be represented as Reserve Strength Ration (RSR). The value of RSR can be used to evaluate the reliability using the limit state function. Defining Z  L/R, where R is the resistance (load carrying capacity) and L is the load effect. Failure occurs when Z < 1, i.e., when the load effect exceeds the resistance. Assuming lognormal distributions, FORM-based reliability index (β) can be evaluated as given below [18, 19] (Table 4):     R 1+V 2  m E   ln Em 1+V 2  R (3) β       ln 1 + VE2 + 1 + VR2 

Table 4 Limit state variables

Parameter

Description

Rm

RSR (from MCS)

Em

Mean environmental load (0.9)

VE

CoV of environmental load (0.06)

VR

CoV of resistance (from MCS)

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Here, the mean and covariance of the jacket resistance of each design can be evaluated from probability density functions. The distribution of RSR can be obtained from combined RBF and Monte Carlo Simulation (MCS). The stochastic variables used are shown in Table 3, which represents the nonlinearity in geometry and material properties. A sample of 50,000 simulations is considered for evaluating properties of RSR distribution. The RBF model is used to approximate the value of RSR to changes in stochastic variables.

5.5 Problem Formulation The optimization problem for minimizing total structural weight with topology or sizing as design variables, subject to various constraints, can be formulated as follows. Here, x represents the vector of jacket member dimensions, namely, diameter and thickness, A is the vector of cross-section area, l represents the length of each member, and ne represents the total number of members. This is a simplified representation of the cost function and other cost components that are incurred in the design life cycle of support structures, such as manufacturing, installation, and maintenance costs are excluded. The optimization problem for minimizing total structural weight with sizing as design variables, subject to various constraints, can be formulated as below. The maximizing function of reliability can be converted to minimize function by taking negative of the function (Table 5). Minimize: ⎫ ⎧ ne  ⎪ ⎪ ⎪ ⎪ ⎨ F 1 (X )  ρn ln An (x) ⎬ (4) n1 ⎪ ⎪ ⎪ ⎭ ⎩ F (X )  −reliability(β)⎪ 2

Subjected to: xL < x < xU β > 3.0

Table 5 Variable bounds

Groups

Diameter bound (m)

Thickness bound (mm)

Legs

(0.7, 1.0)

(10, 30)

Braces

(0.4, 0.6)

(10, 20)

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6 Results and Discussions With the proposed MOPSO algorithm described in the methodology section, the problem discussed above was run multiple times to verify the convergence of the optimization process, which was started from different initial populations. Figure 3 shows the non-dominated optimal solutions of jacket mass and the corresponding values of reliability from RBF-based multi-objective PSO algorithm. In spite of the fact that the Pareto set can provide numerous design solutions, a selection has to be done for the most acceptable solution from Pareto set. Here, we show the “Knee Point” by minimum distance method [11] which allows us deciding an acceptable solution from Pareto set as in Eq. (3).   n  2  Spi  −1 (5) min K  min(Si (x)) i1 where n is the number of the objective components, Spi is the ith objective value in the pth Pareto solution, and K is the distance between knee point and “utopia point”. Because of the multi-objective optimization, seven Pareto solutions are shown in Fig. 3. The Pareto solutions tend toward a lighter mass and maximum reliability level. An optimal solution has been selected by Eq. 5. The decided knee point plate length is third solution with mass  610 ton and β  4.0. The probability of failure is 1.5 × 10−5 which is far below the value 10−4 recommended by DNV. The final design provides a more economic structure than original design with acceptable safety level.

Fig. 3 Pareto optimal front

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7 Conclusion An offshore jacket is considered for nonlinear FE analysis. The jacket mass and structural reliability for collapse limit state are considered as the objective functions. The numerical outcomes for RSR were approximated by radial basis function to create a metamodel. The reliability of the structure was investigated by MCS and FORM. In order to find the multiple solutions, we formulated the problem as a multi-objective optimization. The non-dominated-sorting-based PSO was employed, alongside metamodel. The optimization produced the Pareto optimal solutions, which were appeared to be extremely helpful in the decision-making. The optimal “knee point” accomplishes minimized cost of manufacturing and acceptable level of safety. Acknowledgement The author gratefully acknowledge the valuable technical contribution provided by Prof. S. K. Bhattacharyya and Prof. S. Surendran, both from Department of Ocean engineering, IIT Madras.

References 1. Wong MB (2009) Plastic analysis and design of steel structures (Library of Congress Catalog) 2. American Petroleum Institute-API (2000) Recommended practice for planning, design and constructing fixed offshore platforms—working stress design, 21st edn. American Petroleum Institute, Washington (DC) 3. Det Norske Veritas (1999) ULTIGUIDE—best practice guideline for use of non-linear analysis methods in documentation of ultimate limit states for jacket type offshore structures. Hovik, Norway 4. Soliman M, Frangopol DM, Mondoro A (2016) A probabilistic approach for optimizing inspection, monitoring, and maintenance actions against fatigue of critical ship details. Struct Saf 60:91–101 5. Heredia-Zavoni E, Silva-Gonzalez F, Montes-Lturrizaga R (2008) Reliability analysis of marine platforms subject to fatigue damage for risk based inspection planning. ASME J Offshore Mech Arct Eng 130(4):1–9 6. Karadeniz H, To˘gan V, Dalo˘glu A, Vrouwenvelder T (2010) Reliability-based optimisation of offshore jacket-type structures with an integrated-algorithms system. Ships Offshore Struct 5(1):67–74. https://doi.org/10.1080/17445300903098334 7. Chew K-H, Tai K, Ng E, Muskulus M (2016) Analytical gradient-based optimization of offshore wind turbine substructures under fatigue and extreme loads. Mar Struct 2016(47):23–41 8. SINTEF Group (2001) USFOS getting started. Structural engineering, Marintek, SINTEF Group 9. Chojaczyk AA, Teixeira AP, Neves LC, Cardoso JB, Guedes Soares C (2015) Review and application of artificial neural networks models in reliability analysis of steel structures. Struct Saf 52:78–89 10. DNV2018: Guidelines for offshore structural reliability analysis-general, Appendix B (1995) 11. Li R, Xu P, Peng Y, Ji P (2016) Multi-objective optimization of a high-speed train head based on the FFD method. J Wind Eng Ind Aerodyn 152:41–49 12. Soreide TH, Amdahl J, Eberg E, Holmas T, Hellan O (1993) USFOS—a computer program for progressive collapse analysis of steel structures—theory manual. SINTEF Report, Trondheim, Norway 13. Skallerud B, Amdahl J (2002) Nonlinear analysis of offshore structures. Research Studies Press, UK

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14. Ueda Y, Rasheed SMH (1984) The idealized structural unit method and its application to deep girder structures. Comput Struct 18:277–293 15. Karimirad M, Meissonnier Q, Gao Z, Moan T (2011) Hydro elastic code-to-code comparison for a tension leg spar-type floating wind turbine. Mar Struct 24:412–435 16. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of IEEE international conference on neural networks, pp 1942–1948 17. Gomez HM (2011) Truss optimization with dynamic constraints using a particle swarm algorithm. Expert Syst Appl 38:957–968 18. Ditlevesen O, Madsen HO (1996) In: Willey J (ed) Structural reliability methods. ISBN 0471960861 19. Cornell CA (1967) Bounds on the reliability of structural systems. J Struct Div ASCE 93(1):171–200 20. Perez RE, Behdinan K (2007) Particle swarm approach for structural design optimization. Comput Struct 85:579–88

Dynamic Behaviour of Inverted Catenary Cold Water Pipelines for Seawater Desalination Project R. Saravanan, S. K. Bhattacharya and M. V. Ramana Murthy

Abstract Unburied flexible pipelines are deployed for conveying the cold water for desalination process in coral island. Generally, high-density polyethylene material is used as cold water pipeline, where the pipelines could not be buried in coral seabed considering its buoyancy in seawater and simplistic in deployment configuration. However, such pipelines are subjected to oscillations, due to current in a shallow water region. Hence, it becomes essential to study about the dynamic behaviour of such flexible pipeline. Numerical analysis has been carried out using ORCAFLEX and Shear7 software to ascertain the vortex-induced oscillations and front-end tension. Experimental studies have been carried out in 2 m current flume at Department of Ocean Engineering, IIT Madras. The magnitude, period of oscillations and frontend tension are recorded and processed. Numerical analysis has been carried out and compared with experimental results. Field studies have been carried out in the coastal area of the coral island to ascertain the magnitude and direction of the current during March 2017. The observed data are used in the numerical analysis to confirm the results. Keywords Pipeline · Vortex-Induced oscillation · Current · Drag · Deep water

1 Introduction The projects such as Ocean Thermal Energy Conversion (OTEC), seawater desalination, etc. require cold water to be drawn from deep sea. This paper focuses on the dynamic aspects of the pipeline which is used to draw the cold water for a desalination project. The length of the cold water pipe depends on the temperature of the cold water available at required water depth. Typical desalination project that adopts the R. Saravanan (B) · S. K. Bhattacharya Department of Ocean Engineering, IIT Madras, Chennai, India e-mail: [email protected] M. V. Ramana Murthy Ocean Structures, National Institute of Ocean Technology, Pallikaranai, Chennai, India © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_35

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method of Low-Temperature Thermal Desalination (LTTD) for desalination requires a cold water pipe deployed at a water depth of 400 m, where the seawater temperature is about 12 °C. The LTTD-based desalination project is most suitable for the inhabited island of Lakshadweep, India, because the required water depth to draw the cold water is available at distance of 1200 m from the shore. This pattern of seabed profile allows the planning of desalination plant in which the intake well is located at 5 m water depth for storing the cold water and plant nearer to the shore for desalination process. This is shown in Fig. 1. High-Density Polyethylene (HDPE) has been chosen as the material for cold water pipe as it offers ease in welding. The 1000 m length of the pipeline having 600 mm diameter with 30 mm wall thickness is installed in such way that the front end of the pipeline connected to the intake well and its far end is added with 12 tons weight and lowered down to a depth of 400 m to draw the cold water. After deployment, the buoyancy of the HDPE pipeline takes the form of inverted catenary due to its

Fig. 1 Plan and sectional elevation of cold water pipeline configuration for a desalination plant

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465

buoyancy in which about 300 m length of front portion of the pipeline lies in shallow region as shown in Fig. 1. The pipeline is exposed to nearshore current that results in vortex-induced oscillations. Due to local seabed conditions, this scenario is vulnerable to the pipeline in shallow water region as the pipeline undergoes abrasion with seabed of the coral reef. This pipeline configuration of the desalination plant which was installed at Agatti Island of Lakshadweep India is considered for dynamic analysis of the cold water pipeline in this paper. The importance of the vortex-induced oscillations of a pipeline for the design of cold water pipeline for an OTEC project is well discussed in Griffin [1]. McCormick [2] presented a preliminary study on 1000 m long undersea and 1 m diameter HDPE pipeline configuration for Clathrate desalination plant at Hawaii deployed at a water depth of about 675 m. The front portion of the pipeline is ballasted with weight and lower portion is inverted catenary that floats in the ocean. This pipeline design configuration is to allow the pipeline to move 152 m horizontally and 76 m vertically to accommodate currents. Loentgen et al. [3] described the Vortex-Induced Vibrations (VIV) of deep water riser tower using numerical analysis software such as ORCAFLEX and Shear7. Vandiver [4] explained the research challenges in the VIV prediction of marine risers and mentioned that the very few full-scale tests on VIV have been carried out. Ajeesh et al. [5] carried out the numerical analysis of this configuration with 300 m front portion replaced with mild steel pipe. The present study concentrates on carrying out the study by considering the whole length as HDPE pipeline. The desalination plant considered in this paper is designed with a design life of 20 years and hence, an important part of the desalination system is the cold water pipeline which is expected to provide service for 20 years. However, the pipeline is subjected to vortex-induced oscillations which would reduce the fatigue life of the pipeline. This paper focuses on overall dynamic behaviour of the pipeline.

2 Methodology The main focus of this work is to study the behaviour of the inverted catenary cold water pipeline exposed to real ocean environmental forces. Numerical analysis software is available in the industry to carry out the static and dynamic analysis of the pipeline exposed to current and to predict vortex-induced oscillations. However, real measured ocean current data is necessary to carry out the numerical analysis. Vandiver [4] insisted that current data measured from the field is a must to use in the numerical analysis software. Hence, as a first step in this study, the field data collection such as ocean current profile in the vicinity of the pipeline and bathymetry survey to know the seabed profile are carried out.

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Numerical analysis offers a good insight into the behaviour of such pipeline exposed to ocean current. Numerical analysis tools such as ORCAFLEX, Shear7 and VIVANA are widely used in the industry to ascertain the vortex-induced oscillation of pipelines. Loentgen et al. [3] used Shear7 software for VIV response of riser towers and compared with wake oscillator model and suggested validating the results with experiments. The Shear7 coupled with ORCAFLEX is used for numerical analysis in this study. But before carrying out the numerical analysis, it is required to compare the results of the Shear7 software with experimental studies for a typical inverse catenary pipeline. An experimental study has been carried out with HDPE tube inverted catenary model in a 2 m current flume at the Department of Ocean Engineering, IIT Madras. Experimental results are compared with various inbuilt models available in the software. Based on comparison, appropriate options are chosen for numerical analysis using the software. The field observed data are given as the input for numerical analysis using Shear7 coupled with ORCAFLEX. The results of numerical studies reveal about the behaviour of inverse catenary pipeline from the perspective of vortex-induced oscillations.

3 Field Data Collection 3.1 Location Details The Agatti Island in Arabian Sea, where an LTTD desalination plant is installed, is chosen as the location to carry out the field data collection of current velocity in the vicinity of inverse catenary pipeline connected with desalination plant. The geographical location of the desalination plant established on this island is shown in Fig. 2. The pipeline is deployed with a direction more or less perpendicular to the shore and the pipeline is exposed to long shore current as shown in the same figure. The required survey equipments, data acquisition system and ancillary instruments are transported from main land to the island by ships. The survey to collect the data is conducted between 26 March 2017 and 30 March 2017 during fair weather season.

3.2 Instrumentation and Data Logging System to Measure Current Velocity The Acoustic Doppler Current Profiler (ADCP) uses the Doppler shift to estimate the current velocity by sending sound at a fixed frequency and observing or recording the echoes received from sound scatterers in the water. The ADCP with four-beam transducer faces having 75 kHz frequency is used as the transducer to acquire the

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Fig. 2 Location of current velocity measurement in the vicinity of the desalination plant

Fig. 3 Instrumentation diagram of data acquisition for current velocity

magnitude and direction of current velocity across the depth. The scheme of instrumentation and data collection is shown in Fig. 3. The instrumentation set up arranged on the survey boat is shown in Fig. 4.

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Fig. 4 Instrumentation set up for data acquisition for current velocity and direction

The ADCP is fixed on the side of the survey boat with 0.5 m immersion in the seawater. Data logging cable is connected to a laptop to acquire data using the software WinRiver II. The position of ADCP with respect to GPS coordinates is captured using CEEDUCER instrument and navigation data is stored. The data has been collected up to a depth of 40 m, which is the maximum depth range of the 75 kHz ADCP. The current velocity data has been collected by navigating the survey vessel parallel and perpendicular to the shore in the designated area. Along the depth, the ADCP acquires the current velocity based on the bin size assigned in the data acquisition software. Bin size of 0.5 m has been assigned for data acquisition in this study and stored in the laptop for further data processing. Maximum of eight bins are assigned by the acquisition software when the data were acquired in 40 m water depth.

3.3 Data Processing and Magnitude of Current VmDas software has been used to process the data collected by the ADCP. The variation of current velocity with depth and corresponding direction are measured. These magnitudes and directions of current at 10 and 40 m water depth are shown in Figs. 5 and 6.

Dynamic Behaviour of Inverted Catenary Cold Water Pipelines … Magnitude of current in m/s 0

0.2

469

Direction of current in degrees wrt north (0 deg)

0.4

-150

-50 -0.5

50

150

250

-1

-2

-3

-5

Depth in meteres

Depth in meters

-3.5

-5

-6.5 -7

-8

-9 -9.5

-11

-11

Fig. 5 Variation of magnitude and direction of current measured at 10 m water depth

It can be seen from the field data that the magnitude of current is around 0.35 m/s along the depth. The direction of current indicates that the current flow is oriented towards north-easterly direction at about 20° from north. This means the current flow direction is almost parallel to the shore as shown in Fig. 2, which is perpendicular to the pipeline. This magnitude and direction of the current collected in the field has been considered in the numerical analysis of the pipeline.

4 Experimental Studies 4.1 Model Set up, Instrumentation and Experiment The main aim of the experiments is to observe the oscillation of HDPE tube having inverted catenary profile when exposed to current and compare its response with the results of numerical analysis using the software. Based on validation with

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R. Saravanan et al. Direction of current in degrees wrt to north (0 deg)

Magnitude of current in m/s

0

0 -0.2

0

0.2

0.4

-50

0.6

-25

0 -5

-10

-10

-15

-15

depth in m

-5

-20

-25

25

50

75

100

-20

-25

-30

-30

-35

-35

-40

-40

-45

-45

Fig. 6 Variation of magnitude and direction of current measured at 40 m water depth Table 1 HDPE model tube in experiments

Details

Values

Length of tube

6m

Diameter of tube Material

15 mm HDPE

experimental results, the numerical analysis will be carried out to study the dynamic analysis of prototype. The details of the HDPE model tube tested are given in Table 1. The configuration and instrumentation of the model set up are shown in Fig. 7. The front end of the model is connected to a load cell to record the tension due to current. The load cell data are recorded in a data acquisition system. The underwater accelerometer, PCB Piezotronics make, model No. WJ353B33 having sensitivity

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Fig. 7 Configuration and instrumentation of the model setup in sectional view in current flume Fig. 8 Accelerometer and load cell fixed in the model tube in current flume

100 mV/g with frequency range of 1–4000 Hz has been used to measure the acceleration data. The accelerometer is fixed at 0.9 m from the front end of the model tube as shown in Fig. 8 to record the acceleration due to current velocities such as 8, 10 and 20 cm/s. Similarly, accelerations are measured at 1.5 m from the front end of the tube. Oscilloscope has been used to record the acceleration and to carry out data processing.

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Fig. 9 Typical conversion of acceleration data to displacement using MATLAB

4.2 Data Processing The load cell data are processed to ascertain the wall tension at the front end of the model tube. The acceleration data in the form of voltage are recorded as time series in oscilloscope and multiplied with calibration constant 9.81 m/s2 equivalent to 1 V. MATLAB has been used to carry out the fast Fourier analysis and bandpass filtering of the acceleration data. The filtered acceleration data has been double integrated using MATLAB code to obtain the displacement of the particular node where the accelerometer was fixed. Typical conversion of acceleration data to displacement is shown in Fig. 9.

4.3 Comparison and Validation of Numerical Analysis with Experimental Results Before carrying out the prototype analysis, the actual experimental setup has been modelled and analysed in the ORCAFLEX software and compared and validated with experimental results. The option of Shear7 coupled with ORCAFLEX analysis is used to analyse the model tube having experimental conditions. These analyses results are compared with experimental results and are shown in Figs. 10, 11 and 12 for the accelerometer fixed at 0.9 m location with three different current velocities. It can be observed that the analysis carried out using Shear7 coupled with ORCAFLEX shows good agreement with experimental results.

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0.20

Displacement in mm at 0.9m from front end of tube model

0.15 0.10 0.05 0.00 -0.05 Experiment

-0.10 Shear7 + ORCAFLEX

-0.15 -0.20 -0.25 0

1

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Time in seconds

Fig. 10 Comparison of displacement observed from experiment with numerical analysis for current 8 cm/s

Displacement in mm at 0.9m from front end of tube mode

0.3 0.2 0.1 0.0

Experiment Shear7 + ORCAFLEX

-0.1 -0.2 -0.3

0

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3

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7

Time in seconds

Fig. 11 Comparison of displacement observed from experiment with numerical analysis for current 11 cm/s

The experimental results of the front-end tube wall tension of the model tube for different currents are compared with results of the numerical analysis and are shown in Fig. 13. It can be seen that the comparison is reasonably good. Considering the validation of the numerical analysis results with experimental results as discussed above, the option of Shear7 coupled with ORCAFLEX has been chosen for prototype analysis of the inverted catenary pipelines.

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Displacement in mm at 0.9m from front end of tube model

0.25 0.15 0.05 Expteriment

-0.05

Shear7 + ORCAFLEX -0.15 -0.25 -0.35

0

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Time in sec

Wall tension at front end of model tube

Fig. 12 Comparison of displacement observed from experiment with numerical analysis for current 20 cm/s 1.8 1.6 1.4 1.2 1.0

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Tension in N (ORCAFLEX)

0.4 0.2 0.0 6

8

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Cuurent velocity in cm/sec

Fig. 13 Variation of wall tension due to different currents at front end of model tube

5 Numerical Analysis 5.1 Details of Inverted Catenary Prototype Pipeline Numerical analysis has been carried out as per the specification mentioned in Table 2. The analysis has been carried out considering the pipeline is flooded with seawater. The front-end condition of the pipeline is modelled as anchored and other end condition at 350 m water depth modelled with clump weight of 1.5 tons.

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Table 2 Prototype pipeline details for numerical analysis Details Values Length of pipe

850 m

Outer diameter of pipe

630 mm

Inner diameter of pipe

570 mm

Make of the material Young’s modulus of HDPE pipe

HDPE 1.08E6 kPa

5.2 Numerical Analysis Shear7 is numerical software to estimate the vortex-induced oscillations based on mode superposition method. The ORCAFLEX software can be used for dynamic analysis wherein, options are available to interface the Shear7 software. As seen from the experimental comparison results in Sect. 4.3, the option of coupling Shear7 with ORCAFLEX provides good results and hence, this option is chosen for numerical analysis to estimate the vortex-induced oscillation of the prototype inverted catenary pipeline. The current velocity profile measured in the field has been used for input for numerical analysis. The result of VIV offset at a node 150 m from the front end of the prototype, in response to current velocities 25, 30 and 35 cm/s are shown in Fig. 14. It can be seen that the magnitude of displacement due to VIV increases when the magnitude of current increases. The variation of effective tension along the pipeline due to current has been carried out using Shear7. The comparison of this tension variation based on output of the software for current velocities 25, 30 and 35 cm/s are shown in Fig. 15. The tension along pipeline increases towards bottom of pipeline. 0.4

Displacement in meters

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Current 35 cm/s

-0.2 -0.3 -0.4 0

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Fig. 14 Oscillation of prototype pipeline for different currents at node 150 m from front end

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Current 35cm/s

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Fig. 15 Variation of tension along pipeline due to different currents Table 3 Comparison of effective tension at both ends of pipeline Current velocity in cm/s Effective tension in kN using Shear7 25 30 35

Front end

Bottom end

32.1 31.9 33.0

40.5 41.6 44.1

The effective tension arises at front end and bottom end of the pipeline and it has significant effect on the maintaining the required configuration of the pipeline during its service life. Table 3 shows the estimated value of effective tension on both ends. The maximum tension is about 44.1 kN at bottom end of pipeline. The yield stress of the HDPE pipe is 23 Mpa. The effective tension estimated is well within the permissible limit.

6 Conclusion This paper focuses on the vortex-induced oscillations of inverted catenary cold water pipelines subjected to ocean current in the vicinity of the island based desalination plant. The current data collected from the field in the vicinity of desalination plant indicates maximum of 35 cm/s current velocity in 40 m water depth. This current profile is used as the main input for carrying out the numerical analysis. Based on comparison of results between experimental and numerical studies, it is found that the Shear7 coupled with ORCAFLEX method provides good results.

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On referring to the prototype analysis, maximum of 0.35 m displacement value is observed for inline vortex-induced oscillation with a frequency of 0.1 Hz at a node 150 m from the front end of the pipeline. The effective tension estimated at bottom portion of the pipeline is higher than the front end due to current. The estimated value of tension is nominal considering the yield stress of HDPE pipe. The field current measurement to a depth of 400 m needs to be carried out, as this data will provide more accurate response of the prototype pipeline subjected to current. The experimental studies on fatigue of the pipeline due to vortex-induced oscillation studies will be useful in estimating the fatigue life of the pipeline which has inverted catenary profile. Acknowledgements The constant support of Director, National Institute of Ocean Technology to carry out this study is gratefully acknowledged. The funding provided by Ministry of Earth Sciences, Government of India to carry out the field studies and experimental studies is hereby acknowledged.

References 1. Griffin OM (1981) OTEC cold water pipe design for problems caused by vortex induced oscillations. Ocean Eng 8(2):212 2. McCormick RA (1995), Clathrate desalination plant preliminary research study, water treatment technology program report no. 5, U.S. Department of Interior 3. Loentgen V, Wang A, Germanetto F (2012) Application of wake oscillator models to deep water riser towers for VIV Responses. ISOPE, ISBN 978-1-880653-94-4 (Set), ISBN 1098-6189 (Set) 4. Vandiver JK (1998) Research challenges in the vortex induced vibration prediction of marine risers, OTC 8698 5. Ajeesh MV, Panner Selvam R, Sundaravadivelu R, Dhinesh G, Saravanan R, Phani Kumar SVS, Ramana Murthy MV (2015) Hydrodynamic analysis of an inverted catenary coldwater pipeline of a LTTD plant. In: Proceedings of the ASME 2015, OMAE 2015-41521

Optimization Study of Eight-Legged Fixed Offshore Jacket Platform V. Suryaprakash and N. Sunil Kumar

Abstract Fixed offshore platform plays a major role in oil exploration and production and basically, a huge steel-framed structure used for different purposes such as drilling, processing and living. The quantity of steel required to meet the extreme environment of the ocean will be comparatively high and by using modern techniques and developments, researchers and consultants are trying to adopt the innovative methods to optimize the weight of the jackets. In this paper, a typical eight-legged jacket platform is taken for study and optimization is carried out by concentrating in various aspects such as leg batter, rechecking the member size requirements, bracing arrangement, utilization of FRP mud mats, rechecking the load calculations and contingency factors. The modelling, analysis and design are done using SACS, a 3D finite element software exclusively for offshore structures. Generally, during the tender stage of the projects, and due to the time constraint, many possible checks shall not be done especially for optimization. Being a contractor’s consultant, it is the consultant’s responsibility to provide economical design. This study will provide the fair idea about the possible routes for the optimization. This paper concludes with the final optimum weight of the jacket platform and highlighting the spaces where the weight of the jacket structure can be reduced. The percentage of reduction is summarized in the conclusion for the comparison purpose. Keywords Fixed offshore platforms · Jackets · Optimization · FRP mud mats SACS

1 Introduction Fixed offshore platforms are the widely used structures in the oil and gas industry, and it shall be used for the various purposes such as drilling, processing and living, especially for the shallow water depths, fixed offshore platform is considered as the V. Suryaprakash (B) · N. Sunil Kumar Ports and Highway Structures, L&T Infrastructure Engineering, Chennai, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_36

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suitable one. Basically, the fixed offshore platform consists of the deck supported by means of the jacket. The dimensions of the structure will vary with respect to the purpose of the platform. The jackets are acted as the template for driving the piles. The platform type may be either skirt pile jacket or main pile jacket but the economic and technical influences involved in the decision-making of the structural system of the jacket. This paper mainly concentrates on the processing platform which typically consists of the eight-legged or six-legged platform. Hence, the weight of the typical eight jacket platform shall be from 5000–9000 tonnes (substructure alone). Depending upon the design consultants and the other functional requirements, the weight of the jacket platform will vary. In the present situation, especially after the supply of the crude oil increased rapidly the requirement of fixed offshore platform became fade. Hence, getting new projects in the field of the fixed offshore platform became more challenging and it paves the way for the optimization and innovative ideas to design the project cost-effective.

2 Need for Optimization The current scenario in the oil and gas filed, especially for the fixed offshore platform, the project available is quite low when compared to the earlier decades, however, the design consultants are subjected to work on the innovative solutions and better trialand-error methods to provide the economical design. Hence, winning the project in the tender stage is quite difficult in this competitive field. This paper concentrates on the major weight reduction routes for the jacket platform during the tender stages, and especially concentrates on the modification of the structural system and configuration. For a few decades, the researches and consultants are trying different innovative ideas to reduce the cost of fabrication and installation of the platform and at the same time, the safety of the platform also be ensured. Hence, those innovative ideas are recommended and that helps the consultants to face the challenging ocean environment. The studies based on both the analytical and the experimental shall be done and verified, so that the risk factors and the chances of the failures shall be minimized.

3 Structural Configuration of Jacket 3.1 General The typical eight-legged jacket is selected for the optimization study and the jacket is assumed as the launch type skirt pile jacket. SACS a three dimensional finite element software used for the design and analysis. The basic details assumed for the jacket platform are shown in Table 1.

Optimization Study of Eight-Legged Fixed Offshore … Table 1 Structural configuration

481

S. no

Description

Remarks

1

Design life

25 years

2

Water depth

57.9 m for storm

3

Marine growth

10 cm from + 6 to –30 m

Wave height

5 cm from –30 m to mud line Operating

57.1 m for operating

4

Wave height––11.5 m Wave period––11.0 s Current velocity––1.4 m/s at surface Storm Wave height––17.7 m Wave period––14.5 s Current velocity––1.7 m/s 4

Jacket type

Skirt pile jacket

5

Number of piles

16 no’s

6

Diameter of piles

84 inch

7

No. of risers and J tube

8

Caisson

9

Gross and net pile capacity

Present––1 no’s Future––10 no’s J Tube––1 no’s 1 sump caisson 1 firewater caisson 60.5MN and 54.9MN

10

Pile penetration

110 m below sea bed

11

Number of boat landing and riser guard

1 no. of boat landing 1 no. of riser guard

For the above-mentioned data, the current jacket weight is 6100MT and the optimization study is done from the above benchmark. Typical dimensions of the jacket at the sea deck level and mud mat level are shown in Fig. 1 (Fig. 2). The initial dimensions and all other parameters of the jacket are kept as the benchmark and the optimization process is started from this stage.

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Fig. 1 Sea deck framing dimension––(+) 7.60 m

4 Optimization Methods The optimization is done by changing the structural arrangement, material properties and the other considerations in loads and contingencies.

4.1 Leg Batter Arrangement The suitable leg batter of the jacket shall be found out by comparing the jacket weight [1], pile axial load and the leg batter. Figure 3 shows the comparison between the axial load, self-weight and the leg batter. When the leg batter of the jacket is increased from 7.5 to 9, the optimum design of the jacket is found to be 8.5. Since from 7.5 to 8.5, the self-weight reduction of the jacket is around 1.31% but the pile loads shall be maintained at 28.5MN. The pile load 28.5MN shall be helpful in achieving the factor of safety for the pile in both operating and storm conditions. It has been clearly observed that by increasing the structural batter base, area of the jacket increased which leads to the increase in the pile axial load.

4.2 Utilization of FRP Mud Mats The need and utilization of FRM mud mats are becoming vast recently. Many vendors are supplying readymade FRP mud mats with many advantages such as • High flexural strength and stiffness • Steel weight reduction • Reduction in anodes due to mud mat plate area reduction

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Fig. 2 Mud mat framing dimension––(−) 54.50 m

• Easy to handle. For the analytical purpose, the physical properties [2] of the mud mats are considered in the analysis. The range of those physical properties value shown in Table 2 are collected from various research articles.

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Fig. 3 Lag batter comparison Table 2 Physical properties of FRP MUDMATS

S. no

Description

Remarks

1

Modulus of elasticity

23,000–24,000 N/mm2

2

Moment of inertia (major axis)

1.1 × 106 –1.2 × 106 mm4

3

Density

1750–1950 kg/m3

4

Cross-sectional area

4000–4400 mm2

5

Weight of mud mat per area

0.28–0.32 kN/m2

Thus, the properties of the FRP will change with respect to the vendor specification and hence, the generalized values between those specified ranges are selected for the analysis. On-bottom stability analysis having the greater impact among all the pre-service analysis and the it helps both directly and indirect way such as, • Direct weight reduction of steel plate that helps in reduction of steel tonnage • Indirectly, the reduction of surface area calculation helps in reduced number of anodes in the mud mat zone • Reduction of number of joints for fabrication of the arrangement plan of mud mat framing has been changed. The structural behaviour does not change due to the change in the mud mat properties in the 3D model, however that helps in the greater reduction of the mud line elevation weight and tends to the reduction in the member stresses at the Mudline framing. It has been found that the weight of the mud mat has been reduced to 36% from 759MT to 480MT. Due to this reduction, the mud mat framing member sizes shall

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485

be rearranged and the reduction shall be done and the net reduction weight is around 98MT. The intermediate additional framing members shall be removed.

4.3 Other Routes of Optimization The other options of optimization includes in the following aspects, but it will vary with respect to the projects and the clients [3].

4.3.1

Load Assumptions

The load and load factors/contingencies assumptions shall vary with respect to the client and the location of the project. For instance, at the tender stage, the weight contingency shall be kept around 1.20, and this may affect in buoyancy in the floatation analysis. If the design consultant and client had a mutual agreement, it shall be reduced up to 1.15–1.175, and on the other hand if it is not accepted, this option shall be ruled out.

4.3.2

Member Sizes Rechecking

The member sizes are fixed based upon all in service and pre-service analysis, but it is not the point that all the members are stressed completely in all analysis. There may be the members which are governing only in some analysis other than that the utilization ratio shall be kept at 0.8, and the member size shall be reduced accordingly. Many trial-and-error methods are available in the form of algorithm [4] to find the optimized member size determination. These techniques shall be helpful during the tender stages to find out the optimum member sizes. Another important point to remember is to maintain the symmetric between the jacket while changing the member sizes, so that the cog shift will not be maximum. Another factor influencing the resize is the ‘readily available materials’, and many projects will face this issue like design has to be done only with available member size and thickness in such cases, the optimization shall be done only with the limited member dimensions.

4.3.3

Internal Ring Stiffeners

One of the major advantage in the skirt pile jacket is the joints shall be stiffened by using the internal ring stiffeners. The major fatigue governing joints shall be checked against the tubular joint design to find out punching shear and in such cases, it is not mandatory to change diameter and thickness of the braces, utilization of the internal ring stiffeners which will help both load and strength utilization ratio of the joints.

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The internal ring stiffener number shall be increased until it affects the fabrication scenario, for the further failure in the joints, profile grinding, i.e. smoothening the surface of weld around the joints shall be performed.

4.3.4

Platform Orientation

In many cases, the platform orientation shall not be modelled according to the true north, and this may attract the heavy wave loads and that will result in the higher member size and thickness. Hence, it is necessary to find out the true north of the platform and by orienting the structure accordingly may help in the reduction of the pile load. In some cases due to the change in the orientation of the platform may result in the increase in the pile load also, hence, this factor also depends upon the project location and ocean environment.

5 Conclusion From the study, it has been clearly observed that the innovation in the optimization is directly proportional to the technical advancements. By utilizing the FRP mud mats in this typical study, it is observed that around 98MT shall be saved. Other than this, the construction handling of FRP mud mats are easy when compared to the steel mud mat, and gives higher flexural capacity than the steel mud mat. Leg batter of 1 in 8.5 is suitable for this jacket when compared to other. Other possible routes of the optimization are generalized and this may vary with respect to the project, due to the variance in the location, client and contractor. Hence, from the design consultant’s point, recent advancements and innovative ideas will help this optimizing area.

References 1. Mohammad Nejad M (2010) Optimization of leg batter in fixed offshore platform. In: The international offshore and polar engineering conference. ISBN 978-1-653-77-7 2. AIMS international. http://www.aims-intl.com 3. Samanta SM (2016), A review on advancements of jacket platform. Int J Innov Res Sci Eng Technol 5(6) 4. Kaveh A, Sabeti S (2017) Optimal design of jacket supporting structures for wind turbines CBO and ECBO algorithms. In: Periodica polytechnica civil engineering paper 11651 5. Preetham Rajan N, Kiran Raju S (2017) Optimized design of coastal observatory for Indian gulf conditions. Int J Adv Res Method Eng Technol 1(3):101–104. ISSN 2456 6446

Part III

Port, Harbour and Coastal Structures

Comparative Study of Breaking Wave Forces on a Quasi-Prototype Recurved Seawall R. Ravindar, V. Sriram, Stefan Schimmels and Dimitris Stagonas

Abstract The large-scale experiments were conducted on a quasi-prototype vertical seawall attached with recurve in a large wave flume (GWK) with the slope of 1:10 to the study the breaking wave impact on the structure. Recurves are either curved parapets or walls with entirely curved seaward faces that are effective in reducing wave overtopping without increasing the crest height of the structure. The nondimensionalized impact pressure is plotted along the depth and compared to three recurves and breaking cases. The impact pressure and horizontal impact force compared with traditional theoretical design methodologies like Goda, Minikin, and Blackmore & Hewson’s methods and the variations are reported. Pressure measurements obtained from tactile sensor/pressure pad are compared with a traditional pressure transducer. Keywords Large scale · Recurve · Seawall · Impact pressure · Horizontal force Breaking wave

1 Introduction The seawall is one of the most commonly used structures for the protection of coasts against wave action. Among that, the vertical wall was widely used until the overtopping has to turn into an issue. Later, researchers suggested the use of crown R. Ravindar (B) · V. Sriram (B) Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai, India e-mail: [email protected] V. Sriram e-mail: [email protected] S. Schimmels Forschungszentrum Küste (FZK), Karlsruhe, Germany e-mail: [email protected] D. Stagonas University College London, London, UK e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_37

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wall/parapet/recurve to reduce or entirely avoid overtopping. However, the research on the influence on the inclusion of this additional structure over the design of the structure is still open, and the consensus is yet to reach. Moreover, there are various well-established design methodologies for the standalone vertical wall, are those formulas are effective for the vertical wall with the additional structures? How would incident kinematics be influenced by the recurve? This paper would provide slight insight into the improvement of this theme. In this study, the recurve of three different curvatures are considered. The paper deals with the following points: (i) The influence of two parameters, recurve type (three different angles of extension) and breaking type (slow breaking waves, breaking with small air trap, and breaking with large air trap) for impact pressures on the vertical wall are investigated across the depth. (ii) The pressure and force measurements from the large scale are compared with the traditional procedure used in code provisions to calculate wave impact pressure like extended Goda’s method by Takahashi [9], Minikin’s method [8], and Blackmore & Hewson’s method [2]. This will highlight whether there is any requirement for the new formulae for the vertical wall with an additional structure like recurve. (iii) Finally to increase the clarity on the impact pressure under the recurve, measurement obtained from tactile sensor (over an area) are validated against pressure transducer and the pressure map, pressure time history, and force time history extracted from tactile sensor measurements are discussed, which is one of the novelties of the present study and show the need of 3D measurements are for measuring the impact pressure.

2 Experimental Setup The experiments conducted in a large wave flume (Große Wellenkanal, GWK) at Forschungzentrum Küste (FZK), Hannover, Germany. The dimensions of the flume are 307 m long, 5 m width, and 7 m high equipped with piston type wave generation. The waves were generated by PI Controller based online absorption system, so that the tests were minimal effects of re-reflection. A full-scale quasi-prototype of a vertical seawall with recurve was erected at a distance of 243 m from the wavemaker as shown in Fig. 1. In this study, three types of recurved parapet tested for varying curvature are classified as large, medium, and small as shown in the Fig. 1. Three parameters characterize the recurve such as the horizontal distance (Br ) and vertical distance (Hr ) of the upper edge of the seaward to end of recurve and angle of extremity (αe ). The dimensions of the three recurve investigated in this study is given below. • Small (BrS): Br  0.20 m, Hr  0.45 m, Hm  5.14 m and αe  48° • Medium (BrM): Br  0.40 m, Hr  0.57 m, Hm  5.26 m and αe  70°

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Fig. 1 Experimental setup and configurations of the different recurve wall

• Large (BrL): Br  0.61 m, Hr  0.61 m, Hm  5.30 m and αe  90° The parapet is entirely made up of steel, and vertical wall is made up of steel covered with a Perspex plate on the seaward side to provide a smooth surface. The flume has a flat bottom and an approaching slope of 1:10 that ends at the toe of a seawall. The slope of 1:10 is mainly selected to observe high impact pressure in front of the wall. The slope was constructed using geotextiles filled with sand and concrete block placed on top of it. The tests were conducted for a combination of varying wave periods and wave heights for all three recurves with constant still water depth (d) and the water depth near the structure (hs ) as 4.1 m and 0.8 m, respectively. The water depth is fixed in such a way that maximum impact pressure is observed on recurve wall. The incident wave height (Hi ) is limited between 0.5 m and 0.8 m because Hi less than 0.5 m does not create sufficient impact and greater than 0.8 m created high loads on the wall exceeding the available instrument capability. In the same way for wave period, lesser than 4 s generated standing wave formation in the flume and greater than 8 s produced higher load on the wall. So, the test combinations had boundary constraints and are fixed as shown in Table 1. The categorizations of breaking cases not mentioned in this paper are already explained in [6]. The two types of instrumentations are used to measure wave-induced impact pressure, the tactile sensor (PMS), and pressure transducer. A total of 16 pressure transducers sampled at 5 kHz as shown in Fig. 1 is used. In which, eight are fixed on a recurved parapet and the rest are fixed on a vertical wall. In addition to that to

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Table 1 Wave characteristics reported in the present paper Case id Description Wave height (m) Wave period (s) 1 2 3 4 5 6

H05T8 H06T6 H06T8 H07T4 H07T6 H07T8

0.5 0.6 0.6 0.7 0.7 0.7

8 6 8 4 6 8

Breaking case BWLAT BWSAT BWSAT SBW BWSAT BWLAT

measure wave parameters, 14 wave gages sampled at 100 Hz are used among them 12 placed between wave maker and structure; and 1 placed on wave paddle and another at 3.65 m in front of the wave paddle. The last two are mainly used for the active absorption. Finally, two high-speed video cameras are used to record the incoming and breaking waves. Camera 1 and 2 are recorded with 300 frames per second (fps) and 30 fps, respectively.

3 Impact Pressure and Force on the Vertical Wall Several researchers discussed the impact on the vertical wall, but this section discusses the influence of recurve in effecting dynamic pressure. Figure 2 shows the change of non-dimensional dynamic pressure for different curves with respective breaker cases along the vertical direction. The dots shown in the figure are the local peak dynamic pressure obtained for wave impacts, and red and blue lines indicate the maximum and average peak pressure values, respectively. From Fig. 2, it is clearly evident that there is quite a difference in behavior of dynamic pressure based on the influence of recurve type. Considering the top row (case 4, H07T4) in Fig. 2, the location of maximum dynamic pressure is same for both BrS and BrM at z/d  1.088 but varying for BrL at z/d  1.124. The reason that maximum pressure occurring above SWL is that wave does not break when it hits the vertical wall portion rather it slides along the wall. Moreover, considering the magnitude, the variation is in the increasing order of BrM > BrL > BrS for SBW case. Considering the second row in Fig. 2, maximum pressure occurs near the vicinity of SWL at 0.9561 for BrM and BrL and 1.015 for BrS. The change in magnitude of impact pressure magnitude is in the order of BrL > BrM > BrS for BWSAT case. BWSAT is one of the worst-case scenarios that should be considered for design. For the third row in Fig. 2, maximum pressure also occurs near the vicinity of SWL at 0.9561 for BrS and BrL and 1.015 for BrM. Similarly, for BWLAT case is in the order of BrL > BrS > BrM. Based on this results, it can be depicted that there is quite a difference in impacts for both the parameters, i.e., recurve curvature and breaking case.

Comparative Study of Breaking Wave Forces … h07t4brs

1.2

z/d

1

1.2

1.1

1.1

1

0

1

2

3

0.8

4

0

h07t6brs

1.3

1 0.9

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h07t6Brm

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0.9

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h07t4Brl

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z/d

1.3

493

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4 Comparison of Pressure Distribution of Three Recurves with Existing Prediction Formula The following Figs. 3, 4, and 5 show the comparison of impact pressure obtained from eight 10 bar pressure transducers sampled at 5 kHz with theoretical pressure obtained from impact pressure-based design formula. In Figs. 3, 4, and 5, the event1–event5 with different markers indicates the instantaneous pressure profile of five highest impact events which caused highest impact forces on the vertical wall which was influenced by three recurves, namely small, medium, and large plotted from left to right. The solid black line indicates the highest impact pressure obtained from the theoretical formula for the maximum impact event which is acquired by selecting maximum breaking wave height hb for the respective case. Moreover, all the theoretical methods are developed for the irregular waves and consider statistical wave heights to calculate the pressure and forces. In this set of data, pressure, force, and wave height obtained by zero-down crossing method are directly correlated than

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Fig. 4 Comparison between experimentally measured vertical pressure profiles of five waves creating the highest impact force with the highest predicted pressure profile using extended Goda’s (Takahashi) Method for three recurves. (Regular waves, T  6 s, hs  0.8 m), from the left, small, medium, and large recurves

showing a mathematical relation [5]. Therefore, wave height from wave probe 12 is used for force and pressure calculations in Minikin and Blackmore & Hewson’s Method. But in Goda’s Method, wave height is considered at 5Hs (significant height) from the structure. The impact pressure in kPa is plotted against the vertical distance from the toe in meters. From Fig. 3, the ratio of maximum impact pressure near to SWL for experimental and Minikin Method is in the order of BrL > BrM > BrS with values 2.95, 2.88, and 2, respectively. Similarly, from Fig. 4, the ratio of maximum impact pressure near to SWL for experimental and extended Goda’s (Takahashi) Method is in the order of BrL > BrM > BrS with values 14.88, 14.74, and 11, respectively. Finally, the order of BrL > BrM > BrS with values 4.27, 3.99, and 3, respectively, is found for Blackmore &

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Fig. 5 Comparison between experimentally measured vertical pressure profiles of five waves creating the highest impact force with the highest predicted pressure profile using Blackmore & Hewson’s Method for three recurves. (Regular waves, T  6 s, hs  0.8 m), from the left, small, medium, and large recurves

Hewson’s Method. From this, it is apparently evident that there is quite a difference in impact pressure of identical wave conditions (regular waves, T  6 s and hs  0.8 m) and it directly corresponds to the curvature of the recurve. Even though all three methods underpredict the impact pressure, Minikin Method is considerably close compared to other two techniques. Goda’s Method is underpredicting, and Blackmore & Hewson’s Method does not include the breaking wave height in the calculation of impact pressure instead accounts for water depth at the toe of the structure.

5 Comparison of Force Distribution of Three Recurves with Existing Prediction Formula The following Figs. 6, 7, and 8 show the correlation of horizontal impact force integrated from eight 10 bar pressure transducers sampled at 5 kHz with theoretical force obtained from various design formulas as discussed. The force derived from the integration of pressure measurements is based on the following equation. 1  ∗ [( pn (t) + pn+1 (t)) ∗ z n ] 2 n1 m

Fh (t) 

(1)

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Fig. 6 Comparison between experimentally measured horizontal impact forces on a vertical wall with the predicted horizontal force by Minikin Method for three recurves. (Regular waves, T  6 s, hs  0.8 m), from the left, small, medium, and large recurves

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Fig. 7 Comparison between experimentally measured horizontal impact forces on a vertical wall with the predicted horizontal force by extended Goda’s (Takahashi) Method for three recurves. (Regular waves, T  6 s, hs  0.8 m), from the left, small, medium, and large recurves

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Fig. 8 Comparison between experimentally measured horizontal impact forces on a vertical wall with the predicted horizontal force by Blackmore & Hewson’s Method for three recurves. (Regular waves, T  6 s, hs  0.8 m), from the left, small, medium, and large recurves

height which is considered as incident wave height at location of the structure [5]. The blue markers indicate the theoretically obtained impact force for different design methods. Each figure consists of three images showing force comparison for three recurves, namely small, medium, and large. From the figures, it can be observed that the scatter of impact forces measured at the vertical wall are of different magnitude for different recurves. As similar to pressure distribution, magnitude of force distribution is in the order of BrL > BrM > BrS. Comparing with traditional formulas, Minikin (1963) and [1] tend to overpredict the force than extended Goda (1994) Method, especially in small and medium recurve cases. However, these formulas are provided to calculate the impact pressure and

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forces for a vertical wall, and it used for vertical wall influenced by the recurve just to show that a new or updated formula needed for the vertical wall with recurve by incorporating the effect of recurve.

6 Comparison of Impact Pressure on a Recurve Using Tactile Sensor and Pressure Transducers Tactile sensors are pressure mapping sensor widely used in other fields for mapping contact pressure distribution over an area. The tactile sensor model 5315 from Tekscan Ltd. was used in this experiment. The sensor has a matrix area of 42 × 48 cm2 with sensel density of 1 sensel/cm2 and a total number of 2016 sensels. The following Fig. 9 shows the placement of the tactile sensor in the experimental setup. The detailed explanation about the sensor, its calibration, and equilibration can be found in [7]. The tactile sensor was used and measurements were taken only for large recurve type. Before directly using the results from the tactile sensor, a preliminary comparison is performed between the measurements of the tactile sensor and conventional pressure transducers, and the comparison graph can be found in Fig. 10. Each plus sign in Fig. 10 indicates a measurement from the tactile sensor and it is compared with the pressure transducer at the respective position. The comparison shows a fair agreement between the measurements except in the cases of lower impact where tactile sensor under predicts impact pressure. The reason may be due to the filtering process which is adapted to remove the electrical noise from the interference of the instruments, and this was more pronounced in the tactile sensor (Fig. 11). As tactile sensor measurements match the trend of the pressure transducer, the output of tactile sensor:pressure map, pressure time history, and force time history are analyzed further by comparing the variation for different breaking cases. The impact pressure and force are found to be increasing in following the order of BWSAT

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(H07T6) > BWLAT (H07T8) > SBW (H07T4). The probable reason is that the SBW case neither break nor has the energy to create an impact on recurve and BWLAT case has entrapped larger air during their initial impact on the vertical wall, so its energy is mostly dissipated. BWSAT is the bit of a transition from a flip through a condition that is the reason it possesses a lot of energy causing a significant impact on the order of 40 kPa.

7 Conclusions The quasi-prototype vertical wall attached to three types of recurves (small, medium, and large) constructed in 1:1 scale in FZK with the slope of 1:10 for the investigation of breaking wave impacts. The breaking wave impact pressure for the three recurves obtained from pressure transducer plotted along the depth, and the variation of different recurves with different breaking cases discussed shows that the impact pressure significantly varies on both the considered parameters, i.e., recurve type and breaking type. Later, pressure and force measurements are compared with the traditional pressure formulas. From the comparisons, it is evident that there is a significant difference in pressure and force measured in the vertical wall influenced by different recurves and traditional formula designed for standalone vertical wall couldn’t able to account for the those difference in pressure and force. It recommended that impact pressure formula for the non-overtopping structures like parapet/recurve/crown wall accounting for the effect of recurve has to be proposed for the efficient design of those structures. Finally, the results obtained from tactile sensor: the spatial pressure

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map, force time history, and pressure time history for the recurve were discussed, showing the effectiveness of tactile sensor in obtaining wave impact measurements. Acknowledgements This work was carried out under the funding of DST-SERB Project. The authors would like to thank Forschungszentrum Küste (FZK) members for their hospitality, technical, and scientific support. The first author would like to express his utmost gratitude to the German Academic Exchange Service (DAAD) for supporting him financially throughout his project work in Germany.

References 1. Blackmore PA, Hewson PJ (1984) Experiments on full-scale wave impact pressures. Coast Eng 8(4):331–346 2. British Standards BS-6349 (2000) Maritime structures Part 1: code of practice for general criteria. BSI, London, UK 3. Goda Y (1985) Random seas and design of maritime structures. University of Tokio Press 4. Goda Y (1975) New wave pressure formulae for composite breakwaters. In: Coastal engineering 1974, pp 1702–1720 5. Kisacik D, Verleysen P, Van Bogaert P, Troch P (2010) Comparative study on breaking wave forces on vertical walls with cantilever surfaces. In: The Proceedings of the Twentieth international offshore and polar engineering conference, Beijing, China, 20–25 June 2010 6. Ravindar R, Sriram V, Schimmels S, Stagonas D (2017) Characterization of breaking wave impact on a vertical wall with recurve. ISH J Hydraul Eng 1–9 7. Ravindar R, Schimmels S, Sriram V, Stagonas D (2016) Spatial distribution of impact pressure on a parapet using the tactile sensor. PIANC-COPEDEC IX, Rio de Janeiro, Brazil 8. Shore Protection Manual (1984) 4th edn. vol 2, U.S. Army Engineer, Waterways Experiment Station, U.S. Government Printing Office, Washington DC 9. Takahashi S (2002) Design of vertical breakwaters. PHRI ref. document nr 34

Optimisation of Layout of Semi-enclosed Basin in Micro Tidal Region to Minimise Siltation for Mega Ship by FEM Anil Anant Purohit

and Mandar Mohan Vaidya

Abstract Many developing countries in the world are building infrastructures like roads, rails and ports at an exponential rate and India is not an exception. The infrastructures like berths/docks/quays are being built in India in estuaries/open coast to meet the growing demand for waterborne transport. Many shipyards have started building of mega ships and those situated in creeks/estuaries are augmenting their building/repairing facilities by increasing quay wall/constructing new docks to enhance their productivity. However, siltation is a menace in macro/micro tidal regions and shipyards have to deal with it. The shipyard in Ernakulam channel at Cochin (India) is free from waves, however, discharges from backwaters during monsoon, micro tide and shallowness along quayside with deeper gorge at centre of estuary attracts and traps the sediment in eddy at quayside. This causes heavy siltation of 3–4 m/annum and restrictions on dredging due to environmental laws disallows building of mega ships requiring 4–6 years berthing. Hence to overcome above crises, knowledge of hydrodynamics responsible for siltation, reliable estimation of siltation/annum and technique to minimise siltation is essential. The application of FEM to simulate complex hydro-morphodynamics based on site-specific oceanographic data for monsoon/non-monsoon, analysis of dredging data form the basis to evolve optimal layout of semi-enclosed basin for minimisation of siltation. The hydrodynamics and siltation rates observed in model are 90% in agreement with the prototype and basin configuration with three sheet piles minimises the siltation by 43%. Thus, FEM not only optimises the layout of basin for reducing maintenance dredging but also satisfies environmental laws promoting the building of mega ships. Keywords Eddy · Estuary · Micro tides · Quayside · Siltation

A. A. Purohit (B) · M. M. Vaidya Central Water & Power Research Station, Pune 411024, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_38

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1 Introduction Many developing countries in the world, especially in Asian region like Singapore, Malaysia, South Korea, etc. are developing their infrastructures at an exponential rate to meet the future demand of trade and commerce. India is not an exception and is also developing various infrastructures like road/rail networks, airports and major/minor ports in the country to meet the future needs of transport sector in addition to support developments in power sector, industries, etc. The increase in trade among the various countries in different parts of the continents is due to rapid modernisation in the communication sector at global level and it leads to significant development of various infrastructures. However, the countries having long coastlines will have great scope to prosper by the way of developing various waterfront facilities for transport of goods owing to waterborne transport being a cheapest mode of transport. Fortunately, India have a long coastline of about 7500 km and as such Indian government has set up a plan to develop various waterfront structures in the form of major/minor port facilities to boost the trade and economy. Hence to meet the target of development, it has accepted a strategy of liberalisation and globalisation by promoting development through governmental/non-governmental agencies or joint ventures. These waterfront facilities are proposed to be developed in the form of berthing terminals, quays, jetties and docks either in creeks/estuaries/rivers or on open coast facing the Arabian Sea/Bay of Bengal. The trend of transshipment in the future will be mainly transport of commodities through the container ships of mega/ultra-large capacities and hence, shipbuilding industry in the country has started the process of building new ultra-large ships in their shipyards along with development of allied infrastructures. In this context, shipbuilding industry has started augmenting their existing shipbuilding yards either by the way of increasing quaysides or by constructing new dry docks to allow building of modern ultra-large ships. Many existing shipyards are mostly building ships in creek/estuarine regions and being far inside from open sea, quays/docks are free from disturbance due to sea waves. However, quaysides of these shipyards have to currently carry-out frequent maintenance dredging owing to heavy siltation which happens to be due to nature’s response to the man-made developments. The building of ultra-large ships requires deeper drafts and berthing for longer duration of about 4–6 years for outfitting. As such, it is going to aggravate the problem of siltation requiring extensive frequent maintenance dredging and due to environmental laws; it will further make it impossible/disallow the building/repair of mega ships. Hence to overcome the crises of heavy siltation at a particular site, it is inevitable to find out the various reasons which are responsible for siltation. These reasons may be the processes (hydrodynamic/morphological) which governs the sedimentation at that site; present dredging practices being followed and the period for which ships will be berthed at quayside for outfitting. The measures to reduce siltation can be worked out by studying the hydro-morphodynamic behaviour of the region with the help of numerical modelling which will simulate the flow field using site-specific oceanographic measurements and thereafter suggest the remedial mea-

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sures to reduce the siltation. These measures can be either recommending suitable practical dredging methods and or devising a layout of the temporary structure, viz. sheet piles in association with silt traps at quayside. This paper describes the application of FEM technique adopted to understand the hydro-morphodynamic behaviour responsible for the heavy siltation at quayside based on site-specific oceanographic data for monsoon/non-monsoon seasons. It also suggests the remedial measures to be adopted by evolving a technique for minimising the siltation at quayside of shipyard near Cochin in India.

2 Peculiarities of Cochin Harbour The development of Cochin area as a harbour for waterborne transport was carried out during colonial administration in 1920 and various waterfront facilities were developed on mainland, viz. Ernakulam side by carrying out the dredging and later on the material dredged was used to form an artificial island known as Wellington Island. This island bifurcates the flow coming from upstream of backwaters into two channels, namely Ernakulam and Mattancherry. The various facilities in the form of wharfs, ship lifts, jetties exist in the harbour area and in addition to this oil/container terminals, dry docks and shipyards are also situated. All these waterfront facilities do not face the problem of wave disturbance at berths being far inside from the entrance at Cochin Gut from where ships ply in/out to the Arabian Sea. However, the tidal phenomenon in association with river flow from backwaters during monsoon plays a significant role in planning of any waterfront structure in this region owing to high rate of siltation. As such, minimising high rate of siltation at berths and reducing quantum of maintenance dredging fulfilling the environmental laws are the main problems for the development of waterfront facilities. This issue needs to be resolved properly by understanding the phenomena/parameters responsible for siltation and being site specific, needs attention so that berths can be kept operable. The location of quayside in Ernakulam channel wherein the shipyard is currently facing the problem of siltation is shown in Fig. 1.

2.1 Complexities at Shipyard The complexity in the flow field at shipyard is due to various factors which can be classified as: (i) geographical position, (ii) presence of man-made structures in upper reaches, (iii) complex bathymetry and (iv) significant variation in hydraulic parameters and sediment concentration during monsoon/non-monsoon seasons. These factors are described briefly and field investigations are carried out near the location of shipyard to understand the hydrodynamics prevailing in the region. The location of shipyard is far inside from the entrance to Cochin harbour at Gut and shipyard is situated in Ernakulam channel, wherein the flow is channelized

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Fig. 1 View of Cochin harbour and shipyard area

between the two boundaries of banks. The quayside of shipyard is situated in the close proximity of three parallel bridges on upstream connecting Ernakulam channel to Wellington Island and these bridges also have many piers. The presence of piers leads to significant alterations in the flow downstream of bridge site and affects the flow regime near shipyard. The bathymetry data shows that shallower depths (3–4 m) exists near the quayside while depths in the central gorge portion of the channels are relatively deeper having the depth of about 10 m below Chart Datum (CD). The tides are semi-diurnal with micro tidal ranges and during monsoon season discharges from backwaters brought the sediment which has high concentration in suspension and has cohesive nature (clay). In the view of such complexities, strong flow through central gorge portion is attracted towards quayside during monsoon and results in formation of long eddy along the quayside. This causes settlement of significant quantum of sediment due to lateral exchange of sediment load in suspension from central portion of channel towards quay. However, flow direction during non-monsoon is purely due to tides which alter the flow direction by about 180° during flood and ebb phase. In order to confirm this, the site-specific field investigations on oceanographic parameters during monsoon/non-monsoon seasons are carried out and are described in the following section.

2.2 Bathymetry and Oceanographic Field Data The bathymetry data for the portion of Arabian Sea, Cochin harbour area was taken from Admiralty chart and port authorities; while for Shipyard, the quay portion was

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provided by shipyard authority at close interval of 10 m × 10 m. The oceanographic data on tides, currents, salinity, temperature and suspended sediment concentration in the vicinity of shipyard for one lunar tidal cycle along with bed samples were collected at the site (2012–2013). The various locations at which data is collected are shown in Fig. 2. The shipyard authorities provided the data on maintenance dredging for four years (2010–2013) and were used to estimate the present rate of siltation at the quayside. The data on tides collected at gauges T1 and T2 indicate that there is insignificant amplification in tidal ranges as one compares it with that at shipyard (T1) and Cochin port (T2). The maximum range is 0.95 m and 0.5 m during spring and neap tide, respectively, for both the seasons, viz. monsoon and non-monsoon. The current direction in central gorge portion C1 and C2 has been found to reverse by about 180° during flood/ebb tide for non-monsoon season, while near the quayside at C3, current direction is found to be about 250° N during ebb tide compared to 320°–335° N and 70° N as shown in Fig. 3a during flood compared to 150°–155° N at C1 and C2 locations, respectively. This indicates that flow moves towards quayside from central gorge of Ernakulam channel. The direction of current at C3 during monsoon however constantly changes irrespective of the phase of tide (flood/ebb) as shown in Fig. 3b, which shows that there is a formation of eddy/circulation near the quayside. The strength of current at C1 and C2 are 1.2 m/s and 1.8 m/s during non-monsoon and monsoon conditions, respectively; while at C3, it is feeble and is about 0.05 m/s. The salinity and ambient water temperature are 7–29 ppt and 29°–31 °C, respectively. The suspended sediment concentration (SSC) varies between 0.1 and 0.4

Fig. 2 Location of oceanographic data collection points in Cochin harbour

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Fig. 3 a Plot of current strength and direction at C3 near quayside during non-monsoon. b Plot of current strength and direction at C3 near quayside during monsoon

gm/L during non-monsoon, while 0.2–1.2 gm/L during monsoon. The bed material is cohesive and is silty clay with D50 as 0.0029 mm.

2.3 Present Siltation at Quayside of Shipyards The information on siltation pattern in the Ernakulam channel available with CWPRS for the past few decades reveal that siltation is primarily due to the settlement of suspended sediment, which moves along with tidal influx/efflux (flood/ebb) into-andfro manner during non-monsoon season. However, during monsoon season, high rate

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of SSC from backwaters increases the sediment carrying capacity due to increased discharges and causes high rate of siltation. The shipyard authorities mentioned that the dredging in front of the quayside is carried out whenever the built/repaired ship needs to be taken in/out of the dry dock or during berthing/de-berthing operations at the quayside. The data for the past 4 years (2010–2013) on maintenance dredging is analysed and the siltation computed is shown in Table 1. The last row in Table 1 indicates the percentage of siltation during monsoon per annum and is of the order of 60–70. Hence, after the analysis of data on oceanographic parameters and the present rate of siltation, it reveals that root cause of heavy rate of siltation of about 3 m per annum at quayside is mainly during monsoon season. The flow hydrodynamics, viz. formation of eddy and trapping of sediment attracted towards quayside from central gorge which carries high suspended sediment load is the only source of sediment for siltation. Therefore, for evolving a technique to minimise siltation by planning, temporary structure consisting of sheet pile walls was considered in such a fashion that it will not affect the flow field in the nearby existing waterfront facilities. However, simulation of complex flow phenomena is really a challenging job. This requires modelling work with the application of appropriate numerical technique. The application of rectangular grid has its own limitations and as such it does not truly simulate the flow field at curvilinear portions (i.e. bridge piers) due to approximation on shape as well as unable to simulate the effect of secondary currents. Hence, application of triangular finite element mesh discretization for the estuarine domain is essential to properly simulate the eddies, secondary currents at quayside for estimation of the reliable rate of siltation during the monsoon/nonmonsoon seasons by properly modelling the curvilinear shapes of bridge piers, curved coastline etc. The variable mesh with the finer mesh around bridge piers, coast/bank

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line; while coarser mesh in the open sea portion was adopted for modelling, which not only reduces computation time but also provides reliable information about complex flow field.

3 Model Domain and Flow Simulation The hydrodynamics prevailing near the quayside at shipyard was simulated by developing a numerical model. The numerical model considers a domain which includes part portion of Arabian Sea, Ernakulam, Mattancherry channels and backwaters north and south of shipyard. The global domain area is used to derive boundary conditions for sub-model and this model is used for the simulation of hydrodynamics near quayside. The Telemac software [1] is used for simulating hydro-morphodynamic behaviour of the area. The software considers finite elements to cover the domain area and it solves continuity and momentum equations based on Saint-Venant’s formulation [2] using water levels/current/discharges as liquid boundary conditions.

∂u ∂t ∂v ∂t

∂h  + u · ∇(h) + hdiv( u )  Sh ∂t 1 ∂z   + u · ∇(u)  −g + Sx + div(h νt ∇u) ∂x h ∂z 1   + u · ∇(v)  −g + Sy + div(hνt ∇v) ∂y h

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where h (m) u, v (m/s) g (m/s2 ) ν t (m2 /s) Z (m) t (s) x, y (m) S h (m/s) S x , S y (m/s2 )

depth of water velocity components gravity acceleration momentum diffusion coefficients Free surface elevation time horizontal space coordinates source or sink of fluid source terms represents wind, Coriolis force and bottom friction, a source or a sink of momentum within the domain

The software uses mesh generator, which generates the triangular finite elements of various sizes. The domain area simulated for the existing bathymetry for a global model is about 1061 km2 as shown in Fig. 4a and mesh size of about 500 m × 500 m is adopted for the Arabian Sea portion. The sub-model derived from the global model covers the area from Cochin Gut up to backwaters on north and south having an area of about 186 km2 . This area is shown in white colour in Fig. 4a with mesh sizes varying between 80 m × 80 m and 15 m × 15 m. The model developed is used for the calibration of hydrodynamic conditions

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Fig. 4 a Domain area of Cochin harbour and shipyard adopted for simulating hydrodynamics. b Fine mesh discretization for bridge piers near shipyard

prevailing at shipyard for both, the monsoon and non-monsoon conditions. The small model is further derived from sub-model and has an area of about 2.5 km2 (Fig. 4b). The mesh size adopted for this domain is 5 m × 5 m while fine mesh of 1 m × 1 m was used to simulate bridge piers. Thus, a high-resolution mesh is used for calibration of hydrodynamics and estimation of deposition of sediment at quayside of shipyard. The comparison of results for tidal levels observed in the model and measured in the prototype is shown in Fig. 5a, while for currents [3] is shown in Fig. 5b–d. The above figures indicate that direction of current measured at site and observed in the model for non-monsoon season matches reasonably well, and there is a reversal of direction by 180° during flood and ebb phase of tide. These figures indicate that the model is in good agreement with the prototype for tide levels (90%) as well as for the current strength and direction in the domain area for both monsoon and non-monsoon seasons. However, during monsoon season, the large eddy is seen to be formed at shipyard as shown in Fig. 6, which also confirms with the measurement taken at C3 location at site indicating that there is continuous change of direction of current at quayside. Thus, model is in good agreement with the prototype phenomena near shipyard as far as hydrodynamics is considered and can be used to estimate the rate of siltation.

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Fig. 5 a Comparison of tidal levels in prototype and model near shipyard. b Comparison of current strength at C1 in prototype and model for non-monsoon. c Comparison of current strength at C1 in prototype and model for monsoon. d Comparison of current direction at C1 in prototype and model for non-monsoon

4 Calibration and Validation of Siltation at Quay of Shipyard The shipyard situated in Ernakulam channel is about 6 km inside from the Cochin Gut and is hardly 130 m north of bridges connecting mainland to Wellington Island. The flow in the channel is restricted between the boundaries of bank lines formed by westward side of mainland and eastward side of Wellington Island. Thus, flow velocity in the central gorge portion is maximum due to the deeper depths, and it leads to increase in carrying capacity of sediment load. As the bathymetry in the vicinity of shipyard being very shallow (3–4 m), the flow in the central gorge portion is attracted towards quayside. This inference is drawn based on the field data collected during non-monsoon season (current direction) and is also confirmed by model studies. Also during monsoon season, the flow velocity in central gorge further increases and flow attracted towards quayside creates eddy along quayside irrespective of phase of tide. The flow velocities in eddy are feeble and the sediment attracted towards quayside gets trapped and settles. The information on maintenance dredging in front of the quay wall also shows that siltation is maximum during monsoon season (Table 1). Hence, the rate of siltation is being higher during monsoon (70%), the siltation rates along quayside are calibrated in the model for monsoon using Telemac

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Fig. 6 Formation of large eddy all along quayside at shipyard

Fig. 7 Siltation during monsoon at the quayside of shipyard for existing bathymetry condition

software, wherein hydrodynamics is coupled with sediment module. The sediment transport model is a process-based model, wherein the transport rates are calculated as a function of the time-varying flow field and sediment properties at each node of the triangular grid using finite element technique. The clay/silt sediment present in suspension having variable concentration over time is applied at model boundaries

514 Table 2 Comparison of rate of siltation in model and prototype

A. A. Purohit and M. M. Vaidya Season

Average depth of deposition/siltation in m Model Prototype

Monsoon Non-monsoon

2.3 1.4

2.0–2.2 1.3

and depositional/erosional behaviour of sediment at bottom is estimated based on Krone and Parthenaides formulation [4, 5]. The various factors such as grain size (D50 ) of the bed material, flock diameter of material in suspension, settling velocity of flocculated material, suspended sediment concentration (SSC), salinity, temperature, etc. are considered to estimate the rate of deposition for various seasons [6]. The deposition pattern evolved from the model during monsoon season for existing bathymetry condition at quayside is shown in Fig. 7. The depth of deposition/siltation observed at quayside is computed based on analysis of dredging data supplied by shipyard. The deposition pattern and rate of siltation observed in the model for both monsoon and non-monsoon seasons indicate that deposition observed in the model is reasonably in good agreement with that site as shown in Table 2. The model calibrated for siltation in front of dock gates as shown in Fig. 7 at shipyard are validated for the dredged data supplied for the year 2013, and has been found to be reasonably in good agreement. The shipyard has two dry docks, wherein the ships are built and the depth of about 7 m below Chart Datum (CD) is maintained by carrying out dredging in front of dock gates every year. Similarly, at the quayside maintenance, dredging is performed as and when required. Thus, dredging activity is not a regular activity and this leads to more siltation as noticed in dredged pockets.

5 Factors Affecting Mega Shipbuilding at Quayside The shipyard in order to allow movement of ships in/out of dry dock for sea trials as well as during berthing/de-berthing of ships at quayside is carrying out maintenance dredging as and when it demands. Presently, the ships being built/ repaired at shipyard have smaller lengths as well as beam widths are moderate requiring lesser depths to be maintained at quayside. Despite this, the rate of siltation noticed is very high due to the formation of eddy along the quayside as discussed in paragraph 4. In order to meet the demand of building of mega ships having lengths of the order of 300 m or more with beam widths of about 60 m or so, it requires depths at quay of the order of 7–9 m. The harbour at Cochin being in micro tidal region, the tidal window is less than 1 m and as such to carry-out outfitting of such mega ships at quayside continuously for 4–6 years; it will be highly difficult to maintain the required depth of about 7–9 m owing to significantly high rate of siltation. This will require continuous operation of dredging near the ships berthed at quayside and hence, it will not only be a costly affair but will also affect outfitting operation, delay in delivery of ships, damage to

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ships as well as violation of environmental laws. Also, it will affect the operability of various waterfront facilities in the nearby region. As such, in order to overcome above crises, it is felt that the use of semi-enclosed basin as a temporary structure in association with silt traps on upstream and downstream side of such basin with various configuration of sheet pile structure may be effective. Hence, it was studied to assess its effectiveness in minimising siltation as a short-term measure to be adopted during building of mega ships. Also, the present methodology of dredging adopted is in haphazard manner, it needs to be changed by carrying out dredging all along quayside to a constant depth to avoid formation of eddy at quayside and to reduce siltation. Following options were considered to minimise the siltation at quay. 1. Carrying out dredging all along quayside. 2. Provide staggered sheet pile structure as a temporary semi-enclosed basin at the quayside in association with silt traps. 3. Provide scour jet array systems at the quayside to keep the suspended cohesive material in agitating condition during flood/ebb tidal cycle [7]. The methods to minimise siltation using option (1) and (2) are described in following paragraph as methodology mentioned in (3) cannot be adopted due to environmental laws.

6 Studies for Minimisation of Siltation at Quayside The developed and reasonably well-calibrated model both for hydrodynamics and siltation with existing bathymetry condition for both monsoon and non-monsoon

Fig. 8 Bathymetry of Ernakulam channel––dredging all along quayside to minimise siltation

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Fig. 9 a Bathymetry and layout of semi-enclosed basin––two sheet piles to minimise siltation. b Bathymetry and layout of semi-enclosed basin––three sheet piles to minimise siltation

seasons was used further for modifications to incorporate two options, namely (1) and (2) as mentioned in paragraph 5. The simulation is carried out by applying boundary conditions considered for calibration case and the various parameters used for calibration of silt module of Telemac were also considered for assessing the effectiveness of semi-enclosed basin to minimise the siltation. Based on the studies carried out the layout of semi-enclosed basin is optimised. The model bathymetry

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considered for option (1) consists of carrying out dredging up to a depth of 7 m below CD as shown in Fig. 8. The option (2) consist of semi-enclosed basin with two sheet piles, wherein mega ship will be accommodated and silt traps of size 120 m × 120 m with 10 m depth on either side of the basin is shown in Fig. 9a. Similarly, semi-enclosed basin with three sheet pile walls as shown in Fig. 9b is considered to minimise the siltation. The rate of siltation predicted using model studies for option (1) is given in Fig. 10, while for option (2) consisting of semi-enclosed basin with two sheet pile walls and three sheet pile walls for monsoon season are given in Fig. 11 and Fig. 12, respectively. The rates of siltation along quayside were also predicted for the non-monsoon season for both the options (1) and (2). The siltation rates for the existing bathymetry condition at quayside were compared with those estimated for semi-enclosed basin with two and three pile structures and is given in Table 3. The total volume deposited per annum is in million cum. As the depth in silt trap is kept 10 m below CD and 7 m in the remaining area, the dredging in silt traps can be deferred by a year. Hence, there is a net reduction in dredging efforts by about 43% for the option (2) and is more promising to minimise the siltation along the quayside.

Fig. 10 Predicted siltation for dredging up to 7 m depth along quayside during monsoon

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Fig. 11 Predicted siltation for semi-enclosed basin with two sheet piles monsoon

Fig. 12 Predicted siltation for semi-enclosed basin with three sheet piles monsoon

7 Conclusions The development of various waterfront facilities to cope up the future demand of waterborne transport is essential and such developments are coming up at an exponential rate in developing countries like India. However modern trend of transport

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Table 3 Comparison of siltation at quayside for the existing and semi-enclosed basin condition Siltation at Siltation at silt Siltation in Total % less quayside in traps in million semi-enclosed Vol. in than million cum cum basin in million million cum cum Season M NM M NM M NM Existing 0.430 Nil Option (1)

0.212

0.142

NA

NA

NA

NA

0.354

17

Option (2) (Two 0.129 sheet pile wall)

0.086

0.052

0.031

0.014

0.0078

0.320

25.5

Option (2) 0.107 (Three sheet pile wall)

0.072

0.041

0.024

0.0038

0.0021

0.246

43

Where, M Monsoon season and NM Non-monsoon season

of commodities will be through ultra-large size container ships, many shipyards in the country are augmenting their infrastructure facilities for building of mega ships. These shipyards being in estuaries, siltation is a menace and huge maintenance dredging is inevitable. Thus, frequent dredging poses a problem to build mega ships due to high dredging cost and environmental restrictions. As such to minimise siltation at one of such shipyard at Cochin (India), numerical model studies carried out is found to be promising to develop a technique which helps in minimising the siltation near the quayside. The study carried out reveals that: • The application of FEM modelling with fine grid of triangular elements is quite promising in simulation of complex hydrodynamic conditions prevailing near quayside at Cochin during both monsoon and non-monsoon seasons. The fine mesh used for simulating the coastline and bridge piers in the close vicinity of quayside truly simulates the flow field, viz. formation of eddy and hydraulic parameters are 90% in agreement with the prototype. • The site-specific data in association with numerical model provides a good insight to understand the physical processes taking place at quayside which causes heavy siltation of about 3–4 m/annum. • The coupling of well-calibrated hydrodynamic model with silt module provides the reasonably accurate estimation of depth of deposition/siltation near the quayside for both monsoon and non-monsoon conditions. • The depth in the central gorge portion of estuary being more, i.e. about 10 m, the sediment carrying capacity is significant compared to shallow depth of 3 m at the quayside. Moreover, it exchanges the flux and attracts the clayey sediment in suspension towards the quayside and large eddy at the quayside traps the sediment and settles it at quay. This siltation is significant during monsoon season and is about 70% of the annual rate of siltation. • The studies reveal that if constant depth of 7 m is maintained all along the quayside by carrying out dredging, it minimises the siltation by about 17% in comparison to

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the dredging practice presently followed at site. Thus, the model studies provide a guidance to change in dredging strategy for building of mega ships at quayside. • The use of semi-enclosed basin in association with silt traps on either side of basin to minimise the siltation at quayside for building of mega ship which requires 4–6 years of residency period is found to be promising and reduces siltation by about 25% and 43%, respectively, when two and three sheet piles wall configuration is adopted. Thus, the application of FEM is beneficial in optimising the layout of semi-enclosed basin to minimise the siltation at quayside for case of mega shipbuilding. Acknowledgements The authors are grateful to Dr. V. V. Bhosekar, Director, Central Water and Power Research Station, Pune (India) for her continuous encouragement and motivation for carrying out the research work.

References 1. Hervouet JM (2007) Hydrodynamics of free surface flows, modeling with the finite element method, 1st edn. Wiley, London, West Sussex 2. Telemac modeling system (2002) 2D Hydrodynamics-Version 5.2, User Manual, June 2002, pp 7–8 3. CWPRS (2015) Technical Report No 5253 of Feb 2015 4. Krone RB (1962) Flume studies of the transport of sediment in estuarial shoaling processes, final report. Hydraulic engineering and sanitary engineering research laboratory. University of California, Berkley(CA) 5. Parthenaides E (1962) A study of erosion and deposition of cohesive sediments in salt water. PhD thesis, University of California 6. Whitehouse R, Soulsby R, Roberts W, Mitchener H (2000) Dynamics of estuarine muds. Thomas Telford, London 7. Bailard JA (1987) Controlling sedimentation in Harbour berthing areas, in sedimentation control to reduce maintenance dredging of navigational facilities in estuaries: report and symposium proceedings, Marine Board, commission on engineering and technical systems. National Research Council, National Academy Press, Washington DC, pp 141–152

Evolving Fishing Harbour Layout by Wave Tranquility Study Using Mathematical Model—A Case Study J. D. Agrawal, H. C. Patil, Sagar Chanda and T. Nagendra

Abstract The important parameters needed to be considered for fishery harbour developments are waterside and landside facility. Coastal processes in the area also play a vital role in planning and designing of fishery harbour layout. Wave tranquility studies are important in deciding the orientation and length of the breakwater in fishing harbour. This paper describes a case study of the proposed fishing harbour at Ajanur, in Kerala state, India for evolving a suitable fishing harbour layout from wave tranquility point of view. Two-dimensional mathematical model MIKE21 SW (Spectral Wave model) has been used for the wave climate transformation from offshore region to nearshore location. The model provides the necessary wave conditions in the nearshore region, which are likely to affect the proposed fishing harbour. MIKE-21 BW (Boussinesq Wave model) has been used for wave propagation from the nearshore region to the harbour basin. Four alternative layouts with different breakwater orientation and length were considered for the model studies. It is found that layout 3 and layout 4 provide the maximum number of operation days in a year, however, layout 4 appears to be most suitable layout from the site consideration and economy in the construction. Keywords Fishing harbour · Wave tranquility · MIKE-21 BW · MIKE-21 SW Case study

1 Introduction Due to ever increasing demand for fishes, new fisheries harbours is required to be developed and existing port need to be expanded with deeper and wider approach channel. If a port is to be developed in the zone of high littoral drift, it is of vital

J. D. Agrawal (B) · H. C. Patil · S. Chanda · T. Nagendra Central Water and Power Research Station, Khadakwasla, Pune 411024, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_39

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Fig. 1 Index map and the proposed Ajanur Fishing Harbour layout

importance to predict its effect on the adjacent shoreline and suggest remedial measures to minimise the adverse effects due to construction of the fishing port. Most of the coastal phenomena such as tidal hydrodynamics, sedimentation and wave propagation, which are important for designing the fishing port layout, can be simulated using mathematical models. Wave tranquility inside the fishing port basin is one of the most important criteria in optimising the length and orientation of breakwaters. Typical harbour layout along with index map is given in Fig. 1. Model simulations were carried out for four alternatives layouts of fishing harbour and the predicted safe berthing operation in terms of number of operational days in a year were found out. It is observed that there is appreciable difference in the layouts in terms of number of operational days. The permissible wave height was compared with the simulated wave height and the numbers of operational days of a year were found out. Layout with most economical and suitable from site consideration and maximum number of operational days was finally selected. Thus, it can be stated that wave tranquility studies can be effectively used as a tool to finalise the fishing harbour layouts from wave tranquility point of view.

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2 Mathematical Modelling Techniques Mathematical model studies for examining the wave conditions in the proposed fishery harbour were carried out in two stages. In stage-I, wave transformation from deep waters to nearshore was done and in stage–II, wave tranquility inside proposed harbour was simulated.

2.1 Wave Transformation from Deep Sea to Nearshore Region As waves travel from deep sea to shallow coastal waters, they undergo changes in direction and height due to the processes of refraction and shoaling. The simulation of wave transformation from deep sea to shallow waters was carried out using MIKE21 SW model. This model is a spectral wind wave model based on unstructured mesh, which takes into account of all the important phenomena like wave growth by influence of wind, nonlinear wave–wave interaction and dissipation due to white capping, bottom friction and depth induced breaking. It can also model diffraction effects due to the presence of large structures like breakwaters, groins, etc. The effect of refraction and shoaling of waves due to depth variations and wave current interaction are also considered in the model. The output of the model are the regular wave parameters which include the significant wave height, mean wave period, mean wave direction, directional standard deviation and wave radiation stress. The model simulates the growth, decay and transformation of wind-generated waves and swells in offshore and coastal areas. The governing equation is the wave action balance equation. In horizontal Cartesian coordinates, the conservation equation for wave action is S ∂N → + ∇ . (ν N)  ∂t σ →

→

where N( x , σ , θ , t) is the action density, t is the time, x  (x, y) is the Cartesian → coordinates, ν  (Cx , Cy , Cσ , Cθ ) is the propagation velocity of a wave group in the → four-dimensional phase space x , σ and θ . S is the source term for the energy balance → equation. ∇ is the four-dimensional differential operator in the x , σ and θ space. The equation is solved using cell-centred finite volume method.

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2.2 MIKE-21 BW Wave Simulation Model for Fishing Port Basin The Boussinesq wave models are based on laws of conservation of energy and momentum concepts. The model simulates the processes of shoaling, refraction and diffraction from breakwater tips and bed friction. It also takes into account the partial reflections from the boundaries, piers and breakwaters. This model is based on time-dependent Boussinesq equations [1] for conservation of mass and momentum obtained by integrating the three-dimensional flow equations without neglecting vertical acceleration. They operate in the time domain so that irregular waves can be simulated. These equations include nonlinearity as well as frequency dispersion. The frequency dispersion is included in the flow equations by taking into account the effect of vertical acceleration or the curvature of streamlines on pressure distribution. This model is widely used to simulate wave propagation across the breakwater and to examine the wave height distribution inside the harbour.

3 Model Simulation 3.1 Wave Transformation from Deep Sea to Near-Shore Region Using MIKE-21 SW Model An area of about 115 km by 85 km (Fig. 2) with a flexible mesh (FM) was considered for studies with MIKE-21 SW model which extends beyond the depth of 100 m in deep sea. The model simulation was carried out with all seasons and annual offshore wave climate as shown in Fig. 3 as Rose plot for all the incident wave directions and heights. MIKE 21-SW model output is a frequency distribution of wave heights from different directions at the depth of −10 m in nearshore location. The corresponding annual nearshore wave rose plot is shown in Fig. 4. Based on the MIKE21-SW model results, such as percentage occurrence of wave heights and direction and rose plot, input wave condition for MIKE-21 BW were finalised. This wave data would be given as input to the MIKE21-BW model for nearshore wave simulation.

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Fig. 2 Bathymetry for wave transformation studies

Fig. 3 Offshore wave rose for (annual period)

3.2 Wave Tranquility Studies for Proposed Fishing Harbour Layouts Mathematical model MIKE21-BW was used for studying the wave disturbance inside fishing harbour. The computational model with an area of about 5 km by 4.5 km for each of the four layouts was considered. The model area was discretised with a grid size of 3 m × 3 m. The inshore wave conditions obtained from MIKE-21 SW model

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Fig. 4 Nearshore wave rose for Ajanur (annual period) Table 1 Input wave conditions for wave tranquility studies

Incident wave direction

Incident wave height (m)

SSW SW WSW WEST WNW

1.5 2.0 2.5 2.5 1.5

computations were used as input wave conditions (Table 1). Wave propagation in the fishing harbour basin was simulated. The studies were carried out for four alternative port layouts and wave conditions in the fishing harbour basin were found out. The details of the following four layouts are as follows.

3.2.1

Layout 1

Layout 1 consists of north breakwater and south breakwater, having a length of 458 m and 686 m, respectively. The maximum depth near the toe of the breakwater is about −4 to −4.5 m. Harbour basin depth was considered −3.0 m (Fig. 5).

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Fig. 5 Proposed layout 1

3.2.2

Layout 2

Layout 2 consists of north breakwater and south breakwater having a length of 686 m and 458 m, respectively. The maximum depth near toe of the breakwater is about −4 to −4.4 m depth. Harbour basin depth was considered as −3.0 m (Fig. 6).

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Fig. 6 Proposed layout 2

3.2.3

Layout 3

Layout 3 consists of north breakwater and south breakwater, having a length of 811 m and 334 m, respectively. The maximum depth near the toe of the breakwater is about −4 to −4.5 m. Harbour basin depth was considered −3.0 m (Fig. 7).

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Fig. 7 Proposed layout 3

3.2.4

Layout 4

Layout 4 is similar to layout 3 except that orientation of the northern breakwater was straightened to avoid kink in the harbour. Layouts 4 consist of north breakwater and south breakwater, having a length of 1000 m and 375 m respectively. The maximum depth near toe of the breakwater is about −4 to −4.5 m depth. Harbour basin depth was considered −3.0 m (Fig. 8).

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Fig. 8 Proposed layout 4

The model studies were carried out for all the four layouts for the incident wave heights of 1.5, 2.0, 2.5, 2.5, 1.5 m from SSW, SW, WSW, West, WNW directions, respectively. Surface water elevation, Wave height distribution plots for all the conditions were obtained. A representative plot of surface water elevation and wave height distribution for SSW direction of layout 4 is shown in Figs. 9 and 10. Being a fishing boat shelter harbour, a wave tranquility limit of 0.3 m, i.e. allowable wave height for vessels smaller than 500 tonnes [2] has been taken for calculation of non operational days.

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Fig. 9 Surface wave distribution plot

Wave tranquility study of all the four proposed layouts has indicated that the average wave height in the area is more than 0.3 m. Table 2 provides the different condition for which models were run and their output. Analysis of model study results for different alternative port layouts with incident wave heights and direction indicated (Table 3) that the Layout 1 will have 201 days as operational days in a year. Layout 2 will have 208 days as operational days in a year. It is found that layout 3 and layout 4 provide the maximum number of operation days in a year from the wave tranquility point of view, however, layout 4 appears to be most suitable layout from the site consideration and economy in the construction.

4 Concluding Remarks Wave propagation studies using mathematical model indicated that it is feasible to evolve the fishing harbour layout from wave tranquility point of view which is operational round the year. With mathematical models, various alternative layouts could be studied. Layout 3 and 4 are suitable from wave tranquility point of view, however, layout 4 appears to be most suitable layout from the site consideration and economy in the construction. Computer simulations play an effective tool in designing the fishing harbour layout. The model studies provide information about the post-development scenario, which is very important for any developmental project.

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Fig. 10 Wave height distribution plot

Table 2 Wave height, average wave height and maximum wave heights of all the four layouts Layout

Wave direction

Significant wave height (m)

Column no. 1

2

3

4

5

6

Layout 1

SSW

1.5

19.95

0.58

1.41

Layout 2

Layout 3

Harbour basin area (%) having more than 0.3 m wave height

Average wave height in the area given in col. 4 (m)

Maximum wave height in the harbour (m)

SW

2.0

28.68

0.69

1.57

WSW

2.5

48.04

1.02

2.52

West

2.5

62.21

0.84

2.51

WNW

1.5

41.28

0.50

1.13

SSW

1.50

38.01

0.52

1.20

SW

2.0

55.31

0.68

1.52

WSW

2.5

51.64

0.98

2.28

West

2.5

92.69

0.93

3.99

WNW

1.5

23.41

0.58

1.13

SSW

1.5

1.09

0.35

0.55

SW

2.0

0.10

0.31

0.38 (continued)

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Table 2 (continued) Layout

Wave direction

Significant wave height (m)

Harbour basin area (%) having more than 0.3 m wave height

Average wave height in the area given in col. 4 (m)

Column no. 1

2

3

4

5

6

WSW

2.5

0.08

0.37

0.61

West WNW

2.5 a

0.08 a

0.32 a

0.39 a

SSW

1.5

0.04

0.06

0.37

SW

2.0

0.12

0.07

0.40

WSW

2.5

0.0

0.09

0.28

West

2.5 a

0.0 a

0.09 a

0.25 a

Layout 4

WNW

Maximum wave height in the harbour (m)

a Since the harbour is tranquil for other critical wave directions, it will remain tranquil for this WNW direction also. Due to this reason WNW wave direction was also not studied for layout-3 and layout 4

Table 3 Number of operational days in a year Layout Layout-1 Layout-2 No. of operational days

201 days operation

208 days operation

Layout-3

Layout-4

365 days operation

365 days operation

Acknowledgements The authors are grateful to Dr. (Mrs.) V. V. Bhosekar, Director, Central Water and Power Research Station, Pune for her continuous encouragement and kind permission to publish the paper.

References 1. Abott MB, Madson, PA, Sorenson OR (2001) Scientific documentation of MIKE 21 BW (Boussinesq wave model) 2. Harbours tranquility study using MIKE 21 BW Babak Sherkati azin, DHI technical support manual Publication (2010) 3. CWPRS Technical Report No. 5436, 2016, titled “Wave propagation studies to determine wave climate for the development of fish landing facilities at Ajanur, district Kasaragod, Kerala” 4. MIKE 21 BW Reference manuals (2015) from Danish Hydraulic Institute. Denmark 5. MIKE 21 SW Reference manuals (2015) from Danish Hydraulic Institute. Denmark

Shoreline Change Associated with Coastal Structures at Gopalpur Port, Odisha, East Coast of India Prabin Kumar Kar, Pratap Kumar Mohanty and Balaji Behera

Abstract Gopalpur port is now functioning as an all-weather direct berthing port and is being developed since 2008. Southern and northern groins were constructed during 2008, and following it a series of ten groins were constructed on the north side of northern groin during 2009–2011. Intermediate and southern breakwaters were constructed during 2011–2012 and a berth in between the two breakwaters was constructed during 2012. Shoreline changes associated with these coastal structures are studied through a long-term monitoring (June 2012–June 2016) carried out at monthly interval at south and north of the port covering a stretch of 9 km. Observations include shoreline change using Differential Global Positioning System (DGPS) Arcpad along the berm line, beach profile at every 500 m interval using total station/Real-Time Kinematics Global Positioning System (RTK GPS). It is observed that due to round the year south-to-north longshore sediment transport, accretion occurs at south of coastal structures and erosion occurs to the north of coastal structures. In order to study the shoreline change in detail, Net Shoreline Movement (NSM), Shoreline Change Envelope (SCE), End Point Rate (EPR) and Linear Regression Rate (LRR) are computed at all the transects using Digital Shoreline Analysis System (DSAS) version 4.2, an extension to ESRI Arc-GIS developed by the United States Geological Survey (USGS). The results are presented under three categories such as accretion, moderate erosion and high erosion. The study reveals that the shoreline of Gopalpur port experiences both erosion and accretion. The major stretch of shoreline, mostly on the south of the port, is under accretion category while 2 km shoreline on the north of the port, inside the groin field, is under medium erosion category. However, the sector covering about 1 km stretch under high erosion category lies on the north of the northern groin field. The results clearly show the distinct impacts of the groins and breakwaters on shoreline change at Gopalpur port and have significant implications on the future development of the port.

P. K. Kar · P. K. Mohanty (B) · B. Behera Department of Marine Sciences, Berhampur University, Berhampur 760007, Odisha, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_40

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Keywords Coastal structures · Shoreline change · Beach profile Erosion/accretion · Gopalpur port

1 Introduction Coastal structures are designed to arrest the erosional environment or to promote a well-configured beach [1]. However, erosion is caused due to construction of artificial barriers such as groins and breakwaters [2]. The coastal structures associated with the development of the port are: southern and northern groins constructed during 2008, a series of ten groins to the north of northern groin constructed during 2009–2011, intermediate and southern breakwaters constructed during 2011–2012 and a berth in between the two breakwaters constructed during 2012. Besides, two piers near southern and northern groin existed earlier. The purpose of this artificial construction is to reduce coastal erosion and stabilise the shoreline by enhancing accretion pattern. Further, coastal constructions at this stretch are for the development of cargo facilities and smooth movement of the ships near the surf zone area. As the longshore transport along the coast is from south to north round the year, the groins and breakwaters trap the longshore sediment resulting accretion on the south and erosion on the north of the coastal structures [3]. The morphological change due to the presence of coastal structures was studied by Mohanty et al. [4] before the construction of northern groin field and the two breakwaters. Kar et al. [5] also investigated the shoreline change near Gopalpur during the period 2015 using geospatial techniques. Apart from this, several studies worldwide [6–10] demonstrate the impacts of groins and breakwaters on shoreline change. Therefore, the objective of the present study is to understand the morphological process dominant along the port province and the shoreline change associated with coastal structures in the port. In order to achieve the objective, a long-term (June 2012–June 2016) monitoring of beach profile and shoreline was conducted. Shoreline and beach profiles were monitored at south and north of Gopalpur port at monthly intervals. Different statistical features such as SCE, NSM, EPR and LRR are computed based on observed data for 5 years. Besides, short-term shoreline changes are also studied to identify the hotspot zones of erosion/accretion and to address the impacts of short-term extreme events.

2 Study Area Gopalpur port is located at latitude 19° 18 13 N and longitude 84° 57 52 E along the state of Odisha, East coast of India (Fig. 1). The port is being developed as an all-weather open sea direct berthing port and is at a distance of approximately 166 km from Paradip port on its north and at a distance of 203 km from Vishakhapatnam port on its south. The coastal structures present within the port premises are southern groin

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Fig. 1 Study area showing the station locations at south and north side of Gopalpur port

(530 m), northern groin (362 m), series of 10 groin field of different dimension on the north of the port, southern breakwater (1735 m), intermediate breakwater (360 m), southern pier (500 m), northern pier (400 m) and a berth (Fig. 1). Sandy beach with high sand dunes on the backshore, fishing jetty and Indian Rare Earths Limited (IREL) (the sand mining and processing factory) are located in close proximity to Gopalpur port. The geomorphological study was conducted covering 4.5 km both on the north and south of the port.

3 Materials and Methods Monthly shoreline and beach profile survey was conducted during the period from 2012 to 2016 at Gopalpur port covering a stretch of 9 km on the south and north of the port. Beach profiles were measured at ten locations (Fig. 1) on both sides of the port and the interval between two successive profiles was maintained at 500 m. Beach width and beach volume were computed at each transect using Beach Morphology Analysis Package (BMAP) version 2.0 of the US Army engineer waterways experiment station. BMAP is easy to use for its inherent analytical functions, automated and interactive procedures [11].

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Shoreline positions were monitored using Differential Global Positioning System (DGPS) Arcpad while beach profiles were monitored using Leica SR 1200 RealTime Kinematics (RTK) Global Positioning System (GPS)/Total Station of Trimble make having ±1 cm position accuracy and ±2 cm elevation accuracy. The detail of the survey method employed for beach profile and shoreline measurement is similar to Mohanty et al. [4]. All the observations were carried out during spring low tide because of the presence of wider beach at that time. The study uses the methods of Remote Sensing Technology and DGPS Arcpad survey integrated in a Geographical Information System (GIS) environment to create the information of long-term shoreline change. It may be mentioned that the shoreline in the present study refers to the undisturbed first berm near midshore during lowest low tide at the observation time. Further, the analysis of shoreline change is carried out between a fixed baseline created near backshore with the help of DSAS software, an extension tool of Arc-GIS and the first berm position which is collected with the help of DGPS Arcpad near south and north of the port. Five attributes such as 1. Object ID (represents a unique number for every transect), 2. shape, 3. shape length, 4. date (represents the actual observation date) and 5. uncertainty values are used in DSAS for analysis. All shoreline files are merged in a single line on the attribute table and a single shapefile of multiple shorelines is created with respect to the baseline for further analysis. Shoreline change statistics such as NSM, SCE, EPR and LRR are calculated following Thieler et al. [12]. The distance of the berm line from the reference line indicates the length of the shoreline. The spatio-temporal changes in the berm positions are analysed in a GIS environment using ArcView GIS software (Version 3.2a). NSM is the distance between the oldest and newest shoreline with respect to the baseline while SCE represents the distance between the nearest and farthest shorelines with respect to the baseline for each transect without any relationship with time period. EPR is the ratio of shoreline movement distance to the time elapsed between the oldest and the most recent shoreline. LRR is determined by fitting the least squares regression line to all shoreline points of a particular transect and represents the slope of the line. LRR has the following advantages such as (a) accessing the entire data file without changing the trend or accuracy (b) the method is computational only (c) based on statistical concepts and (d) easy to use [13].

4 Results and Discussion The results of the present study are described for two sectors, namely Gopalpur Port South (GPLS) and Gopalpur Port North (GPLN) (Fig. 1). Shoreline change and the statistics followed by beach profile and its volume/width change are discussed. The details of coastal structures near the port are described in Table 1.

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Table 1 Length and elevation of coastal structure near Gopalpur Port (2012–2016) Structure type Length (m) Elevation after construction (m)

Distance between two successive coastal structure (m)

2012

2013

2014

2015

2016

1249

1079.02

1098

1537

1626.12

3.96

0

305

233.70

225

223.3

220.35

3.56

1281.54

530

441

440

436

435

2.56

1117.63

500

500

500

500

500

6.5

82.2

Northern pier

400

400

400

400

400

6.5

144

Northern groin-1

362.36

274

270.00

268.32

268.01

2.63

22.2

Groin-2 Groin-3 Groin-4 Groin-5 Groin-6 Groin-7 Groin-8 Groin-9 Groin-10 Groin-11

21.40 36.86 72.18 45.39 32.67 43.19 16.18 9.90 23.79 28.45

15.76 21.85 56.13 15.34 22.02 39.76 29.69 43.42 30.24 19.05

14.23 20.25 55.12 14.66 20.22 38.21 28.29 41.25 30.00 19.00

9.80 18.22 54.20 14.12 18.21 35.12 26.08 39.20 28.32 17.50

7.25 17.32 50.25 14.08 18.11 35.35 25.89 38.25 28.33 16.92

3.65 5.0 5.25 4.61 6.10 6.15 5.98 6.15 7.20 9.6

750 200 261 250 237 185 185 195 180 285

Southern breakwater Intermediate breakwater Southern groin Southern pier

4.1 General Oceanographic Conditions Near Study Area During the period 2008–09, wave, tide and currents were measured near Gopalpur port and the data presented here correspond to the said observation. The mean spring tidal range is 2.39 m and neap tidal range is 0.85 m with highest during August and lowest during January. Wave height ranges from 0.25 to 0.97 m during the observation period. Wave period ranges from 7.2 s during premonsoon period to 10.8 s during winter period. Significant wave height ranges from 0.26 to 3.29 m round the year. The details of oceanographic conditions are described by Mohanty et al. [3, 4].

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4.2 Shoreline Position Figure 2 describes positions of the shoreline and their interannual change at both south and north of the port. The shoreline in the present study refers to the berm position at highest high water line and its shifting towards land/sea with respect to time subjected to erosion/deposition. The distance between the shoreline and the baseline is the shoreline length. It is observed that during the period from 2012 to 2016, the length of the shoreline in winter (December) is more than the length during monsoon (June) for every year. However, in the year 2013 and 2014, the length of shoreline is significantly less as compared to other periods. It is because, very severe cyclonic storm Phailin crossed Odisha coast (south of Gopalpur) on 12 October 2013 and caused severe damage to the coastal structures. Its impact continued towards south and north of Gopalpur port till next year. After construction of southern breakwater at 2.5 km south of southern groin, a healthy and stable beach developed further south in the succeeding years (Fig. 2). The average length of the shoreline from 0 to 2.5 km on port south is less than the length from 3 to 4.5 km. The length of the shoreline gradually decreased between 0 and 1 km, i.e. to the north of southern breakwater while the length of shoreline gradually increased to the south of southern breakwater. This could be due to the influence of coastal structures. Similarly at the north of Gopalpur port, the shoreline shows an increasing trend from northern groin to the end of groin field while it shows a decreasing trend beyond the groin field. Seasonal variation of shoreline indicates that the beach between 0.5 and 2.5 km (inside the groin field) north of northern groin is comparatively stable and shows minimum oscillation with time.

Fig. 2 Change in shoreline at south side and north side of Gopalpur port from 2012 to 2016

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4.3 Shoreline Change Rate Seasonal Shoreline Change Rate (SCR) is presented in Fig. 3 and discussed in this section. It is observed that there is definite impact of coastal structures (groins and breakwaters) at both south and north of Gopalpur port. For monsoon and post monsoon, 2012 is taken as reference period while for northeast (NE) monsoon and premonsoon, 2013 is taken as reference period. It is also observed that the rate of change towards south far exceeds the rate of change towards north. It is observed that south of Gopalpur port, the SCR is positive beyond 2 km which indicates the huge accumulation of beach sediments. Round the year sediment transport from south to north helps accretion of sediment on the south of southern breakwater and hence the wider shoreline at south of southern breakwater. On the other hand, north of breakwater, the beach is sediment starved and hence the SCR is negligibly negative. However, the SCR shows enhancement in the succeeding years for every season. Despite the beach nourishment at north of northern groin (0 km), the SCR is negative, which could be due to the impact of wave approach and coastal structures. Inside the groin field, the SCR is positive, because the shore perpendicular groins help trapping the sediments within the groin field. However, the SCR is negative beyond the groin (from 3 km north of northern groin). In the succeeding years, the wave-induced energy washed the groin field slowly (Table 1) and consequently, the negative SCR increased. Though the construction of coastal structures and beach nourishment north of Gopalpur port helps to check the erosion to some extent, it is not full proof to abate erosion. Therefore, the groin field must maintain its stability followed by plantation of dune vegetation to arrest erosion and to maintain a stabilised beach on the port north.

4.4 Statistics of Shoreline Change Change in shoreline and its statistics such as NSM, SCE, EPR and LRR are computed and the results are briefly discussed in this section. This approach for shoreline study minimises the potential errors and hence is considered as one of the best methods by many authors [14–16]. Table 2 depicts the statistical features of shoreline change at different transects of Gopalpur port south and north. SCE, the distance between closest and farthest shoreline with respect to baseline, is found maximum at 2.5 km, located south of southern breakwater, at GPLS while it is maximum at 3.0 km, located north of northern groin at GPLN. The results indicate that the shoreline oscillation is dynamic at south of southern breakwater and north of northern groin field. NSM indicates the difference of the oldest and youngest shoreline of every transect. NSM is distinctly negative at GPLN, which suggests that the length of the shoreline during recent observation is less as compared to June, 2012. On the other hand, NSM is negative from 0 to 1 km and distinctly positive from 2.5 km

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Fig. 3 Seasonal shoreline change rate at Gopalpur port south and north

to further south at GPLS. This clearly suggests the impact of southern breakwater on the shoreline to the south and north of it. The shoreline shifted 66–336 m towards ocean and made the beach wider at GPLS. EPR method indicates the distance of the shoreline divided by the time elapsed between the oldest and the youngest shoreline.

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Table 2 Shoreline change statistics at Gopalpur Port south (GPLS) and Gopalpur Port North (GPLN) (NA––not available) SCE (m) NSM (m) EPR (m/yr) LRR (m/yr) 0 km 0.5 km 1.0 km 1.5 km 2.0 km 2.5 km 3.0 km 3.5 km 4.0 km 4.5 km

GPLS

GPLN

GPLS

GPLN

GPLS

GPLN

GPLS

GPLN

117.5 113.1 215.6 NA NA 350.5 239.6 175.6 122.3 89.5

93.5 73.7 47.0 37.2 52.2 102.5 132.8 91.7 73.3 71.5

−109.9 −84.69 −3.48 NA NA 336.95 214.5 150.25 98.12 66.31

−35.4 −23.64 −12.85 −14.71 −22.63 −82.99 −122.36 −77.32 −50.22 −36.91

−2.29 −1.76 −0.07 NA NA 7.02 4.47 3.13 2.04 1.38

−0.7 −0.5 −0.3 −0.3 −0.5 −1.7 −2.5 −1.6 −1.0 −0.8

−1.3 −1.5 −0.07 NA NA 6.3 4.7 3.6 2.4 1.8

−0.9 −0.2 0.1 0.0 0.1 −0.3 −2.0 −1.6 −1.2 −1.5

As evident from Table 2, EPR is positive at every transect from 2.5 to 4.5 km south of southern groin and suggests that the beach is growing slowly and gradually while it is negative between 0 and 1 km, i.e. north of intermediate breakwater. EPR is negligibly small but negative at GPLN. LRR is the rate of change or slope of a line determined by fitting least square regression to all the shoreline points of a particular transect. It is calculated by plotting the shoreline positions with respect to time and is depicted in Table 2. The rate of change is positive at GPLS south of southern breakwater with maximum (6.3 m/year) at 2.5 km, which gradually reduces further south. LRR is distinctly negative at GPLN and also between 0 and 1 km of GPLS. The results further suggest that at Gopalpur port north side, the negative rate of change is minimum inside the groin field and gradually increases beyond the groin field. This pattern of beach change significantly affects the beach stability at GPLN.

4.5 Beach Morphology Beach profiles of three transects at south (GPLS_1, GPLS_6 and GPLS_10) and three transects at north (GPLN_1, GPLN_6 and GPLN_10) are presented in Fig. 4. GPLS_1 represents north of intermediate breakwater, GPLS_6 represents south of southern breakwater and GPLS_10 represents extreme south of Gopalpur port. Similarly, GPLN_1 represents just north of northern groin, GPLN_6 represents inside the groin field and GPLN_10 represents extreme north of Gopalpur port beyond the groin field. The beach is narrower at GPLN compared to GPLS. VSCS Phailin had landfall south of Gopalpur on 12 October 2013 and its impacts are very much apparent at GPLS_10, which is closer to the tourist beach. Later, the beach was restored in the subsequent months and shows the impact of coastal structures. At GPLS_1, the beach was wider during 2012–13 and reduced in the succeeding months. Beach

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Fig. 4 Beach profile observations at selected stations of Gopalpur port south and north

profile of GPLS_6, located south of southern breakwater, is quite distinct from others and is the widest. It could be due to interruption of the south to northward flowing longshore sediment transport by the breakwater and hence deposition of sediment to the south of southern breakwater. GPLS_10 shows gradual increase in beach width and depositional environment during observation period. Beach profile at Gopalpur south indicates stable berm at backshore, moderate slope at midshore and absence of ridges towards foreshore while two distinct steep slopes are observed during December 2012 and 2013 at GPLS_10. The beach at GPLN_1 is relatively flat at the backshore and midshore compared to other transects. However, steep sloping profiles of foreshore are prominent at GPLN. Steep sloping profile at GPLN_10 is very distinct during 2014–2016, which

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had gentle slope during 2012–2013. There is gradual decrease in beach width in the successive months at GPLN_10 which is responsible for erosion. Beach profile study also indicates clearly the impact of groin and breakwaters on the south and north of Gopalpur port during the period of observation.

4.6 Erosion/Accretion Environment Table 3 describes the Seasonal change in beach width and volume at south and north side of Gopalpur port from June 2012 to June 2016. Significant change in volume and width are observed associated with coastal structures and compacted with seasonal variation. The beach at south of southern groin shows predominantly depositional environment. Particularly at GPLS_6, located south of southern breakwater, the beach width and beach volume change are always positive and with relatively higher magnitude compared to other transects. However negative beach volume and width are also occasionally observed at the study area. The beach is very narrow to the north of northern groin. Predominantly negative change for both beach width and volume are observed at GPLN during the observation period. Table 3 Beach width and beach volume change adjacent to the south and north of Gopalpur port Changes in beach volume (m3 /m)

Changes in beach width (m) GPLS

GPLS_1

GPLS_3

GPLS_6

June 12–December 12

−29.15

−8.6

38.91

December 12–June 13

−17.61

28.11

19.23

13.45

June 13–December 13

−24.57

−27.17

38.64

−5.62

December 13–June 14

−13.19

38.9

25.25

June 14–December 14

−1.0

−5.8

32.0

31.5

December 14–June 15

20.67

−2.41

55.9

June 15–December 15

−26.76

19.4

55.05

December 15–June 16 GPLN

7.06 GPLN_1

6.97

−6.41

27.74

GPLN_3

GPLN_6

GPLS_10 GPLS_1

GPLS_3

−18.69

−54.68

110.21

39.07

82.72

382.53

68.53

−224.68

−37.67

35.69

−63.33

−51.13

GPLS_6

GPLS_10 −48.19

36.62

−11.05

63.24

69.58

−20.68

−5.39

55.13

99.88

12.87

141.38

−24.98

157.26

28.47

−1.93

−70.89

−6.18

123.45

−0.91

−15.36

−28.71

48.88

−60.86

GPLN_10 GPLN_1

13.07 GPLN_3

GPLN_6

−16.07

−95.46

−117.79

18.50

15.71

156.29

−120.56

−61.98

−72.14

4.79

−19.42

−79.34

53.39

−18.94

56.95

−36.18

−14.69

−56.30

June 12–December 12

2.16

0.77

−9.66

December 12–June 13

0.55

5.52

−24.45

June 13–December 13

−25.24

12.72

−6.94

0.62

December 13–June 14

25.24

−0.69

19.11

−7

June 14–December 14

−3.6

−4.14

−6.96

−21.87

−22.23

−11.69

December 14–June 15

−15.8

9.7 −30.49

GPLN_10

−5.97

32.02

1.13

−61.19

−7.97

105.98

2.29

June 15–December 15

5.78

11.47

−2.8

10.94

−0.26

17.98

−45.36

−9.47

December 15–June 16

−0.89

−11.77

26.99

−10.24

20.27

−18.31

202.59

8.512

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5 Conclusion Impacts of coastal structures at south and north of Gopalpur port are investigated from 2012 to 2016. Shoreline and beach profile observations clearly demonstrate the distinct impacts of the coastal structures at both sides of the port. The results conclude that the major stretch of the shoreline, 2 km south of southern breakwater, is under accretion category while 2 km shoreline towards north of the port, inside the groin field, is under medium erosion category. However, the sector covering about 1 km stretch to the north of the northern groin field is under high erosion category. The results of the present study suggest that the integrated approach shall act as a guiding principle for the development of Gopalpur port and shall be helpful for the Integrated Coastal Zone Management Programme of Odisha state. Results also indicate that long-term monitoring of shoreline is essential for sustainable development of the Gopalpur Port. Acknowledgements This study is the part of our Environmental Monitoring research project funded by Gopalpur Port Limited. We thank the authorities of Gopalpur port and acknowledge the support and help of Berhampur University. Mr. Shraban Kumar Barik was an author for this paper because of his contribution. We dedicate this paper to Mr. Barik who passed away recently.

References 1. Ranasinghe R, Turner IL (2006) Shoreline response to submerged structures: a review. Coast Eng 53:65–79 2. Vaidya AM, Kori SK, Kudale MD (2015) Shoreline response to coastal structures. Aquat Procedia 4:333–340 3. Mohanty PK, Barik SK, Kar PK, Behera B, Mishra P (2015) Impact of ports on shoreline change along Odisha coast. Procedia Eng 116:647–654 4. Mohanty PK, Patra SK, Bramha S, Seth B, Pradhan U, Behera B, Mishra P, Panda US (2012) Impact of groins on beach morphology: a case study near Gopalpur Port, east coast of India. J. Coast Res 28(1):132–142. West Palm Beach (Florida), ISSN 0749-0208 5. Kar PK, Mohanty PK, Barik SK, Behera B, Pradhan UK, Patra SK, Mishra P, Panda US, Panda US, Bramha S (2017) Shoreline change: a study along South Odisha coast using statistical and geospatial technique. Int Res J Earth Sci 5(1):1–7. ISSN 2321-2527 6. Özölçer IH, Kömürcü MI (2007) Effects of straight groin parameters on amount of accretion. Indian J Mar Sci 36(3):173–182 7. Badici P, Kamphuis JW, Hamilton DG (1994) Physical experiments on the effect of groins on shore morphology. In: Proceedings of the 24th coastal engineering conference, pp 1782–1796 8. Bakker WT (1968) Mathematical theory about sand waves and its application on the Dutch Wadden Isle of Vlieland. Shore Beach 36(2):4–14 9. Komar PD (1998) Beach processes and sedimentation. Prentice Hall Inc, Upper Saddle River, New Jersey, 544p 10. Cuadrado DG, Gomez EA, Ginsberg SS (2005) Tidal and longshore sediment transport associated to a coastal structure. Estuar Coast Shelf Sci 62:291–300 11. Mack C (2002) Pawleys Island profile change analysis using beach morphology analysis package. In: Ewing L, Wallendorf L (eds) Proceeding of the solutions to coastal disasters ’02 conference. American Society of Civil Engineers, San Diego, California, pp 623–634

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12. Thieler ER, Himmelstoss EA, Zichichi JL, Ergul A (2009) Digital shoreline analysis system (DSAS) version 4.0-an ArcGIS extension for calculating shoreline change: U.S. geological survey open-file report 2008-1278 13. Mujabar PS, Chandrasekhar N (2011). A shoreline change analysis along the coast between Kanyakumari and Tuticorin, India, using digital shoreline analysis system. Geo-spatial Inf Sci 14(4):282–293 14. Fenster MS, Dolan R, Elder J (1993) A new method for predicting shoreline positions from historical data. J Coast Res 9(1):147–171 15. Dolan R, Fenster MS, Holme SJ (1991) Temporal analysis of shoreline recession and accretion. J Coast Res 7(3):723–744 16. Saxena S, Purvaja R, Mary Divya Suganya G, Ramesh R (2012) Coastal hazard mapping in the Cuddalore region, South India. Nat Hazards. https://doi.org/10.1007/s11069-012-0362-7

Experimental Studies on Hydrodynamic Performance of an Artificial Reef Lokesha, S. A. Sannasiraj and V. Sundar

Abstract A two-dimensional experimental study has been conducted on nonperforated and perforated artificial trapezoidal reefs in order to plan and prescribe suitable coastal protection measures against erosion. Multiple units of reef have been tested in order to reduce the wave transmission. However, the results for a single reef are presented in this paper. It mainly focuses on the influence of perforations and water depth on the artificial reef as a possible wave attenuator. The percentage of reduction in wave transmission is quantified. The results on the variations of transmission, reflection and loss coefficients along with the dynamic pressure exerted on the reef due to regular waves as a function of relative reef width for its different relative depths of submergence are reported in this paper. Keywords Artificial reef · Wave attenuator · Relative water depth Wave transmission · Wave energy

1 Introduction The reasons behind the coastal and island erosion are due to natural phenomena such as waves, tides, currents and also the sediment shortfall due to man-made activities such as coral and sand mining or erection of coastal-related structures. Over the years, the coastal erosion has been either short or long-term problem across the coastlines around the globe which hampers the livelihood of the community and activities. There has been a continuous effort from engineers and scientists to counter against the coastal erosion through hard or soft measures. The structures such as seawalls, Lokesha (B) · S. A. Sannasiraj · V. Sundar Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai 600036, India e-mail: [email protected] S. A. Sannasiraj e-mail: [email protected] V. Sundar e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_41

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breakwaters, groins and gabions are the hard methods to combat coastal erosion. In the recent times, the management of coastal zone has been diverted to the application of soft measure which is believed to serve as an eco-friendly solution. The innovation of new alternative materials and concept of shore protection has become inevitable due to non-availability of natural rock in certain locations and also the cost involved in the transportation of natural rock at the site is expensive. At present, materials such as geo-bags, geo-containers, reef balls and prefabricated units are effectively being adopted in coastal and island protection because of easy placement, less cost and eco-friendly solution.

1.1 Artificial Reef as Submerged Breakwater Submerged breakwaters are popularly used as a coastal defence structure allowing sufficient wave transmission. The submerged breakwaters are used in situations such as in reducing the wave oscillations inside the basin and deposition of silt at the entrance channel of the harbour, in providing a home for marine habitat and enhance the marine growth. The submerged breakwater admits the flow of water column from offshore to onshore and vice versa be the very important aspect of controlling the beach contamination. The various parameters that influence the amount of coastal protection are the dimensions of the breakwater, its position and placement with respect to shore, hydrodynamic behaviour of the structure, wave conditions including its angle of approach [1]. The submerged breakwaters can be effectively used as wave attenuators [2]. The breadth, depth of submergence and shape of submerged breakwater has a greater impact on the transmission and reflection coefficient which in turn decides the capability of the submerged breakwater structure in adopting against coastal protection. The physical model studies on the hemicylindrical, rectangular and flexible type of breakwater were conducted to assess the hydrodynamic properties such as wave transmission and reflection [3]. The results revealed that rectangular model dissipates more energy compared to a hemicylindrical model for the rigid type of breakwaters and vice versa for a flexible type of breakwater. The experiments on culvert pipe blocks with constrictive sections were executed and compared with conventional blocks and permeable rubble mound breakwaters [4]. The wave energy dissipation for culvert pipe blocks with constrictive sections was more compared to conventional blocks and whereas, when compared with permeable rubble mound breakwater was found be to same. The physical model studies on submerged rectangular stepped breakwater were performed to evaluate the hydrodynamic characteristics of submerged breakwater [5]. The dissipation of wave energy is found to be a maximum of 71.25% for three rectangular vertical submerged breakwaters and a minimum of 11.26% for a single rectangular vertical submerged breakwater. A series of experiments were conducted to examine the dynamic performance of submerged semicircular breakwater [6]. The wave transmission, reflection, pressures, horizontal and vertical forces on submerged semicircular breakwater have been evaluated. The

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model is subjected to regular waves with perforation ranging 7–17% for the cases seaside perforated and fully perforated. It was concluded that the optimum percentage of perforation was found to be 11% and also the recommended relative depth of submergence of breakwater was 1.2. Artificial reefs are man-made obstacles which are in submerged condition and placed on the seabed. These reefs act as a barrier and offer friction resulting in the dissipation of wave energy. The shape, size and materials used for artificial reefs are the key parameters in deciding the amount of attenuation of wave energy. The uses of artificial reef strengthen the diving, fishing and surfing activities. The reef ball units primarily used to enhance the marine growth and also to act as submerged breakwater throughout the southern Caribbean coast of the Dominican Republic [7]. The reef ball dimensions of 1.3 m height and diameter of 1.5 and 1.6 m were position at the nearshore region to balance the beach equilibrium, enhance the marine growth and tourism. Literature review reveals that there is still a search for new types of reefs that could effectively reduce transmission through dissipation of incident energy. One such structure is proposed herein, a detailed investigation on the hydrodynamic characteristics of which is carried out in the laboratory. The tests have been carried out for non-perforated and perforated trapezoidal submerged reef.

2 Experimental Setup A model scale of 1:5 is adopted to conduct a series of two-dimensional experimental studies on artificial reef unit in a shallow water wave flume of dimensions with length of 72.5 m, width of 2 m and depth of 2.7 m, in the Ocean Engineering Department, Indian Institute of Technology Madras, Chennai, India. The experiments have been conducted with a perforated and non-perforated reef of height (hr ) 0.4 m in three different water depths (hw ) of 0.50, 0.55 and 0.60 m. The dimensions of the artificial reef are chosen as top breadth, B  0.2, bottom breadth, B  0.5 m, a longitudinal length, L  1.95 m, height, hr  0.4 m and porosity of 11% based on the recommendations given by [6] on submerged breakwaters. The non-perforated and perforated models with pressure transducers fixed on it for registering the pressure time histories are shown in Fig. 1a. The installation of the perforated reef model is projected in Fig. 1b. The artificial reef model has been rigidly fixed over a false bottom with a slope of 1:30, and the gap between the model and wave paddle is kept as 36.65 m. The composite wave elevations registered by 3 number wave probes, with the nearest one placed at a distance of 7.5 m in front of the model. The distance among the wave probes was varied as a function of wave period as suggested by [8]. A wave gauge at a distance of 8.5 m behind the model registered the wave transmission past the structure. The sectional and plan view of the experimental facility and model setup is shown in Fig. 2. The range of wave heights and wave periods employed on the model is 0.05 m to 0.3 m and 1.6 s to 5.8 s, respectively.

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(a)

Impermeable Reef

Permeable Reef

Pressure sensors

(b)

Placement of model

Fixing the model

Fig. 1 a Non-perforated and perforated reef model with locations of pressure sensors. b Installation of perforated reef model and fixing the model in the flume

3 Results and Discussion 3.1 General The important hydrodynamic characteristics governing the wave structure interaction are wave transmission coefficient (Kt ), wave reflection coefficient (Kr ) and energy loss coefficient (Kl ). The performance of the artificial reef is measured by these hydrodynamic characteristics. The wave transmission coefficient is defined as the ratio of wave height measured on the lee side of model (Ht ) to the wave height measured on the seaside of the model (Hi ). The reflection coefficient is calculated using the two-point method [8]. As per the law of conservation of energy, the incident energy is the summation of transmitted energy, reflected energy and energy loss (K t2 + K r2 + K l2  1).

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Fig. 2 Experimental facility and model setup for the study

The loss coefficient is arrived as Kl 

 1 − (K t2 + K r2 )

The tests were carried out for the artificial reef with relative crest width (B/L) for three different hw of 0.6, 0.55 and 0.5 m such that hw /hr  1.5, 1.375 and 1.25.

3.2 Transmission Coefficient, Reflection Coefficient, Energy Loss Coefficient and Dimensionless Pressure (Pmax /Hi ) for Non-perforated Artificial Reef The variations of Kt with B/L for three hw /hr ratios are shown in Fig. 3a. It is observed that for all the hw /hr , the Kt decreases up to about 0.5 within the range of B/L from 0.014 to 0.04. Further, the increase in relative crest width (B/L) has a very marginal decrease in Kt . It is also noticed that the Kt decreases with a decrease in hw /hr . The range of Kt for hw /hr , of 1.5, 1.375 and 1.25 is 0.67–0.97, 0.58–0.95 and 0.51–0.92, respectively. The variations of Kr with B/L are depicted in Fig. 3b. It is noticed that for all the hw /hr , ratio considered, the Kr gradually increases up to about 0.5 with an increase in B/L. The range of Kr for hw /hr of 1.5, 1.375 and 1.25 is 0.04–0.40, 0.12–0.47 and 0.16–0.58, respectively.

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(a)

1

(b)

0.8

0.6

0.6

hw / hr = 1.5 hw / hr = 1.375 hw / hr = 1.25

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Kr

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0.4 hw / hr = 1.5 hw / hr = 1.375 hw / hr = 1.25

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0.9

0.8

0

0

0.7 0.6 0.5 0.4

0

0.02

0.04 B/L

0.06

0.08

Fig. 3 Effect of hw /hr ratio on a transmission coefficient (Kt ), b reflection coefficient (Kr ), c energy loss coefficient (Kl ) and d dimensionless pressure (Pmax /Hi ) for non-perforated artificial reef

The variations of Kl with B/L are shown in Fig. 3c. It is observed that for all the hw /hr , the Kl increases with an increase for B/L from 0.014 to 0.04. Further, an increase in B/L is found to exhibit just a marginal increase in Kl . It is also noticed that the Kl increases with a decrease in hw /hr ratio. The range of Kl for hw /hr of 1.5, 1.375 and 1.25 is 0.2–0.61, 0.27–0.68 and 0.33–0.70, respectively. The variations of Pmax /Hi against B/L for all the z/hw are found to show a similar trend and found to decrease with an increase in B/L as longer waves, i.e. lesser B/L exert higher pressures. Further, Pmax /Hi is found to decrease with an increase in the absolute value of z/hw . As the pressure sensor being a constant, it is the effect of the water depth or the free surface that is brought out in the above variation. The range of Pmax /Hi for z/hw of −0.583, −0.545 and −0.5 is 0.55–0.85, 0.56–0.9 and 0.6–0.95, respectively.

Experimental Studies on Hydrodynamic Performance … 1

(b) 1

0.8

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0.4 hw / hr = 1.5 hw / hr = 1.375 hw / hr = 1.25

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0

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z/hw = -0.583 z/hw = -0.545 z/hw = -0.500

0.8 Pmax/Hi

Kl

hw / hr = 1.5 hw / hr = 1.375 hw / hr = 1.25

Kr

(a)

555

0.7 0.6 0.5 0.4

0

0.02

0.04 B/L

0.06

0.08

Fig. 4 Effect of hw /hr ratio on a transmission coefficient (Kt ), b reflection coefficient (Kr ), c energy loss coefficient (Kl ) and d dimensionless pressure (Pmax /Hi ) for perforated artificial reef

3.3 Transmission Coefficient, Reflection Coefficient, Energy Loss Coefficient and Dimensionless Pressure (Pmax /Hi ) for Perforated Artificial Reef The variations of Kt , Kr and Kl for the perforated artificial reef with B/L for three different ratios of hw /hr projected in Fig. 4a–c are found to exhibit a variation similar to that observed for the non-perforated reef as discussed earlier. The range of Kt for hw /hr of 1.5, 1.375 and 1.25 is 0.61–0.95, 0.51–0.92 and 0.43–0.85, respectively. The range of Kr for hw /hr 1.5, 1.375 and 1.25 is 0.03–0.32, 0.04–0.38 and 0.08–0.49, respectively. The range of Kl for hw /hr ratio 1.5, 1.375 and 1.25 is 0.3–0.71, 0.38–0.76 and 0.51–0.75, respectively. The variations of Pmax /Hi with B/L for all the z/hw are found to be similar as observed for the non-perforated reef model as discussed earlier. The range of Pmax /Hi for z/hw of −0.583, −0.545 and −0.5 is 0.45–0.8, 0.55–0.85 and 0.56–0.92, respectively.

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3.4 Influence of Perforations on Transmission Coefficient, Reflection Coefficient, Energy Loss Coefficient and Dimensionless Pressure (Pmax/Hi) The variations of Kt , Kr and Kl for non-perforated and perforated artificial reef models with B/L for the different hw /hr are superposed in Fig. 5. From the comparison of the results obtained for both non-perforated and perforated artificial reef, the percentage reduction in average wave transmission coefficient for hw /hr ratio 1.5, 1.375 and 1.25 is found to be 3.5%, 3.4% and 4.5%, respectively. The percentage reduction in average reflection coefficient for hw /hr ratio 1.5, 1.375 and 1.25 is found to be 15%, 25% and 19%, respectively. The percentage of increase in average energy loss coefficient for hw /hr ratio 1.5, 1.375 and 1.25 is found to be 14%, 10% and 13%, respectively. The variations of dimensionless pressure, Pmax/ Hi , for non-perforated and perforated artificial reef models with B/L for the pressure port location with different relative depth of submergence of port, z/hw , are superposed in Fig. 5d. The variations in the pressures shown above are obtained from the pressure gauge placed on the front facing of the reef located at the centre. The results indicate that the perforation of 11% of the surface area is found to decrease the pressures marginally due to a decrease in the reflection of the incident waves. Comparing the results of the non-perforated and perforated reef, the percentage of reduction in average Pmax /Hi for z/hw ratio −0.583, −0.545 and −0.5 are found to be 7.2%, 8.7% and 5.8%, respectively.

4 Conclusions A submerged non-perforated artificial reef model and with perforations 11% of surface area are tested in a wave flume subjected to regular waves of wave height and wave period ranging from 0.05 m to 0.3 m of 1.6 s to 5.8 s, respectively. The tests covered wave steepness of range 0.003–0.097. The relative crest width of the reef varied between from 0.014 to 0.065. The hydrodynamic performance of an artificial reef is evaluated by estimating the wave transmission coefficient (Kt ), reflection coefficient (Kr ), energy loss coefficient (Kl ) and dimensionless pressure (Pmax/ Hi ). The following conclusions are drawn from the study: • For both the non-perforated and perforated artificial reef, the Kt decreases with a decrease in the hw /hr of the reef, whereas the Kr and Kl are found to increase. • The percentage reduction in average Kt and Kr for perforated artificial reef compared with non-perforated artificial reef with hw /hr  1.5 is 3.5% and 15%, and that with hw /hr  1.375 is 3.4% and 25% and that with hw /hr  1.25 is 4.5% and 19%, respectively. • The percentage increase in average Kl for perforated artificial reef when compared with non-perforated artificial reef with hw /hr ratios of 1.5, 1.375 and 1.25 is found to be 14%, 10% and 13%, respectively.

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(a)

(b)

(c)

(d)

Fig. 5 Effect of perforations on a transmission coefficient (Kt ), b reflection coefficient (Kr ), c energy loss coefficient (Kl ) and d dimensionless pressure (Pmax /Hi )

• It is evident that the percentage reduction in average Kt , Kr and percentage increase in average Kl are minimal when the non-perforated reef is replaced by the perforated reef. But the replaced perforated artificial reef serves as an obstruction in

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dissipating the incident wave energy and additionally provides a shelter for marine habitats in order to enhance the marine growth. • The effect of percentage of perforations of 11% on the reduction in pressures exerted on the reef is marginal. This means that the reef will be stable as perforated which is likely to accelerate refuge for marine species and for mariculture of suspended mussels in unsheltered areas of high primary productivity.

References 1. Pilarczyk KW (2003) Design of low-crested (submerged) structures: an overview, 6th COPEDEC. In: International conference on coastal and port engineering in development countries, Sri Lanka 2. Dattari J, Raman H, Shankar NJ (1979) Performance characteristics of submerged breakwaters. In: 16 international conference on coastal engineering, American Society of Civil Engineers, New York, pp 2152–2171 3. Dimitrios GS, Muhammad RH, Demetri PT (2003) Performance of hemi-cylindrical and rectangular submerged breakwater. Ocean Eng 30:813–828 4. Lai J-W, Kuo C-T, Hsu T-W (2008) Physical model test on wave transmission to culvert pipes block with constrictive sections. In: Taiwan-polish joint seminar on coastal protection, pp A15–A24 5. Mohamed ESY (2014) Effect of submerged rectangular stepped breakwater for the defence of the shoreline. Int J Civil Eng Technol 5:106–118 6. Dhinakaran G, Sundar V, Sundaravadivelu R, Kai UG (2011) Performance of perforated submerged semicircular breakwaters due to non-breaking waves. J Eng Maritime Environ Proc IMechE, Part M 226(1):36–50 7. Harris LE (2009) Artificial reefs for ecosystem restoration and coastal erosion protection with aquaculture and recreational amenities 8. Goda Y, Suzuki Y (1976) Estimation of incident and reflected waves in random wave experiments. In: Proceedings 15th international conference on coastal engineering, vol 1. ASCE, New York, pp 828–845

Prediction of Wave Transmission over an Outer Submerged Reef of Tandem Breakwater Using RBF-Based Support Vector Regression Technique Geetha Kuntoji , Subba Rao and Manu

Abstract The development of a mathematical model to determine transmitted wave height over a submerged reef of the tandem breakwater is complex. Therefore, it is necessary for researchers to adopt the physical model study to determine the parameters that influence the performance of breakwaters quantitatively. Physical modelling is laborious, expensive and lengthy in the procedure which makes it inconvenient for immediate needs. From the history, the development of the soft computing model shows that the soft computing techniques can be applied successfully to the prediction of the wave characteristics by making use of experimental data available. Similarly, attempt is made to predict the wave transmission over a submerged reef of tandem breakwater based on the data of Subba Rao developed in 2004 on a tandem breakwater in a 2D wave flume available at NITK Surathkal India using Support Vector Regression (SVR) model with different kernel functions. The non-dimensional input parameters used for the development of the models are five in number. Those inputs are incident wave steepness (Hi/gT2 ), relative reef crest width (B/Lo ), relative reef submergence (F/Hi ), relative reef crest height (h/d), depth parameter (d/gT2 ) and the output as (Ht /Htmax ). The 202 data points (70%) are used for training and the 86 data points (30%) for testing out of 288 total data points. The statistical parameters are computed using the predicted and observed data points after training and testing the SVR models. The RBF kernel gives good correlation to the prediction of transmitted wave heights during testing with RMSE as 0.09 and MAE as 0.07. Therefore, the SVR with RBF kernel function can be adopted as an alternative technique to predict the wave characteristics such as wave transmission over a submerged reef of the tandem breakwater.

G. Kuntoji (B) · S. Rao · Manu National Institute of Technology Karnataka, Surathkal, Mangalore 575025, Karnataka, India e-mail: [email protected] S. Rao e-mail: [email protected] Manu e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_42

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Keywords Submerged reef · Tandem breakwater Support vector regression (SVR) · Wave transmission (Ht /Htmax )

1 Introduction India has got a fast-growing economy which has been possible due to the improvements in connectivity from coast to the interior parts of the country. These have brought too much stress on the coastal environment such as beach erosion. Therefore, a need for protective structures along the coast arises. The coastal structures built to protect the harbour and shores such as seawalls, groins, offshore breakwaters and artificial nourishments are required to withstand the destructive forces of the sea waves [6]. These structures have been tried to overcome the problem of erosion and also for maintaining tranquillity condition inside port and harbour and even for loading cargo and passengers. Some of them have been effective while some others have failed to accomplish the activity assigned to them. The failure might be because of opposite position and outline or wrong decision of protective measures. The reason for the erosion is because of the grouping of wave intensity at a particular place. Subsequently, there is a need to dissipate the wave intensity before it reaches the coast. Breakwaters are one of the protective measures to reduce the wave intensity. Breakwaters are the most commonly used protective structure which is used to reduce the high concentration of waves to protect the harbour, and also used as a facility for loading passengers and cargo. Tandem breakwater is the one in which a submerged reef is placed in front of the main breakwater so that the effect of waves on the main protective structure will be reduced significantly, which in turn result in the economic design of breakwater as shown in Fig. 1 [2]. The present paper predicts transmission coefficients associated with the submerged reef. Final layout and cross section of the breakwater selected after conducting physical model studies. Soft computing techniques can be used to model various problems of real case scenario where mathematical modelling is difficult. Support Vector Regression (SVR) is a machine learning tool where algorithms can be formulated for data analysis, to recognize patterns, to classify data, regression analysis, etc. Present paper deals with the application of SVR in the prediction of wave transmission associated with submerged reef using data from [5]. In the actual field conditions, the submerged reef interferes with the incoming wave field to: • • • • • • •

create partial obstruction, change the water particle velocity and motion, reflect some of the wave energy, offer friction and resistance to wave motion, change wave configuration, induce wave breaking and cause turbulence, result in wave energy dissipation and energy loss, and

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Fig. 1 Evolution of tandem breakwater (Source [2])

• transmit smaller waves with reduced energy. Thus, the introduction of the submerged reef in front of emerged main breakwater causes attenuation of incoming waves resulting in some wave energy dissipation before it impinges on the emergent main breakwater. In this way, the submerged reef offers protection to inner breakwater from extreme waves. Therefore, the wave impact on the emerged main breakwater can be reduced using lighter armour units by the introduction of a submerged reef in the front and design it economically. Soft computing is the combination of approaches used to outline the model to solve the real-world problems. So that it can be modelled efficiently; at the same time, these issues are difficult to model, mathematically. Soft computing is an association of techniques that work synergistically and provide various forms of flexible information. These models also show the processing capability for handling ambiguous real-life issues. It aims to exploit the advantages of the technique such as the

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ability to tolerate the imprecision and uncertainty involved in the classical models. It also handles approximate reasoning and partial truth to achieve flexible and low-cost and less laborious solutions. The precepts guide to devise techniques of computation that leads to an acceptable solution at low cost. Soft computing differs from conventional (hard) computing. Soft computing tries to find the solution to problems which are very hard to answer.

2 Support Vector Regression In machine learning, Support Vector Regression (SVR) considered as one of the directed learning models with associated learning algorithms that interpret the data and identify the patterns for classifying the data and conducting the regression analysis. The regression analysis goes stepwise as shown in the following.

2.1 Structure of the SVR Vapnik [1] developed SVR, which is getting acceptance because of its striking features and its better performance. SVR uses Structural Risk Minimization (SRM) principle for the formulation which is better than outdated Empirical Risk Minimization (ERM) principle which conventional neural networks use. SVR, primarily used for classification problems, and then its use were extended to regression problems [4]. For a training set {(xi , yi ), i  1, …, n}. Here xi and yi are ith input training pattern and corresponding target output and have n data sets for training. For non-linear case Support Vector Regression (SVR) has the form: f(x, α)  (w · ϕ(x)) + b

(1)

where w is the weight vector, b is the bias and ϕ(x) is a mapping function to a higher dimensional feature space from input features. The regression problem will be similar to minimizing the regularized risk function [3] 1 L (yi , f(xi , w)) n i=1 n

R (f ) 

(2)

where ⎧ ⎨

  ε, ifyi − f(xi , w) ≤ ε L(yi , f(xi , w))    ⎩ y − f(xi , w) − ε, otherwise i

(3)

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where ε is insensitive loss function; on substitution in Eq. (2), optimization object will be [7], Minimize,  n  n   1 ∗ w · w+C · ξi + ξi (4) 2 i=1 i=1 where ⎧ ⎪ ⎪ ⎨ subject to

⎪ ⎪ ⎩

yi − w · xi − b ≤ ε + ξi∗ w .xi + b − yi ≤ ε + ξi , i  1, . . . , n ξi , ξi∗ ≥ 0

where the constant C > 0 means penalty degree of the sample with error exceeds epsilon; ξi, ξi* are slack variables. By using this optimization, a dual problem can be attained by maximizing the function, maximize, n 

yi (αi∗ − αi∗ ) − ε

i1

n n  1 ∗ (αi∗ − αi∗ ) − (αi − αi )(αi∗ − αi ){ϕ(xi ) · ϕ(x j )} 2 i1 i,j1

(5) where

subject to

⎧ n  ⎪ ⎨ α∗ − αi  0 i i=1

⎪ ⎩ 0 ≤ α∗ , α ≤ C i i

where α*i and αi are Lagrange multiplier and (ϕ(xi ) · ϕ(xj )  K(xi , xj )) is kernel function. By using the above maximization function, the non-linear regression function obtained is n   ∗  ∗ αi − αi K(xi , x) + b f x, α , α 

(6)

i 1

where w · ϕ(x) 

 αi∗ − αi K(xi , x)

(7)

SVs

b −

1  ∗ αi − αi [K(xr , xi ) + K(xs , xi )] 2 SVs

(8)

where xr and xs are Support Vectors (SVs), number of support vectors, 0 ≤ α*i , αi ≤ C.

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There are various kernel functions like linear, polynomial, radial basis function, sigmoid kernel, etc. Here, we have obtained a precise result from the polynomial kernel with a second degree (quadratic kernel). A form of polynomial kernel used here is  K xi , x j  ((γ ∗ x ∗ y) + c)d

(9)

where γ is a kernel function parameter, c is the coefficient of the polynomial when c  0 polynomial is homogenous, and d is the degree of the polynomial.

2.2 Statistical Measures The accuracy of the SVR model is checked with the help of statistical parameters like Root Mean Square Error (RMSE), Nash–Sutcliffe Efficiency (NSE), Mean Absolute Error (MAE), Scatter Index (SI) and Correlation Coefficient (CC). A good model will have minimum RMSE, MAE, SI values and maximum NSE and CC values. Let Opi and Ppi be the observed and predicted values, and Opi and Ppi be the average of observed and predicted values for n number of observations then the above statistical parameters is found as follows. RMSE is calculated using the formula:

N 2 1 RMSE  (Ppi − Opi )2 (10) i0 N NSE is calculated using the formula:

N

(Ppi − Opi )2 NSE  1 − Ni1 2 i1 (Opi − Opi ) SI is calculated using the formula: 

N 2 1 SI 

N

i0 (Ppi

− Opi )2

Opi

CC is calculated using the formula:

N i1 (Ppi − Ppi )(Opi − Opi ) 

CC  

N N 2 2 (P − P ) pi i1 pi i1 (Opi − Opi ) MAE is calculated using the formula:

(11)

(12)

(13)

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 1  Ppi − Opi  n 1 n

MAE =

(14)

3 Experimental Work and Data Initially, experimental data (Fig. 2) collected from Subba Rao and the consistency of the data are checked using the time series plots. The experimental data set 288 are segregated for training and testing based on trial-and-error method, such that all the variations of data are covered in both training and testing data set used for the development of SVR model. Then the SVR model is developed using different kernel functions, and optimal parameters affecting the performance of model are finalized. The efficiency of the SVR model with different kernel functions is checked by comparing the statistical parameters obtained. Then experiments are conducted for the test conditions as shown in Table 1, to measure the transmitted wave heights (Ht/ Htmax ) over a submerged reef of the tandem breakwater. This total combination of the test conditions gave a data length of 288.

Fig. 2 Experimental set-up of tandem breakwater Table 1 Test conditions of experiment Incident wave height

Hi (m)

0.10, 0.12, 0.14, 0.16

Wave period

T (s)

1.5, 2.0, 2.5

D (m)

0.30, 0.35, 0.40

Water depth Spacing X (m)

X1 X  2.5 X4

B  0.10 Reef crest width B (m) B  0.10, 0.20, 0.30, 0.40 B  0.10, 0.20, 0.30

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3.1 Purpose of the Work To predict the transmitted wave heights of a submerged reef of the tandem breakwater, Support Vector Regression (SVR) applied with the suitable kernel function.

3.2 Methodology Adopted Step 1: Step 2: Step 3: Step 4: Step 5:

Data collection, Consistency check of data, Separation of data for training and testing, SVR model generation and Evaluation and comparison of statistical parameters.

3.3 Present Study To predict the transmitted wave heights of a submerged reef of the tandem breakwater SVR technique is applied. The data for modelling are collected from the experiments conducted on the physical model of tandem breakwater by Subba Rao in 2004 at Marine Structures wave flume lab in Applied Mechanics and Hydraulics Department, NITK Surathkal. There are five input parameters in the length of 288 number of data set. Those data points are sorted randomly based on trial-and-error technique such that 70% for training and 30% for testing. After normalization or standardization of the data, time series plots used for checking the consistency of data. The input consists of incident wave steepness (Hi /gT2 ), relative reef crest width (B/Lo ), relative reef submergence (F/Hi ), relative reef crest height (h/d), depth parameter (d/gT2 ) and the output as (Ht /Htmax ). The statistical parameters evaluate the accuracy of the SVR models using measured values vs. predicted values.

4 Results and Discussions Incident wave steepness (Hi /gT2 ), relative reef crest width (B/Lo ), relative reef submergence (F/Hi ), relative reef crest height (h/d) and depth parameter (d/gT2 ) inputs influence the output Ht /Htmax . The training is achieved using 202 data points (70%) and testing with 86 data points (30%).

Prediction of Wave Transmission over an Outer Submerged Reef … Table 2 Optimal parameters for SVR models for predicting Ht /Htmax Kernel type Linear Polynomial RBF

567

Sigmoid

C γ

1426 0.00104

214 0.00015

372 0.00004

412 0.00123

ε d nsv

– – 86

– 3 86

3 – 86

4 – 86

Table 3 Statistical parameters for SVR models for predicting Ht /Htmax Statistical Different kernel types measure Linear Polynomial RBF RMSE MAE NSE CC SI

Sigmoid

Train

Test

Train

Test

Train

Test

Train

Test

0.1089 0.0834 0.7280 0.8568 0.2947

0.1082 0.0783 0.6673 0.8181 0.2912

0.0923 0.0719 0.8181 0.8915 0.2485

0.0891 0.0668 0.7577 0.8709 0.2410

0.0920 0.0768 0.8059 0.9027 0.2489

0.0828 0.0686 0.8050 0.9012 0.2229

0.1279 0.0966 0.6247 0.8540 0.3462

0.1231 0.0893 0.5694 0.8055 0.3313

The statistical parameters are computed using the predicted and observed values after training and testing of SVR models as shown in Table 3. The number of support vectors (nsv) for all the SVR models shown in Table 2. The SVR model with RBF kernel function gives high CC (Training CC  0.9027, Testing CC  0.9012) when compared to all other kernel function. The better selection of SVR and kernel parameters decides the performance of these models. In case of RBF kernel, the optimal width (γ) obtained by the manual search is found to be 3. The optimal value of d (degree) in case of polynomial kernel function obtained by the manual search is 3. The number of support vectors to predict the transmitted wave heights of a submerged reef of the tandem breakwater is same for all the kernel functions. K-fold cross-validation search finds the optimal values of C, ε, γ. Table 3 shows the statistical parameters that are found to compare the models using different kernel functions. It is observed that the SVR model with RBF kernel function shows better generalization performance with CC  0.9012, RMSE  0.0828, SI  0.2229, NSE  0.8050, MAE  0.0686 for testing when compared to all other kernel functions. The scatter diagram shows CC of SVR models for testing data as shown in Fig. 3. The comparison of predicted Ht /Htmax with measured values by SVR models with various kernel functions indicates that SVR model with RBF Kernel function is the best model using RMSE, NSE and MAE (Fig. 4).

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Fig. 3 Scatter plots of SVR for different kernel functions to predict Ht /Htmax

5 Summary From all the above results, it can be summarized as follows: • The RBF kernel function gives the best CC as 0.9027 and 0.9012 for the prediction of transmitted wave height for training and testing, respectively. • The RBF kernel function give the minimum values for the statistical parameters like RMSE  0.0920 and 0.0828, MAE  0.0768 and 0.0686, NSE  0.8059 and 0.8050 and SI  0.2489 and 0.2229 for the prediction of transmitted wave height in training and testing, respectively.

6 Conclusions The development of a mathematical model to determine the transmitted wave height of tandem breakwater is complicated and time-consuming. Therefore, it is necessary for researchers to adopt the physical model study to determine the parameters that

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Fig. 4 RMSE, NSE and MAE values for training and testing in prediction of Ht /Htmax using different kernel functions, respectively

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influence the performance of breakwaters quantitatively. Physical modelling is a laborious process and expensive, which makes it inconvenient for immediate needs. Therefore, the development of the support vector regression models found important. The results of this study are matched and agree well with that of the field. Based on the results of the present investigation, the conclusions are as follows: • The RBF kernel gives 90% correlation for the prediction of transmitted wave height in testing with RMSE  0.09, NSE  80%, MAE  0.07 and SI  0.23. • The RBF kernel gives the best results for the prediction of transmitted wave height with five influencing input parameters. • The SVR model with the RBF kernel function is the efficient and accurate model for the present problem compared to all other kernel functions. Acknowledgements The authors are thankful to the Head of the Department of Applied Mechanics and Hydraulics and Director, National Institute of Technology Karnataka, Surathkal, Mangaluru, India for their constant support and encouragement in the preparation of this paper.

References 1. Cortes C, Vapnik (1995) V Support vector networks. Mach Learn 20:273–297 2. Cox JC, Clark (1992) design development of a tandem breakwater system for Hammond Indiana. In: Proceedings of conference on coastal structures and breakwaters, ICE, Thomas Telford Publishers London, pp 111–121 3. Lee JJ, Kim DK, Chang SK, Lee JH (2007) Application of support vector regression for the prediction of concrete strength. Comput Concrete 4(4):299–316 4. Stitson MO, Weston JAE, Gammerman A, Vork V, Vapnik V (1996) Theory of support vector machines. Technical Report, Department of Computer Science, Royal Holloway College, University of London, CSD-TR-96-17 5. Subba R, Shirlal KG (2004) Experimental investigation on the stability of Tandem breakwater, R&D project, sponsored by MHRD GoI, NITK, Surathkal, India 6. Shirlal KG, Subba R, Venkata G, Manu (2006) Stability of breakwater defensed by a seaward submerged reef. J Ocean Eng 33:829–846 7. Shirlal KG, Subba R (2003) Laboratory studies on the stability of tandem breakwater. ISH J Hydraul Eng 9(1):36–45

Assisting Pumps for Dredging Mridul K. Sarkar and Sritama Sarkar

Abstract Widely varying particle sizes commonly encountered in dredging situations have a broad range of settling velocities. To reduce suction side losses of an on-board centrifugal dredge pump, normally the suction side velocities are kept comparatively lower. This velocity may sometimes reach the threshold of settling velocity, inducing heterogeneous flow within the pipe that would cause increased abrasion within the inner surface of the suction tube and triggers blockage in the suction side of the centrifugal dredge pump. Two types of pumping devices were developed and used in actual dredging. The results were found satisfactory. To reduce abrasion an energy input in the form of high-velocity water jets to the boundary layer was done. The jets are placed spirally along the inner surface of the pump tube. This spiral pumping device placed before the centrifugal dredge pump also gives a pre-rotation of the mixture assisting the dredge pump thus increasing overall pumping efficiency of the pumping system. Another method to avoid blockage in the suction side and consequently within the delivery pipeline is to place a peripheral-type educator pump in series with the centrifugal dredge pump between the suction mouth of the dredging system and the centrifugal dredge pump. The driving powers of both the systems are high-pressure water. This paper describes briefly these two assisting pumping systems. Keywords Dredge pump · Annular pump · Solid handling · Spiral vortex pump

M. K. Sarkar (B) Excavation & Equipment Manufacturing (P) Ltd., Kolkata, India e-mail: [email protected] M. K. Sarkar Australian Maritime College, University of Tasmania, Hobart, Australia S. Sarkar Subsea Engineering, London Offshore Consultants Ltd., London, UK e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_43

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1 Introduction Three problems are very common in the suction side of a centrifugal dredging pump, namely, (i) abrasion, (ii) blockage and (iii) cavitation. Abrasion and blockage of the pipeline are directly dependent on the mixture velocity and shock wave within the pipe, as well as on the particle size of the solid to be pumped. Cavitation, on the other hand, is dependent on the pressure difference between the suction vacuum and delivery pressure, which indirectly depends on mixture velocity and particle size. • With deeper dredging depths, the situations become more critical and need attention. Submersible centrifugal dredging pumps are installed on dredge ladder to address the problem. This pump in series before the dredge pump on-board reduces the suction side pipeline length of the on-board dredge pump and adds extra energy to the mixture flow. The energy input by the submersible dredge pump is similar to the longitudinal flow characteristics of the on-board dredge pump, but does not affect the cross-sectional velocity profile of the suction pipeline. Furthermore, the drive of the centrifugal underwater dredge pump is an extra listing to the maintenance schedule. • Two locations of the suction pipeline cross section need extra energy to reduce heterogeneous flow inducing higher abrasion rates and pipe blockage. The two locations are the centre and the boundary layer near the inner surface of the pipeline. Two types of high-pressure water-driven jet pumps were developed and tested in inland micro-dredging. An encircled jetting unit along with the types of these pumps was also tested at the site. The abrasion and the pipeline blockage mechanics with relations to mixture flow regimes are discussed in this paper. The constructions of the two types of pumps are briefly described afterwards. Performances of the pumps are stated in a few words. Future applications of the pumps are also depicted in the conclusion.

2 Problems 2.1 Dredging Situations In a hydraulic dredging system, suction side of the pump is the most vulnerable portion. Solid production is initially dominated by the intake of the solid–liquid mixture as well as transport of the slurry in the suction tube. The suction tube is unified with the ladder and moves in vertical as well as horizontal directions with either vertical or horizontal or inclined configuration. During dredging operations, the suction tube along with the ladder moves downwards normally to a maximum limit of 45° from the horizontal. In case of spud or ‘Christmas tree’ operations, the swing in a horizontal plane is to an extent of 40° from the central position. In actual dredging situations, the material to be dredged, the particle size and/or shape

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and volumetric concentration of the mixture change. Dredging may be done from the water level to a maximum water depth, controlled by the suction tube/ladder configurations.

2.2 Flow Characteristics Flow in the suction side of dredge pumps could be horizontal, inclined or vertical depending on the suction tube configuration. In the two-phase flow occurring in the suction tube, the flow pattern could be either homogeneous or heterogeneous. Depending on the particle shape, size and mixture velocity, heterogeneous flow can be fully stratified, partially stratified, or fully suspended. If the intensity of turbulence is not sufficient to suspend any solid particle, then it is fully stratified with either a stationary or moving bed. With all solid particles suspended uniformly across the pipe cross section, a pseudo-homogeneous flow pattern occurs. Partially stratified flow is the most common flow pattern in dredging having a concentration gradient across a pipeline cross section. Depending on the suction tube configuration, the concentration gradient across the tube cross section also varies. With bigger particle sizes and appropriate flow velocities, sometimes ‘bouncing ball’ type of flow is also observed (Fig. 1). With the changing operating conditions as depicted above, the flow conditions within the suction sub-system change with some detrimental effects. Ideal flow conditions for a pumping mixture is pseudo-homogeneous flow, which rarely happens. With reducing velocities within the suction tube, the flow pattern becomes heterogeneous. When the higher density mixture comes lower, it is a layered heterogeneous flow. With lesser velocity, the higher density mixture forms a solid bed which moves at a lesser velocity than the mixture and is called a sliding bed heterogeneous flow. There is normally a difference between the lower layer higher density moving bed and the upper layer lower velocity, known as the ‘slip factor’. If the mixture velocity falls further, then the flow could be stalled causing blockage of the suction tube. Depending on the variation of operating conditions and mixture density, the velocity vectors along a cross section of the pipe also vary with time. There would also be changes of velocity along the longitudinal direction of the suction tube. A further effect from the shock waves depending on the velocity variations along longitudinal directions due to density variation of mixture with time, partial or complete blockage of the pipeline can occur with complete stoppage of pumping. All these factors contribute to change the velocity vectors of the flowing mixture, both in transverse and longitudinal directions within the pipeline. Consequently, motions of the solid particles within the pipe accelerate abrasion. With partial blockage, the suction vacuum would rise and the entrapped gases or air bubbles would explode on the discharge side of the pump causing cavitation effect. In extreme cases, there would be a sudden failure of the dredge pump. With the phenomena in the suction side of the dredge pump described above, the delivery side of the pumping system is also affected. With the heterogeneous flow,

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Fig. 1 Flow pattern of two-phase flow in dredging pipeline. Vm , mixture velocity, Cvi , spatial concentration, Cvd , delivered concentration

the solid particles come in contact with the inner surface of the delivery pipeline causing higher abrasion rates and may cause a total blockage of the delivery pipeline in the worst possible situation. Obviously, the effect would be lower efficiency, higher maintenance cost and more idle time. The above problems are related to lower velocities than the desired velocity which should be above the settling velocity of the solid particles met in a specific hydraulic dredging condition. The velocities within a pipe cross section are not constant but vary from zero at the pipe inner surface in a parabolic form towards the centre of the pipe. Hence, the boundary layer near the pipe inner surface is also critical for the damaging effects. NPSH available in a hydraulic dredging system is normally fixed depending on the design and operating range. The suction side of a centrifugal dredge pump has restricted available NPSH, which limits the flow and depth of dredging.

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3 Solutions 3.1 Submersible Ladder Pump Submersible centrifugal dredge pumps are installed on the ladder boom of a dredger to overcome these limitations. The submersible ladder and on-board dredge pumps have normally similar characteristics, thus not influencing greatly the flow pattern within the suction tube. The volumetric concentration of mixture in the suction tube also remains the same.

3.2 Assisting Pumps Centrifugal dredge pump induces a parabolic velocity distribution in the cross section of the suction tube, with zero velocity near the surface of the pipe to maximum at the centre. Solid particles tend to settle downwards towards the pipe inner surface when the flow velocity falls below the threshold and suction tube configuration is either horizontal or inclined. An extra velocity near the centre of the pipe or near the boundary layer would stimulate the solid particles to suspend and move towards the centrifugal dredge pump. The input of extra energy with a centrally placed highpressure jet was tried beforehand. The inherent problem is the resistance and drag effects caused by the partly exposed jet pipe centrally within the dredge suction tube. To reduce the drag, the suction mouth may be placed perpendicularly with the jet pipe, but it increases the loss due to the bend. This drawback was overcome with the placement of multiple jet nozzles placed at the circumference of the suction pipe. The nozzles are inclined at equal angles with the centre line of the suction pipe, so that all the high-pressure jets meet at the centre of the suction pipe to form a single high-pressure jet at the centre of the suction tube. With the momentum transfer, the solid particles near the inner surface of the suction pipe would be lifted up from the enveloping low-velocity mixture flow. A diverging pipeline (diffuser) is sometimes placed after the multiple jet pump or ‘Peripheral Eductor Pump’ (PEP), to transform the velocity head to pressure head. The diverging angle is carefully chosen to avoid flow separation. Water-driven Peripheral Eductor Pump (PEP) can influence the flow patterns by reducing the volumetric concentration and providing more pressure energy by transforming the velocity energy of the driving water jets. Two types of PEP were used in actual dredging work. For dredging in closed chambers, a unified head with jetting system for loosening the soil along with the PEP is connected to the centrifugal dredge pump through a flexible pipeline (Fig. 2). The head is moved within the chamber for feeding the soils to the suction mouth of the head. A modified version is a ‘U’ shaped jetting head for loosening along with the PEP (Fig. 3). In case of normal dredging, the PEP is a part of the ladder placed after the loosening tool (jets/cutter) and the suction bell-mouth. With these submersible units without any moving parts

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Fig. 2 Annular solid handling pump

Fig. 3 Eductor solid handling pump with jet head

and placed in series with the centrifugal dredge pump placed above water level, the depth of dredging can be increased. The Spiral Eductor Pump (SEP) helps the flow transformation by providing more velocity energy to the flow near the pipe inner surface. Placed after the PEP, it provides a pre-rotation to the flow before the suction eye of the centrifugal dredge pump and reduces the volumetric concentration of the mixture, thus reducing abrasion and the risk of blockage. To reduce abrasion in the inner surface of the suction tube, extra energy is imparted near the boundary layer by a number of jets placed in a spiral. A block diagram of all the suction side of a dredging unit is shown in Fig. 4. Testing of a ‘Spiral Eductor Pump (SEP)’ and a picture of the same is shown in Fig. 5. Both the PEP and SEP reduce the possibility of cavitation by contributing a positive head in the suction side.

4 Construction The dredging assisting pump systems (both PEP and SEP) are modular. However if necessary, it can be unified together. A construction detail of the ‘Peripheral Eductor Pump or PEP’ is shown schematically in Fig. 6. Driving nozzles around the suction pipes are placed in the same level and placed at an angle of the axis of the suction

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Fig. 4 Suction side of a dredging unit with PEP and SEP

Fig. 5 Spiral Eductor Pump (SEP)

tube. The tips of the nozzles are flushed with the inner surface of the suction tube. The high-pressure driving water is fed to a surrounding chamber around the suction tube. The nozzles are welded to the chamber. The angles of the nozzles are so placed that the driving water makes a high-velocity central water core within the mixture flow in the suction tube. A ‘Spiral Eductor Pump or SEP’ is placed after ‘Peripheral Eductor Pump or PEP’ in the mixture flow direction. A construction detail of the ‘Spiral Eductor Pump or SEP’ is shown schematically in Fig. 7.

5 Performance The two systems were used in inland micro-dredging applications, and the results were found satisfactory. Compared to the pumping with a centrifugal dredge pump, it was observed that the blockage of suction tube was reduced by almost 80% when the assisting pumps were used in parallel with the centrifugal dredge pump. In both the situations, the tests were done with the same delivery configurations (Fig. 8).

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Fig. 6 Peripheral Eductor Pump (PEP)

Fig. 7 Spiral Eductor Pump (SEP)

Abrasion rates of suction tube were measured by the average pipe thickness measured at different points before and after dredging operations, and observing the (average pipe thickness after dredging/average pipe thickness before dredging). It was found that the abrasion rate was decreased by 12% on an average with the assist-

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No. of Blockage

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Case I: CDP

4

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2

Case III: CDP & SEP

0 Project 1 Project 2 Project 3 Project 4 Case Ref. Fig. 8 Suction pipe blockage reduction

Pipe t_av. Rdctn. (%) with PEP 50 40 30 20

t_av. Rdctn. (%)

10 0 Pipe Pipe Pipe Pipe Pipe Pipe Pipe Pipe Pipe Pipe 1 2 3 4 5 6 7 8 9 10

Fig. 9 Suction pipe abrasion reduction

ing pumps, which were tested after a fixed dredging operational time for both the cases (Fig. 9). Increased depth of dredging to an extent of 240% was done with the artifices over the initial depth of dredging without the assisting pumps. Higher depths were not tried. No data was collected or analysed on the cavitation performance.

6 Conclusion Abrasion, blockage, cavitation in the suction tube and dredging depth limitation due to limited available NPSH are constraints to dredging operations. These are related to the velocity of flow within the suction tube. Submersible centrifugal dredge pump on ladder is a suitable option, but it is complex and involves higher Capex and Opex. Peripheral Eductor Pump (PEP) and Spiral Eductor Pump (PEP) could be a cheaper alternative. These two types of pumps were designed and tested in inland dredging, and the performances were found satisfactory. It could be effectively used in confined spaces.

A Study to Identify Locations Suitable of Deep Sea Port Operations in the State of West Bengal Bal Krishna, B. Chaudhuri and P. K. Bhaskaran

Abstract There is a long pending need for a deep-drafted port in West Bengal which will serve complete East and North East region of India. The port operation in Hooghly estuary starts in Kolkata in the eighteenth century. This is the only riverine port in India which started its operation with an approach channel of around 232 km from the sea (Sand Heads). Thereafter, due to problem of siltation and to accommodate the bigger size of vessels, another Satellite Dock System (Haldia Dock Complex, i.e. HDC) started its operation from 1974 with 9.5 m average draft, whereas the draft available at Kolkata Dock System (KDS) at that time was varying between 7.5 and 8.0 m. Due to adverse morphological transformation, over the decade, at present, the natural depth in and in front of Hooghly estuary varies between 5 and 7 m. So, looking for deep-drafted port in and in front of Hooghly estuary is ruled out. It is required to see the site on East side and West side of Hooghly estuary. Unfortunately, on East and West, the extent of coastline is small. On the East side lies the Sundarban Delta mostly formed by alluvial sediment brought by Hooghly estuary. Subsoil is mostly formed of silty clay unsuitable for port construction. It is also observed that while flood flow enters the estuary with equally distributed over width, the ebb flow moves to East after leaving the estuary. Any attempt to develop a port on East side has to tackle with enormous sediment brought by the estuary. Hence, one has to look towards West for deep-drafted port. Coastline in this stretch is limited. On West side, characteristics of the formation of channels like Eden channel and channel West of Eastern brace, which are wide in deep region and gradually narrows down as they move upstream, indicate that they are flood channels. The advantage of flood channels is that here it is not required to tackle the sediment brought by estuary. They are stable and maintained more or less at same location. Another expectation is that during prehistoric era when reaching of sand to B. Krishna (B) WAPCOS Ltd., Pune, India e-mail: [email protected] B. Chaudhuri Kolkata Port Trust, Kolkata, India P. K. Bhaskaran Department of Ocean Engineering & Naval Architecture IIT, Kharagpur, India © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_44

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Fig. 1 a Hooghly River Stretch within the State of West Bengal. b Index plan of Bhagirathi-Hooghly Estuary

coast through river was not intercepted by dams and movement along coast was not intercepted by port structures and approach channel, West side of Hooghly estuary has intercepted the sand. Outfall of estuary works as sand barrier. There is good chance that subsoil in this area is formed of sand. Existence of number of sand heads for centuries is proof of that. Submerged sands on two sides will give protection from cyclones. Coastal formation dictates that deep-drafted port in this region has to be formed as Island port. Considering all these aspects, the deep flood channel West of eastern brace provides excellent site for deep-drafted Island port. An attempt has been made in this paper to logically reinforce the merits in favour of Island port in reference to other available options, within the jurisdiction of West Bengal. Keywords Sedimentation · Morphological transformation · Tidal range Tidal current · Neap/spring · Cyclonic time · Maintenance dredging Navigational channel · VTMS

1 Introduction India has got coastline of around 6400 km. However, the state of West Bengal is not blessed with most of its length. The coastline along the right as well as in the left bank is limited before the river Hooghly debouches into the Bay of Bengal. Moreover, the interstate boundary restricts the length of the coastline along the right bank as Odisha border starts after Digha as shown in Fig. 1a.

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Fig. 1 (continued)

The trail of Bhagirathi-Hooghly river from the outfall of the Feeder Canal of Farakka Barrage to Saugor Island is shown vide Fig. 1b. The river BhagirathiHooghly and its estuary provides the waterway for movement of vessels, barges and ships to the inland as port operating locations (jetties, berths, impounded docks, virtual jetties, etc.) from the sea. It is a well-known fact that since the inception of port facilities in the State of West Bengal in the form of Calcutta Port Commissioners

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(presently Kolkata Port Trust) the locations of port operations got shifted as well as drifted southward commensurate to the requirement of the shipping and change in ship size. There is a long pending need for a deep drafted port in West Bengal which will serve complete East and North East region of India. The port operation in Hooghly estuary started in Kolkata in the eigteenth century. This is the only riverine port in India which started its operation with an approach channel of around 232 km from the sea (Sand Heads). Thereafter due to the problem of siltation and to accommodate the bigger size of vessels, another Satellite Dock System (Haldia Dock complex, i.e. HDC) started its operation from 1974 with 9.5 m average draft whereas, the draft available at Kolkata Dock System (KDS) at that time was varying between 7.5–8.0 m. Estuarine port has advantage and disadvantage particularly on the bank or in the influence zone of mighty Hooghly estuary. The estuary provides depths for navigation channel both inland and in sea. The influence of Hooghly estuary extends almost 100 km on both sides. But the disadvantage is that depth and alignment of the channel depend on natural force of the estuary. It is extremely difficult to change the natural depths. Due to adverse morphological transformation, over the decade, at present, the natural depth in and in front of Hooghly estuary varies between 5 and 7 m. So looking for deep-drafted port in and in front of Hooghly estuary is ruled out. It is required to see the site on the East side and West side of Hooghly estuary. Unfortunately, on East and West, the extent of coastline is small. On the East side lies the Sundarban Delta mostly formed by alluvial sediment brought by Hooghly estuary. Subsoil is mostly formed of silty clay unsuitable for port construction. It is also observed that while flood flow enters the estuary with equally distributed over width, the ebb flow moves to East after leaving the estuary. Any attempt to develop a port on East side has to tackle with enormous sediment brought by the estuary. Hence, one has to look towards West for deep-drafted port. Coastline in this stretch is limited. On West side, characteristics of the formation of channels like Eden channel and channel West of Eastern brace, which are wide in the deep region and gradually narrows down as they move upstream, indicate that they are flood channels. The advantage of flood channels is that tackling the sediment brought by estuary is not required. They are stable and maintained more or less at same location. Another expectation is that during a prehistoric era when reaching of sand to coast through river was not intercepted by dams and movement along the coast was not intercepted by port structures and approach channel, West side of Hooghly estuary has intercepted the sand. Outfall of estuary works as sand barrier. There is a good chance that subsoil in this area is formed of sand. The existence of number of sand heads for centuries is proof of that. Submerged sands on two sides will give protection from cyclones. Coastal formation dictates that deep drafted port in this region has to be formed as Island port. Considering all these aspects, the deep flood channel west of eastern brace provides excellent site for deep-drafted Island port.

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In the following deliberation, an attempt has been made to logically reinforce the merits in favour of Island port in reference to other available options, within the jurisdiction of West Bengal.

2 Present Status of Port Operation Port operations are carried out in the following locations: • • • • •

Kolkata (Left bank) Haldia (Right bank) Buj Buj (Open Riverine jetties along left bank) Diamond Harbour (Mid-River Transfer of Cargo) Saugor Anchorage (Mid-River/Sea Transfer of Cargo, i.e. one form of ‘Transloading’) Besides this, the waterway leading to the Port (Dock Systems of Kolkata and Haldia) and its upstream through the inland waterway (NW-1) facilitate cargo movement of inland water transport.

3 General Behaviour of Hooghly Estuary 3.1 Tide Tides in Hooghly River and Estuary are semi-diurnal in nature. The spring tidal range is 4.0 m with 5.0 m as high water and 1.0 m as Low water. The neap tidal range is 2.0 m with 4.0 m as high water and 2.0 m as low water. The tidal range is 4.5 m. The MSL is stated to be 2.82 m in this area. Tides are recorded at Saugor tidal station and are used for prediction of tides at Saugor Island. The predicted tides as published by survey of India for the year 2010 were analysed. It can be seen that approximately 43% of time, the range is less than 3 m while 57% of time, the tidal range is more than 3 m. The analysis of low and high waters is also carried out. It can be seen that 100% of time high water is higher than 3 m. While 82.5% of time, low water is more than 1 m. Figure 2 illustrates a simultaneous tidal curve in Hooghly estuary.

3.2 Current Hooghly River being tidal in nature, the effect of tidal current reaches up to a distance of 130 km upstream of Kolkata, a place called Nabadwip. However, the current was not strong ever to turn the flow in the opposite direction. The significance of tidal current is felt up to 50 km upstream of Kolkata, a place called Tribeni. The tidal

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Fig. 2 Simultaneous tidal curve

current varies from stretch to stretch and its strength depends on the state of flow (flood or ebb) as well as range of tides. On an average, the maximum strength of flood current below Hooghly Point varies between 1.85 and 3 m/s. Whereas the strength of ebb current varies from 1.3 to 2 m/s. The strength of tidal current during neap tide reduced considerably and varies from 0.3 to 1.45 m/s over the whole tidal cycle.

3.3 Waves Surface waves in the coastal zone of West Bengal are mainly due to wind. Sea waves in this region rarely become destructive except during cyclonic storm. During South West, the wind speed rises above 100 km/h and is usually accompanied by spring tides. When cyclonic incidences coincide with spring tides wave height can raise over 5.0 m. Ripple waves also appear in the month of October, November and December when wind-generated wave height varies approximately from 0.2 to 0.35 m. From the month of April to August, comparatively larger waves form in the shelf region and they start breaking, when they approach coastal margins. During this period, wave height raises to 2 m, which causes maximum scouring on land masses. Wave action, micro- and macro-tidal cycles and longshore currents are recorded in most of Islands in this ecosystem. During the cyclonic time, the water depth over tidal flats exceeds 7.0 m which will allow 5.0 m waves to touch the Sagar Island.

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3.4 Wind The weather station at Saugor records wind speed and direction at every minute. The wind data for the year 2007 as was available from Kolkata Port Trust, was analysed monthly and the wind rose diagrams have been prepared (source: CWPRS). The rose diagrams are shown in Fig. 3. The wind data is grouped in three parts; the South West monsoon from June to September, North East monsoon from November to January and February to May being Pre-monsoon period. During South-West monsoon, wind are from SW, SSW and South with maximum wind speed of 68 km/h while during North-East monsoon period, they are from North, NNE and North-East division with wind speed of 50 km/h. While during remaining period they are from SSW, South, SSE and SE with maximum wind speed of 54 km/h.

4 Approach Channel Leading to Haldia and Kolkata and Their Maintenance The approach channel leading to Kolkata is 230 km long whereas the same leading to Haldia Dock Complex and Oil Jetties is 117 km long as its present state. The present navigational channel leading to Haldia is a new channel which has been operationalized on and from March, 2016. The channel bypasses the stretch known as Lower Auckland Bar (LAB) which connects eastern Channel in the outer estuary with Upper Auckland Bar in the inner estuary. This stretch of the navigational channel was badly suffered by siltation from 2009 onwards and in spite of vigorous maintenance dredging the governing depth in the navigational channel at Lower Auckland Bar could not be improved significantly. As a matter of fact, maintenance dredging of the order of 8 Mm3 /year was required to maintain a depth of 4.5/4.6 m. The look out of an alternative channel was on from 2009 when the navigable depth of LAB reduced to all time low of 3.7 m. A study of old satellite images and hydrographic charts coupled with mathematical model analysis leads to establish the feasibility of operation via the alternate channel named as Eden Channel which ultimately with all its requirement (laying of buoys, installation of Vessel Traffic Management System) came into operation as a trail run during 2012–13. This channel is blessed by flood flow and thus required very less dredging for maintaining comport level of depth in comparison to LAB. Thus, a considerable volume of maintenance dredging has reduced to maintain the navigational channel leading to Haldia. The channel leading to Kolkata is more or less self-maintained in most of the part below Diamond Harbour, i.e. lower part of inner estuary. It requires very insignificant dredging 0.5/1.0 Mm3 /year for maintaining comfort level of depth in the upper part of inner estuary leading to Kolkata Dock System. Thus, the overall maintenance dredging quantum of Kolkata Port Trust has reduced from 16 Mm3 /year to 9–10 Mm3 /year from 2016-17. At present, the average draft of approach channel leading to Haldia varies between 7.8 and 8.3 m on an average whereas that leading to Kolkata varies

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between 6.8 and 7.5 m on an average. With the demand of deeper drafts around the World, the Government of India has stressed to deepen all the Major ports in India up to 12.5 m draft, which as per present scenario (looking at the port operation in Kolkata and Haldia) appeared to be not achievable for Kolkata Port Trust, the only major port in the State of West Bengal. Apart from maintenance dredging, the navigational channels leading to the dock systems of the port (KoPT) require nominal bank protection work and river training work in the form of pitching, revetment and spurs.

5 Selection of Deeper Drafted Location for Future Port Operation Thus, the hunt for a location to operate the port facilities at a significant deeper draft was on for quite a significant time. While identifying the probable location, the prime importance cum weightage was given on the following points: • • • • • • •

Natural depth available Trend of self-maintenance of the depth in the area Distance of the approach channel Dredging requirement (both capital and maintenance) Available draft (with and without tide) Railroad connectivity Cost.

In line with the above considerations locations are available in the following points: • South-Western fringe of Saugor Island • Tajpur at the right bank of River Hooghly in between Digha and Mandarmoni Again port may be conceived as impounded dock or in the form of open riverine/estuarine jetties. In a tidal port, the impound docks are generally operated through lock gates and thus became restrictive in nature for handling vessels at all state of tide. Thus, the impounded dock concept has been avoided while conceptualizing the port handling facilities at South–West fringe of Saugor Island by KoPT as well as the consultant (RITES). Similarly while analysing the physiography of the region, tides, currents, waves, winds, etc. prevailing over the region along the right bank below Haldia, the concept of impounded dock may not get a place with open estuarine operation. The open riverine operation in the vicinity of Tajpur does not present bright prospect as the area, apart from suffering from coastal erosion is quite shallow up to a distance of 10 km (approx.) from the bank. Thus, the following options appear to be available for selection of a deep drafted port location: • S-W fringe of Saugor Island (expected draft around 10 m with tide)

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• The area in the vicinity of the Tajpur bank with breakwaters and long approach channel aligning over shallow patches expected to be created with huge capital dredging and sustained with significant maintenance dredging (expected draft around 10 m with tide) • Island port with breakwater at a relatively deeper location which is self-maintained over the years with significantly less distance of approach channel (expected draft around 15 m with tide).

6 Conceptual Plan and Preliminary Analyses A. South-western fringe of Saugor Island The approach channel leading to the proposed port location (turning basin, tentative location of jetties, etc.) including port layout is shown in Figs. 4 and 5. The recent bathymetric chart as available and the sedimentation pattern over the area are shown vide Figs. 6 and 7. If one looks at the strength and weakness of the location, the long approach channel and the outer estuarine bars (Middleton and Gasper) allowing an average draft of 10 m with tide (assuming self-maintained depth over Gasper and Middleton varying between 6.3–6.9 m) are the restrictive constituents for achieving higher draft. In order to achieve a draft of 13.5 m with tide, the entire approach channel leading to Saugor port location, manoeuvering over Gasper and Middleton will require a deepening to the extent of 4 m on an average. Thus, the capital dredging requirement as well as maintenance dredging requirement will be huge and may be cost prohibitive. Apart from this, the other key point is the Railroad Connectivity with the mainland until and unless the mainland gets connected with the Saugor Island and the Railway line further gets extended up to the port location, the evacuation of the Cargo is not possible to make the port fully operational. B. Port Facility at Tajpur NearShore The proposed location of Tajpur Port NearShore is shown in Fig. 8. Tajpur port site is connected to NH-6 via NH-116 from Kolaghat to Nandakumar Crossing in way to Haldia at a distance of 30 km. This is a four-lane road. Thereafter, a two-lane road leads to Digha via NH-116B. Mandarmoni, Tajpur Port site (proposed) and Sankarpur Fish Harbour are connected to NH-116B via Trunk routes. The distance from Nandakumar to Tajpur is approximately 80 km, whereas the distance from Haldia to Tajpur via Nandakumar is around 100 km. The proposed Tajpur Port site (nearest railway station being Ramnagar) is connected to Tamluk on the PanskuraHaldia line. The road and railway links are running parallel to the coastline at a distance of 9 and 10 km, respectively. Odisha border at Chandaneswar is 25 km from the proposed Tajpur Port site. The road joins NH-6 at Kharagpur via NH-16. This road is fairly wide and the distance between Tajputr and Kharagpur is about 110 km.

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Fig. 4 The approach channel leading to the proposed port location

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Fig. 5 Proposed port layout

However, there is no direct rail connectivity available between Tajpur and Kharagpur at present. Figure 9 shows the available admiralty charts of the Bay of Bengal. The chart is indicative in nature and shows the prevailing depth contours, orientation of shoals and sands including the present navigational channels leading to Haldia and Kolkata. As per the chart, the nearest 10 and 20 m contours are situated at a distance of 22 and 55 km from the shore. The following technical details are required to be considered for developing a port near shore at proposed Tajpur site: • The proposed site at Tajpur is along the open coast and therefore would need breakwaters to provide tranquillity for round the year operations.

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Fig. 6 Present bathymetry of Hooghly Estuary

• The 10 m contour is about 22 km and 20 m contour is about 55 km from the shoreline. Thus, a very long outer channel will be required for linking the deep contours with the deepen port operational area within the breakwaters. • The outer channel will obviously run through shallow areas and thus will require more capital and maintenance dredging effort. • From the orientation of contours, it appears that the longitudinal stretch of the outer channel connecting the port operational area within the breakwater and with the deeper contour will run in somewhat transverse direction to the prevailing tidal flow which may accentuate siltation rate and pose problem for maintaining the required depth in the channel. • In view of the distant deep water contour, a two-way channel (450–500 m width) may be required for the effective port operation. C. Island Port connecting Tajpur Shoreline with the Proposed Port operational Area Encompassing Deep Contours by Breakwater. On the strength of the available admiralty chart, the hydro-morphological parameters are analysed for the conceptualization of the Deep Drafted Port (around 15 m draft with tide). The conceptualization plan and its physical manifestations are detailed below :

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Fig. 7 Sedimentation pattern

• The concept was of Island Port (Fig. 10), surrounded by breakwater, wherein the depth within the breakwater, i.e. shelved region was planned of the order of 16.5–17.0 m, whereas the approach channel was thought of the depth of 14.5–15.0 m. • Figure 10 also shows the conceptual plan of the deep drafted port facility within the breakwater, shore connectivity for transportation to Secondary storage on the reclaimed area near bank, Primary storage within the breakwater and Approach

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Fig. 8 Proposed port location near shore at Tajpur with railroad connectivity

Fig. 9 Admiralty chart showing bathymetric details

Channel linking the breakwater up to a depth of around 13.0 m (existing), which is proposed to be deepened up to 14.5–15.0 m depth and the area beyond having depth greater than 15.0 m. • The connectivity from reclaimed land at bank to the breakwater is 13.0 km, whereas the approach channel length stands as 19.0 km. • Prima facie, the proposed deep drafted port within the deep water appears to be the only appropriate option as a port near the bank within the breakwater appears to be not feasible and that would again require huge maintenance dredging for deepening the shallowest part and going across the flow, whereas, the option identified, run through a deep area which is self-maintained over the decades, favoured by dominant wind direction.

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Fig. 10 Layout of Island port connecting Tajpur Bank

• Only the portion of approach channel and the mouth of the breakwater are expected to require maintenance dredging which is estimated to be nominal. • The hydro-morphological behaviour of the deepened channel resembles deepening the approach channel of a sea port and expected to behave positively towards the sustenance of depth upon deepening.

7 Observation The following table brings out the gist of the above discussion.

A Study to Identify Locations Suitable of Deep Sea … Location of port operation

Available average draft with tide

Possibility of deepening

Kolkata

6.8–7.5 m

May not be feasible for significant increase in depth

Buj Buj

6.8–7.5 m

Not feasible

Diamond Harbour

Around 9.0–9.5 m

No permanent jetty is available at present

Saugor

Around 10 m

Tajpur (near shore)

Around 9.5–10 m

Deepening will require capital dredging over the entire approach channel necessitating huge cost. Maintenance of increase depth will also be uncertain Deepening will require huge capital and maintenance dredging cost

Tajpur (off shore, i.e. Island Port)

Around 15 m

The port may take a significant deeper draft and may further be deepened by another 2–2.5 m phase-wise depending on the demand of cargo

597 Remarks

Only lighterage operation, i.e. transfer of cargo is undertaken within the river Deepening may cost prohibitive

Maintenance of the depth in the deepen channels will be costly as well as uncertain Appears to be the best location for deep-drafted port. The initial cost of port development with capital dredging and other infrastructure will be high. However, the maintenance dredging cost will be nominal

8 Conclusion The detail discussion, analyses observations of the conceptual plan and its physical manifestations lead to infer that the best location with respect to potential and prospect towards the development of deep drafted port within the State of West Bengal goes to Tajpur area with the option of island port. However, detailed prototype data collection, geotechnical investigation and mathematical modelling are required to focus and freeze the pivotal issues requiring deepening of the navigational channel leading to the proposed port area and its sustenance of the depth in the long run. Acknowledgements The authors are indebted to the competent authorities of CWPRS, KoPT and WAPCOS for providing the required information and wish to convey their sincerest thanks for the constant support and encouragement bestowed towards publication of the paper.

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References 1. Ghosh SN (1997) Tidal hydraulic engineering. Oxford and IBH Publishing Co. Pvt. Ltd., New Delhi 2. Kray CJ (1970) Supership effect on waterway depth and alignments. J Waterways and Harbours Div ASCE 96. WW2 paper 7305, May 3. Manaus MC, Irving R (1976) Reclamation dredging and instrumentation proc symposium on dredging, London Institution of Civil Engineers (London) 4. Shariff S (2005) Cost benefit in dredging projects, expertise in laying and maintenance of discharge pipelines. Dredging Seminar 2005, DCI of India 5. van de Ridder KH, de Wit PC (1987) The effective development of trailing suction hopper dredgers in the port of Rotterdam. Maintenance dredging. Proc. Of conference organised by ICE, London at Bristol, 1987 Thomas Talford

Interaction of Wave with an Open Caisson Yan-Xiang Lin, Da-Wei Chen and Jiahn-Horng Chen

Abstract Harbour resonance provides a possible way to amplify wave energy for wave energy converters (WEC) operating in regions with medium wave energy density. In the present paper, we conducted computationally a study on the amplification effect for a cylindrical caisson for different incidence angles of wave and wave numbers. Also studied here is the effect of some appendages on the caisson on wave amplifications. The open source code OpenFOAM was employed for all computations. The volume of fluid (VOF) method was employed to obtain the free surface. Features of wave patterns inside the caisson are also discussed. The results show that proper combinations of these parameters can result in significant wave amplifications in the caisson. Keywords Harbour resonance · Wave amplification · Caisson · Wave energy

1 Introduction The wave energy is a promising renewable resource for energy supply even though it is immature at the present status of technological development [1]. Since it is almost everywhere in the ocean, the wave can be an abundant energy source in the world. Furthermore, wave energy is also more reliable than wind and solar energy [2]. Various devices have been developed and several classifications were proposed for them according to different features (see, e.g. [3]). It is well known that wave energy is strongly dependent on the wave height, it is no surprise that most researchers focus on the area between 40° and 60° in both hemispheres. If the factor of closeness to shore is further considered, then the most promising regions include Greenland, Iceland, and British Isles in north hemisphere and Australia, New Zealand, Chile and South Africa in south hemisphere [4]. All wave energy converters (WECs) which have been proposed are primarily designed for this kind of area. In fact, the most active countries Y.-X. Lin · D.-W. Chen · J.-H. Chen (B) National Taiwan Ocean University, Keelung, Taiwan e-mail: [email protected]; [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_45

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devoted to developing WECs are those located in the above-mentioned areas. The regions of medium wave energy resources with 15–20 kW/m in equatorial waters are usually only of interest to local developers and researchers. They are not in the mainstream of wave energy development. Unfortunately, the coastal waters of most Asian countries are in the ‘unpromising’ regions. There are a few studies available in the literature which attempted to develop WEC systems particularly for these regions. They analysed the local wave characteristics and attempted to find a new path of the WEC design for waves of medium energy density. As some examples, Alamian et al. [5] evaluated the technologies for harnessing wave energy in Caspian Sea and concluded that the point-absorber type would be most suitable. Later, a point-absorber WEC was proposed specifically for Caspian Sea by Alamian et al. [6]. Liu et al. [7] proposed a combined-oscillatingbuoy-based WEC for waters in China. They design a hydraulic accumulator system to collect and store energy from smaller waves to increase the total efficiency. However, they find that more optimization must be conducted before the goal can be reached. Kim et al. [8, 9] proposed a conceptual dual-buoy WEC to enhance energy extraction efficiency and to broaden the frequency range for energy extraction. Furthermore, Gunawaradane et al. [10] considered the low wave energy oceanic climate in Sri Lanka and proposed to employ the device ‘Pendulor’ which was invented in Japan. Rather than focusing on the improvement of WEC system, Tao et al. [11] considered the Bragg resonance effect on wave focusing for a point absorber. They conducted a series of experiments to show that energy extraction from a standing wave field due to Bragg resonance effect can be remarkably increased compared to that in a propagating wavefield without the effect. Therefore, the resonant interaction becomes an alternative to enhance the wave energy density and wave power capture at nearshore regions of low wave energy density. In addition to the low/medium wave energy density, what could be even worse is that East Asia is situated in the typhoon belt in the Pacific and visited by 14 typhoons every year on average according to the past 50-year record [12]. Typhoon is a severe weather phenomenon which brings forth huge energy in a very short time period and could result in damaging or destroying wave energy converters. Therefore, how to protect the systems from its ravage is one of the important issues when one attempts to develop and deploy WECs to harness wave energy in the Asian ocean climate. Therefore, to design a proper WEC for Asian waters, we need not only to take the wave density but also the typhoon issue into consideration. However, the later one has not been seriously addressed in the literature. We propose a new concept of wave energy extraction by combining an open caisson and a point-absorber WEC. A caisson is a common structure used in harbour engineering. The main idea is that we attempt to create harbour resonance in the caisson so as to amplify the wave height inside it and, therefore, the energy extraction. Meanwhile, the caisson can also provide proper protection for WEC inside it when extreme weather such as typhoons occurs. Harbour resonance is a wellknown physical phenomenon in harbour engineering. It occurs when incident waves from outside the harbour trigger one of the particular natural modes of the partially enclosed harbour water [13]. Similarly, a properly designed caisson can also induce

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such a physical phenomenon. As far as harbour engineering is concerned, harbour resonance is what should be avoided. Nevertheless, resonance inside the caisson is in the present study, we focus on the possible resonance of caisson due to an incident wave. Further study on the wave energy extraction will be conducted subsequently.

2 Physical Problem A WEC of diameter d 1 , shown in Fig. 1, is placed in the water of infinite domain with constant depth h. the WEC consists of two parts. The first part is the caisson with an opening of angle θ and the second part is the point absorber inside the caisson for which only the moving part (float) is shown. The length of the caisson is hc > h. The conceptual design of the WEC is that, except the moving part which floats on the water surface, all other parts, such as the power take-off and generator, are in the air. A wave of period T and height H moves toward the caisson at an angle of α, the angle between the symmetry line of the caisson and the wave propagation direction. Due to the wave incidence into the semi-enclosed caisson, the water inside it oscillates with a wave height S. The ratio of the wave height S inside the caisson to the incident wave height H is called the amplification factor R. To study the effect of caisson geometry on resonance, two different arrangements, without and with waveguides, are investigated, as shown in Fig. 1a and b, respectively. The waveguide mounted on the caisson wall at two sides of the entrance is a part of a circular cylinder of radius r 2 . Since our focus of the present study is the wave amplification inside the caisson, no WEC system description will be made here. In the following study, only the open caisson is considered here.

(a) Caisson A

(b) Caisson B

Fig. 1 Two types of caisson in an infinite water domain of finite depth

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For the present physical problem, the hydrodynamic behaviours outside and inside the caisson are governed by the continuity and momentum equations ∇ ·u 0  ∂u + (u · ∇)u  −∇ p + μ∇ 2 u, ρ ∂t 

(1) (2)

where u is the velocity, ρ the water density, p the pressure, and μ the dynamic viscosity of the water, and t the time. Viscous effects can be important on the boundary of caisson and, therefore, are taken into consideration here. To account for the turbulent effects, we have to decompose the velocity and pressure fields into the time-averaged and fluctuating terms u  u¯ + u , where the time-averaged terms are  T0 1 u¯  u dt, T0 0

p  p¯ + p  ,

p¯ 

1 T0



(3)

T0

p dt

(4)

0

in which T 0 denote some proper time interval. Then the fluctuating terms are the difference between the physical quantities and the time-averaged quantities. If we substitute Eq. (3) in Eqs. (1) and (2) and take time average, then the governing equations become the Reynolds-averaged Navier–Stokes equations ∇ · u¯  0  ∂ u¯ + (u¯ · ∇)u¯  −∇ p¯ + μ∇ 2 u¯ + ∇ · λ ρ ∂t 

(5) (6)

where λ is the Reynolds stress tensor due to the fluctuating physical terms. The Reynolds stresses incorporate the effects of the unresolved turbulent fluctuations on the mean flow. These apparent turbulent stresses significantly enhance momentum transport in the mean flow. They lead to 22 additional unknown quantities and, hence, the closure problem for the RANS equations. The way to cure this problem is the introduction of turbulence models in order to appropriately model the Reynolds stress. Various models have been proposed. Here we adopt the standard k-ε model for further analysis. To solve the differential equation system, we need to specify proper boundary conditions. Physically, we assume that the flow domain is infinite in all horizontal directions. The incident wave is specified far upstream. A no-slip condition is prescribed on the boundaries of the caisson surface and the bottom. Furthermore, the usual kinematic and dynamic boundary conditions must be satisfied on the free surface. The interaction between the incident wave and the caisson results in local wave reflection and refraction which are part of the solution.

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In the present study, we set h  12.2 m, r 1  9.14 m, r 2  4 .57 m, H  2 .4 m and θ  60°. The incident wave period varies within the range of interest from 7 to 40 s. Three different incident angles were selected for study; that is, α  0°, 15°, and 30°.

3 Numerical Approach The present study is conducted by numerical computations. Computationally, we are not able to solve a problem in an infinite domain. The domain must be truncated so that it becomes finite. After a series of careful examination of computed data, we decided the truncated region as follows. Shown in Fig. 2, the length, width and depth of the domain are L  L 1 + L 2  180 m + 120 m  300 m, W  W 1 + W 2  30 m + 30 m  60 m, and H t  H air + H water  12.2 m + 12.2 m  24.4 m, respectively. A structured mesh is generated and the total number of grid points is about 2,000,000. With the truncated domain, we specify the wave absorption condition on the downstream truncated boundary and on the side truncated boundary. The volume of fluid method was used for the treatment of the free surface. Therefore, the fluid density and viscosity in the vicinity of the free surface are expressed as the mixture of water and air, ρ  βρw + (1 − β)ρa

(7)

μ  βμw + (1 − β)μa

(8)

Hair = 12 m

Hwater = 12 m

z y

x

Fig. 2 Truncated domain for computational purpose

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Here, the subscripts w and a represent water and air, respectively. The fraction function β is the volume fraction of water in the grid cell. The fields for all variables and properties are shared by the phases and represent volume-averaged values. The open source code OpenFOAM was adopted for the study. The OLAFOAM model based on OpenFOAM with the finite volume method approach was employed. OLAFOAM consists of a well-developed set of solvers in which water waves can be actively generated and absorbed on the boundaries. It can be employed to simulate the interaction between waves and coastal structures [14]. The SIMPLE algorithm was used for the iterations of the velocity and pressure fields and the PISO algorithm for the time marching.

4 Results and Discussions 4.1 Model Validation for Wave Decay Waves travelling through the caisson with viscous effects is one of the vital issues in a long numerical tank. Before proceeding to the present study, we first investigated the numerical wave attenuation. A solitary wave was adopted for validating the present approach. According to Keulegan [15], the formula for wave attenuation of a solitary wave in the viscous flow can be expressed as 

Hx h

 41

 

H h

 14 +

  2h μ 1 x 1+ · , 1/2 2/3 12 B g h h

(9)

where H x is the wave height at position x and B the width of wave tank. Later, Mei [16] modified Keulegan’s formula by the perturbation method and proposed a revised formula  μ x 1 1 (10) · (Hx ) 4  (H ) 4 + 0.08356 g 1/2 h 2 h The non-dimensional wave height variation as the solitary wave travels downstream in the above numerical tank is shown in Fig. 3. It is obvious that the numerical wave attenuations in the present study is comparable to those by the two theoretical analyses. The deviation of the computational results from the theoretical value is less than 0.6–0.8% even at a distance of x/ h ≥ 20. We may conclude that the wave travelling could be reasonably simulated in the present wave tank.

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0.2100

H/h

0.2000

η h/ 0.1900

Keulegan (1948) Mei (1989) Present Model

0.1800

0

4

8

x/h x/h

12

16

20

Fig. 3 Variation of dimensionless water surface elevation (H/h) at different distances (x/h)

4.2 Amplification Factor The amplification factor R is the ratio of the oscillating wave height S inside the caisson to the undisturbed incident wave height H. In this study, the wave height S at the centre of circular caisson was picked for computing the amplification factor. Figures 4 and 5 show the result for the caisson with and without waveguides at different angles α of incident waves. For Caisson A, we may find that the amplification factor does not sensitively vary with the incident wave period unless T is small. For T > 11 s, the value of R somewhat levels off to around 2.0. For applications to wave energy harvest, this implies that the caisson can be employed for a wide range of wave period without losing too much performance. Since the wave energy is proportional to the square of its height, the result implies that the presence of the caisson can enhance four times as much the energy harnessing with the same WEC. In Fig. 4a, we can also find that the effect of the incident angle of the wave on the amplification factor is not significant for θ ≤ 15°, if we compare the values of R at θ  0° to those at θ  15° for different wave periods. Even at θ  30°, the influence is still limited though the value of the amplification factor does somewhat decrease. Hence, we may say that the amplified wave inside the caisson can keep its wave height within a reasonable range of incident wave angles and periods. This is a very important feature as far as the wave energy harnessing is concerned. For Caisson B which has a pair of waveguides attached to the caisson at the wave entrance. The story is somewhat different from that of Caisson A. First of all, it is clear that the amplification factors R can reach a much larger value than that of Caisson A. The value of R for Caisson B can be more than three, which means that the highest wave energy within Caisson B is more than twice as much as that within Caisson A. However, the variation of R with respect to T is also much more significant than that for Caisson A. The maximum value of R does not vary significantly for different incident wave angles, but the wave periods corresponding to this maximum are not the same. The best operation range of Caisson B will be limited to a smaller region of the incident wave angles and periods. It appears that caissons with and without the waveguides have their own different merits. Nevertheless, if we examine the curves

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20 17 15

13

11

9

Amplification Factor R=S/H

4 incident angle of 0 degree incident angle of 15 degree incident angle of 30 degree

3

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ka

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4 incident angle of 0 degree incident angle of 15 degree incident angle of 30 degree

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(b) Caisson B Fig. 4 Comparisons of the amplification factors for caisson A and B at different angles of incident waves

of the amplification factor, we can easily find that the value of Caisson B is always larger than that of Caisson A at the same incident wave angle and period. We may conclude that two types of caissons can effectively magnify the wave energy inside it and the caisson with the waveguide is a better one for the use of wave energy harnessing. In Fig. 5, we plot the same curves in Fig. 4. For the comparison purpose, we mark the computed data on the plot. It should be mentioned that all the values of R in the present computations do not exceed 3.0; however, the trend lines appear to show that the amplification factor can exceed 3.0 somewhere between the computed data points for Caisson B.

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607 Wave period, T (sec)

30 25

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Amplification Factor R=S/H

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2.92

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ka

(c) α = 30°

Fig. 5 Comparisons of the amplification factors for the caisson with and without wave guides

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4.3 Wave Patterns in Caisson It is obvious that the caisson with a pair of waveguides leads to much better wave amplifications. To understand the physics behind it, we study the hydrodynamic behaviours as waves pass the two caissons. The case at T = 15 s is selected for discussion. Shown in Figs. 6 and 7 are the velocity fields in a cycle and the wave height distributions in different phases of wave propagation at α  0° and 30°, respectively. The time at t/T  0/6 corresponds to the wave trough phase and t/T  3/6 the crest phase in the entrance region of the caisson. In the plot, the colour shows the water level with the red and blue colours denoting the water surface below and above the mean water line, respectively. Shown in Fig. 6, the wave propagates at α  0°. As expected, the wave is symmetric. In Fig. 6a, the wave trough approaches the caissons at t/T  0/6 and the water surrounding the caisson opening begins to move into the caisson. As the wave trough passes the caisson at t/T  1/6, the water inside the caisson gradually rises, as shown in Fig. 6b. At these two stages, we can see that the flow speed distribution at the entrance of Caisson B is much bigger than that of Caisson A. This results in a higher surface elevation in the caisson. Furthermore, it is interesting that the fluid around the outside wall of the caisson flows in the reverse direction. However, it is no surprise because at the wave trough, the particle velocity is in the opposite direction to that at the wave crest. As wave crests approach the caissons, the water reaches its highest elevation for both caissons in Fig. 6c. Then a wave reflection from the caisson wall results and water inside the caisson moves toward the opening in the opposite direction. The reflecting wave interacts with the incoming wave trough. This can be seen in Fig. 6c–e. We find that the high-speed region near the opening area is bigger for Caisson B as shown in Fig. 6e. It appears to imply that there is a stronger wave reflection for Caisson B. More water comes out from the caisson and, then, a lower water surface level results inside the caisson at this stage, as shown in Fig. 6f. Therefore, we can see that the wave height inside Caisson B is obviously bigger than that inside Caisson A. The waveguide plays a role of collecting water into and discharging water from the caisson. It is quite effective. It makes the entrance of the caisson smoother and water can easily move in and out in a smoother way. Figure 7 shows the flow physics for an oblique incident wave at α= 30°. The results clearly exhibit asymmetric wavefronts when the wave passes the caissons. The flow in this situation is similar qualitatively to that when the incident angle is zero. Again, the velocity distribution near the opening of Caisson B exhibits a bigger magnitude, compared to that of Caisson A. In additions, when the incident wave angle α increases, the fluid enters and leaves the caissons with higher flow speeds. This could be due to less influences from the incident waves. Moreover, the flow speeds at α= 30° for Caissons B are higher than those for Caisson A. Again, this results in a bigger wave height inside Caisson B. Furthermore, the wave behind downstream of the caisson exhibits a smaller amplitude for both cases. This also implies that the wave can be effectively reduced with the presence of a caisson.

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609

(a) t/T = 0/6

(b) t/T = 1/6

(c) t/T = 2/6

(d) t/T = 3/6

(e) t/T = 4/6

(f) t/T = 5/6 Caisson A

Caisson B

Fig. 6 The velocity fields for both caissons at different phases at α  0°

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(a) t/T = 0/6

(b) t/T = 1/6

(c) t/T = 2/6

(d) t/T = 3/6

(e) t/T = 4/6

(f) t/T = 5/6 Caisson A

Caisson B

Fig. 7 The velocity fields for both caissons at different phases at α  30°

Interaction of Wave with an Open Caisson

611 0.5

gh

0.25

Flow Speed u

Flow Speed u

gh

0.5

0 α = 0º α = 15º α = 30º

-0.25 -0.5 0/6

1/6

2/6

3/6

4/6

0.25 0 α = 0º α = 15º α = 30º

-0.25 -0.5 0/6

5/6

1/6

2/6

3/6

4/6

5/6

t/T

t/T

(a) Caisson A

(b) Caisson B

Fig. 8 Comparisons of the flow speeds at the caisson opening for different incident angles 0.5

Caisson A Caisson B

-0.25 -0.5 0/6

1/6

2/6

3/6

0.25

Flow Speed u

0

0.5

gh

gh

0.25

Flow Speed u

Flow Speed u

gh

0.5

0 Caisson A Caisson B

-0.25

4/6 5/6

t/T

(a) α = 0°

-0.5 0/6

1/6

2/6

3/6

4/6 5/6

0.25 0 Caisson A Caisson B

-0.25 -0.5 0/6

1/6

2/6

t/T

(b) α = 15°

3/6

4/6 5/6

t/T

(c) α = 30°

Fig. 9 Comparisons of the flow speeds at the caisson opening for caissons A and B

Figures 8 and 9 show the average flow speeds at the caisson opening when the water comes into and flows out from the caissons. It seems that there is no simple rule to present their variation in time and incident wave angle. Nevertheless, it is evident that the distribution does not show a strong dependence on the incident wave angle. This should be a good sign that the wave direction is not a sensitive factor to the wave amplification inside the caisson. This is true for both caissons.

5 Concluding Remarks Two types of open caissons with an opening angle θ  60° were studied for the effect of wave amplification due to resonance. One of the caisson has a pair of waveguides and the other one does not. Both caissons have the same radius of r 1  9.14 m. The wave guide has a radius of r 1 /2. The incident wave height H of 2.43 m was specified and the interaction of the caisson with the incident waves with wave periods T  9–30 s were studied. The investigation shows that both types of caissons can magnify the wave energy effectively. However, the maximum amplification factor R can reach 3 for the caisson with waveguides (Caisson B) and 2 for the one without

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guides (Caisson A). This implies that the wave energy inside the caisson is nine times in Caisson B and four times in Caisson A as much as that of the incoming wave. The wave energy in Caisson B is more than twice as much as in Caisson A. Therefore, Caisson B is much better than Caisson A in terms of its capability of wave magnification. The design of waveguide exhibits its effectiveness in making the incident wave more smoothly interacting with the caisson. However, Caisson A exhibits. Moreover, we also examined the flow velocity in a wave cycle to understand the water accumulation inside the caissons. We found that the waveguides enhance not only the wave energy concentration into by collecting the surrounding water, but also energy dispersions by guiding the water outflow. This results in a bigger wave height inside the caisson. More study will be conducted in the future to understand the capability of this type of caisson in the application of wave energy harvesting in the ocean with medium wave energy. Acknowledgements This study is make possible through the support of Ministry of Science and Technology under the grant MOST 106-2221-E-019-040-MY2. The authors would like express their thanks to the support.

References 1. Uihlein A, Magagna D (2016) Wave and tidal current energy—a review of the current state of research beyond technology. Renew Sust Energ Rev 58:1070–1081. https://doi.org/10.1016/j. rser.2015.12.284 2. Villate JL (2010) Situacion actual de las energías marinas y perspectivas de futuro. In: Seminario Anual de Automatica, Electronica e Instrumentacion (SAAEI). Bilbao, Spain 3. López I, Andreu J, Ceballos S, de Alegría IM, Kortabarria I (2013) Review of wave energy technologies and the necessary power-equipment. Renew Sust Energ Rev 27:413–434. https:// doi.org/10.1016/j.rser.2013.07.009 4. Barstow S, Mork G, Lonseth L, Mathisen J (2009) World waves wave energy resource assessments from the deep ocean to the coast. Europ Wave Tidal Energy Conf 1:149–159 5. Alamian R, Shafaghat R, Jalal Miri S, Yazdanshenas N, Shakeri M (2014) Evaluation of technologies for harvesting wave energy in Caspian Sea. Sust Energ Rev 32:468–476. https:// doi.org/10.1016/j.rser.2014.01.036 6. Alamian R, Shafaghat R, Farhadi M, Bayani R (2016) Experimental evaluation of IRWEC1, a novel offshore wave energy converter. Int J Eng 29:1292–1299. https://doi.org/10.5829/idosi. ije.2016.29.09c.15 7. Liu Z, Qu N, Han Z, Zhang J, Zhang S, Li M, Shi H (2016) Study on energy conversion and storage system for a prototype buoys-array wave energy converter. Energ Sust Dev 34:100–110. https://doi.org/10.1016/j.esd.2016.07.004 8. Kim J, Hweon HM, Jeong WM, Cho IH, Cho HY (2015) Design of the dual-buoy wave energy converter based on actual wave data of East Sea. Int J Nav Archit Ocean Eng 7:739–749. https://doi.org/10.1515/ijnaoe-2015-0052 9. Kim J, Koh HJ, Cho IH, Kim MH, Kweon HM (2017) Experimental study of wave energy extraction by a dual-buoy heaving system. Int J Nav Archit Ocean Eng 9:25–34. https://doi. org/10.1016/j.ijnaoe.2016.07.002

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10. Gunawaradane SDGSP, Abeysekara MP, Uyanwaththa DMAR, Tennakoon SB, Wijekoon WMJS, Ranasinghe RAPC (2010) Model study on “pendulor” type wave energy device to utilize ocean wave energy in Sri Lanka. In: International conference on sustainable built environment (ICSBE-2010), Kandy 11. Tao A, Yan J, Wang Y, Zheng J, Fan J, Qin C (2017) Wave power focusing due to the Bragg resonance. China Ocean Eng 31:458–465. https://doi.org/10.1007/s13344-017-0052-z 12. Yap W, Lee Y, Gouramanis C, Switzer AD, Yu F, Lau AYA, Terry JP (2015) A historical typhoon database for the southern and eastern Chinese coastal regions, 1951-2012. Ocean Coast Manag 108:109–115. https://doi.org/10.1016/j.ocecoaman.2014.05.024 13. Rabinovich AB (2009) Seiches and harbour oscillations. In: Kim YC (ed) Handbook of coastal and ocean engineering. World Scientific Publication, Singapore, pp 193–236 14. Iturrioz A, Guanche R, Lara JL, Vidal C, Losada IJ (2015) Validation of OpenFOAM® for oscillating water column three-dimensional modelling. Ocean Eng 107:222–236. https://doi. org/10.1016/j.oceaneng.2015.07.051 15. Keulegan GH (1978) Gradual damping of solitary wave. J Res Natl Bur Stand 40(6):487–498 16. Mei CC (1989) The applied dynamics of ocean surface waves. World Scientific Publication, Singapore

Layout, Foundation Design, and Dredging Methodology of Multipurpose Terminal R. Sundaravadivelu, M. Sasirekha, S. Kreesa Kumaran and S. M. Madhumathy

Abstract This study assesses the optimal of two layouts to develop new terminal to handle coastal vessels and port crafts at JNPT. The new terminal is planned to handle liquid and general cargo vessels up to 10 m draft and port craft vessels up to 5 m draft. The site is located adjacent to the existing ferry terminal and parallel to the fourth container terminal. L-shaped jetty of 315 × 30 m and 150 × 15 m for the coastal vessels and port craft vessels in alternative I. Alternative II is parallel to fourth container terminal having dimensions 270 × 30 along with two approach jetties of dimension 70 m × 15 m. The weathered basalt rock are found from (−)1.0 m to −3.0 m in Alternative II and from −11.0 to (−)13.0 m CD in alternative 1. Considering the soil profile, founding level shall be five times the pile diameter in alternative II and 1.5 D in alternative I. The berth is designed for LHM 550 type cranes. The stitch drilling to dredge the trench in alternative II before construction of berth. The Deck Top level is (+)7.00 m in both alternatives and the backup area has to be reclaimed up to the Deck top level. Keywords Cargos · Weathered basalt rock · Cranes · Dredging · Alternatives Natural flow · Wave · Current pattern

R. Sundaravadivelu · M. Sasirekha (B) · S. Kreesa Kumaran Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai, India e-mail: [email protected] R. Sundaravadivelu e-mail: [email protected] S. Kreesa Kumaran e-mail: [email protected] S. M. Madhumathy Department of Civil Engineering, Alagappa Chettiar College of Engineering and Technology, Karaikudi, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_46

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1 Introduction Due to increase in demand of liquid and general cargos in recent decades, cargos are imported from various countries to cope up current demand. Cargos such as petroleum oil and lubricants, iron ore, fertilizers are handled in the coastal berth. Tankers, mixed cargo freighters, and bulk cargo carriers having a loaded draft up to 10 m are berthed in coastal berth. To facilitate the berthing of 10 m draft vessel, dredging has to be carried out up to (−)11.00, where existing water depth is less. The rock dredging varies from (−)2 m to (−)10 m w.r.t. the existing bed level in alternative II. Backup area is reclaimed parallel to the berth for stacking purpose. Liquid cargos are handled by using pipelines and general cargos with help of Mobile harbor crane (MHC). Port craft vessels of draft 5 m are berthed in port craft berth.

2 Site Location JNPT is located on the west coast of India at 18.9499° N, 72.9512° E lies in the Uran taluk of Navi-Mumbai. The site is located adjacent to the existing ferry terminal and parallel to the fourth container terminal. The overall layout of Jawaharlal Nehru Port (JNP) is shown in Fig. 1. The site location is shown in Fig. 2.

Fig. 1 Jawaharlal Nehru port layout

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Site Location

Fig. 2 Site location

3 Environmental Condition 3.1 Tidal Data Tidal data prevailed at JNPT are furnished in Table 1.

Table 1 Tidal data S.no.

Description

Height (m)

1

Mean sea level

(+)2.51

2

Mean low water spring tides

(+)0.76

3

Mean low water neap tides

(+)1.86

4

Mean high water spring tides

(+)4.42

5

Mean high water neap tides

(+)3.30

6

Lowest low water recorded

(−)0.46

7

Highest low water recorded

(+)2.74

8

Highest high water recorded

(+)5.39

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3.2 Soil Profile The soil investigation was carried out in proposed site location. Fifteen marine boreholes were driven and soil parameters were collected layer-wise. Four boreholes fall in the proposed jetty location. The location of boreholes is shown in Fig. 3. The layer-wise soil profile is as follows and shown in Fig. 4. The two boreholes (SBH-5 and SBH-8) are considered for the design of pile foundation. Details of the borehole, bed levels are mentioned in Table 2. Based on the existing bed levels in site berthing arrangement is planned. Borehole profile of the site condition is shown in Fig. 4.

Fig. 3 Location of bore hole Table 2 Soil profile for alternative II Borehole no. Bed level (m) with respect to CD

Hard rock level (m) with respect to CD

SBH-5

(−)1.865

(−)12.76

SBH-8

(−)1.135

(−)1.135

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Fig. 4 Soil profile

4 Details of Vessel 4.1 Vessel Data Berthing and mooring calculations are carried out based on the maximum vessel size of 16,000 DWT. The vessel specifications are given in Table 3. Berthing Velocity and angle of berthing are taken from IS 4651 PART 3-1974.

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Description

Coastal vessel

1

Dead weight tonnage

16,000

2 3

Draft Overall length

9m 150 m

4 5

Width Berthing velocity (m/s)

20 m 0.3

6

Berthing angle (°)

10

5 General Arrangement of Alternatives with Berthing Arrangement 5.1 Alternative I Alternative I is to construct L-shaped jetty of 315 × 30 m and 150 × 15 m for coastal vessels and port craft vessels respectively. Coastal vessel berth is parallel to fourth container terminal and port craft vessel berth is adjacent to the ferry terminal respectively. In proposed berth four rows of 1200 mm diameter piles at center-tocenter distance of 6 m in lateral direction. In the port Craft berth 2 rows of 1000 mm diameter pile at 7 m c/c distance in cross-sectional direction, cantilever of 2.5 m on both sides of the berth. The rear side of both Coastal and Port Craft berth is provided with touch pile sheet pile wall of 1300 mm c/c. Touch pile walls are provided to protect the existing ferry terminal from sliding.

5.2 Alternative II A Coastal berth and port craft berth has an overall dimension of 270 × 30 m. The Coastal berth (200 × 30 m) is parallel to the IV container terminal and approach trestle of 70 m is perpendicular to the coastal vessel to connect reclaimed area and the berth. First 200 m is utilized by coastal vessels and rest by port craft vessels. The berthing jetty is divided into three modules with an expansion gap of 40 mm. Module 1 and 2 100 m each for catering to coastal vessels. Module-3 of remaining 70 m is proposed for catering to port craft vessels. Two Approach Trestles (AT) each of size 70 m × 15 m, shall be provided as an approach to the berthing jetty from reclamation area. Expansion Gap (EG-1) of 40 mm in between Module 1, 2 and 3 and (EG-2) 100 mm between Berthing jetty and Approach Trestle. Five rows of 1200 mm diameter piles at center-to-center distance of 6 m in cross-sectional direction, cantilever length on berthing side and rear side is 2.4 m and 3.0 m respectively. To transport the POL from the berth to landside 4 no’s of 300 mm Diameter pipes running from face of the berth to land through Approach

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Fig. 5 General arrangement of alternative I

trestle. For handling dry cargos and general cargo LHM 550 with Turing radius of 13.5 m. To retain the filling in the reclamation area, rock bunds are provided on all three sides in the slope of 1:5. The plan of the alternative II is shown in Figs. 5 and 6.

6 Structural Analysis Structural analysis is carried out using STAAD Pro V8i. STAAD Pro V8i is a structural engineering software in which 3D model generation, analysis, and multimaterial design have been carried out. The basic three activities are performed by the software such as model generation, the calculations to obtain the analytical results and result verification. All facilitated by tools contained in the program’s graphical environment. STAAD Pro opens input files to the modeling mode for reviewing geometry, load, analysis, and design input. Comprehensive reports that include both numerical (tabular) and graphical results are created for easy interpretation. It is capable of analyzing any structure exposed to different types of loading. It can easily accommodate the design and loading requirements of international standards. 3D analysis shall be carried out using STAAD ProV8i package for various critical load combinations. The P-δ analysis will be carried out.

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Fig. 6 General arrangement of alternative II

7 Foundation Design Foundation Design has been carried out considering soil parameter at the nearest location. The static capacity of the pile is derived based on IS 2911. Pile geotechnical capacity calculations are calculated as per IS 2911 guidelines for bored cast-in situ RC piles. A minimum factor of safety of 3 is considered for calculating the safe pile bearing capacity. The allowable load Qap on the pile for rock is given below Qu  Cub Nc Ab + Cus As

(1)

While considering the soil profile from site, the rocks are found to Weathered rock with N value > 100. Considering the rock profile and Shear strength of Basalt rock the founding level shall be five times diameter of pile penetration into the weathered rock. So in contract clause, rock termination criteria will be 3T × 600 mm drop height × 20 blows/min ≤ 300 mm hr.

8 Dredging Dredging and rock removal is required because water depths in the area are currently too shallow for safe access for tankers, mixed cargo freighters, and bulk cargo carriers, etc., required to create a safe shipping channel through the harbor, along with a

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berthing area for vessels. For dredging, soil profile is taken into account and the dredging area is divided into two different levels. For Berthing coastal vessel of draft up to 10 m it is recommended to dredge (−)11.0 m included with kneel clearance for the length of first 200 m. In port craft vessel berth (−)6.0 m is dredged due to the presence of weather rock from bed level of (−)1.135 m.

8.1 Cutter-Suction Dredger For rock dredging cutter suction are used. These dredgers are available in various range of sizes, among them, cutter-suction dredgers are a popular type of dredger. A small cutter-suction dredger can handle small volumes of weeds and weakly cemented sediments. Figure 7 shows the cutter-suction dredgers, which can dredge from −3.0 to −7.0 m. It consists of dredging ladder which is centrally hinged and two mountable pontoons. Figure 8 shows the medium-size dredger which is utilized for medium-scale dredging works. The dredged sand mixture is discharged a distance away. A booster pump shall be used for longer distance.

Fig. 7 Typical cutter-suction dredgers

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Fig. 8 Medium cutter-suction dredgers

9 Dredging Sequence of Alternative II The site consists of weathered basalt rock from range of (−)1.135 to (−)12.76 m. The rock dredging is done by using stitch drilling method for Alternative II. Two dredge depths are considered based on the bed profile. It is proposed to dredge up to (−)11.0 m and (−)6.0 m in module 1, 2, and module 3 region respectively. The trench of 10 m wide and depth of (−)11.0 m on open type berthing structure on rock results in development of time-dependent vertical and horizontal sub-soil separation. After trench dredging approach trestle piles are driven. The maximum deflection due to dredging, takes place at the interface of the dredge level with pile. The dredging of trench along with the berthing jetty cross section is shown in Fig. 9. After construction of the berthing structure remaining portions are dredged.

10 Conclusion In brownfield port development project there are a lot of constraints and the planners need to overcome the same by carrying out comparative studies considering various parameters such as ease of berthing, minimal disturbance to other terminals, optimal use of space, minimal rock dredging, and optimized development cost. In this project, such attempts were made to reach at an optimal layout for developing a multipurpose cargo and port development. Alternative II was studied after developing alternative I. Alternative II will allow smooth inflow of water without disturbing its natural flow. The development of alternative II has no impact over the existing wave and

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Fig. 9 Cross section of alternative II with trench dredging

current patterns. In Alternative II is better navigational aspects, with lesser overall project completion time, with less rock dredging, feasibility of handling both POL and General cargoes unlike in Alternative I. The Alternative I is 30 crores more than Alternative II. It is the informed opinion of the port planners to recommend alternative II.

References 1. Indian Standard, IS (1974) IS 4651 Part 3: code of practice for planning and design of port and harbours, India 2. Indian Standards, IS 2911 guidelines for bored cast-in-situ RC piles

Part IV

Ocean Renewable Energy

Study on Suitable Electrode for Energy Harvesting Using Galvanic Cell in Seawater G. Nithya Sivakami, V. T. Perarasu and S. Sakthivel Murugan

Abstract The present work aims to study galvanic cells using sea water as multicomponent electrolyte for energy harvesting. The electrochemical performances of Galvanic cells were carried out by measuring electric potentials by understanding the nature of conductivity of electrodes. Various combinations of electrodes like Graphite, Zinc, Copper, Aluminium, Brass and Iron were tested. A maximum yield of 1.1 V was obtained using the combination of Graphite–Iron as Cathode–Anode. The effect of sea water pH on electric potential was analysed using sea water from different parts of Bay of Bengal with varying depths. The electric potential obtained is further studied with respect to surface area of electrodes and galvanic corrosion of the coupled electrodes. The feasibility to apply Graphite–Iron as the electrodes to sea water battery for efficient energy harvesting was studied. Keywords Electric potential · Galvanic cell · Multicomponent electrolyte Seawater battery

1 Introduction Recently there is a growth in aquatic explorations such as marine ecosystem observation, pollution detection, and surveillance for undersea infrastructure. The idle technology for these applications is underwater sensor networks. It is found that energy supply is a critical issue for the achievable performance and usability. Battery power cannot withstand the long-term operation of underwater sensor networks. To compensate this, an energy harvesting has shown great potential. There are needs to harvest energy in the water and use the harvested energy to power electronic devices G. Nithya Sivakami (B) · V. T. Perarasu A.C. Tech, Anna University, Chennai, India e-mail: [email protected] S. Sakthivel Murugan (B) SSN College of Engineering, Chennai, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_47

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in the water. Galvanic cell is one of the promising energy technologies used for the sustainable future with its high energy efficiency and environment friendly nature Galvanic cell is the basics of modern batteries that help our society to work smoothly. Seawater-activated batteries represent primary reserve applications, which utilize seawater as the electrolyte. They are stored dry until activated at the time of use by the addition of seawater. When brought into use, seawater is drawn inside by immersing batteries in the sea, and used without modification as electrolyte leading to activation within a few seconds [1]. Generally, anode materials in primary batteries include lithium, calcium, and aluminium, and sodium, magnesium. Additionally, these batteries have high voltages and are capable of high current density discharges [2]. Various types of metal halides, such as silver chloride, for the cathode (positive active material) are in practical use, depending on the application. The water-activated batteries based on this technology are widely used to power small devices such as son buoys, radio buoys, lifesaving equipment, marine markers, and emergency lights because of their marked performance in all aspects [3]. The advantages include high power and energy density, Instantaneous activation, Long un-activated shelf life, No maintenance, Reliable, Rugged, Safe and Light weight—easy portable. It has short comings like high self-discharge rate after activation, once activated the electrodes must be replaced [4]. Various types of metal electrodes where employed, depending on the application. The cell itself can be built in many shapes and configurations—cylindrical, button, flat and prismatic—and the cell components are designed to accommodate the particular cell shape [5]. According to the application, cylindrical electrode is preferred in order to reduce the corrosion rate also to increase the shelf life of the electrode.

2 Materials and Method The following cylindrical metal rods with terminals with the mentioned volume were used as electrodes Copper (10.13 cm3 ), Aluminium (10.6 cm3 ), Iron (9.54 cm3 ), Zinc (9.54 cm3 ), Graphite (15.38 cm3 ), Brass (10.13 cm3 ) which is shown in Fig. 1. Seawater samples from the following locations in Bay of Bengal were collected at various depth Akkarai beach, Chennai port, Mahabalipuram, Kalpakkam, Pondicherry, Cuddalore and Poompuhar-2 at various depths. Hydrochloric Acid (HCl) was obtained from Merck, Germany. The required materials were commercially available analytical purity and used without further purification. The deionized water (18 M cm) was used throughout the experiments. The metal rods were cleaned to remove the surface impurities by cleaning in low concentrated hydrochloric acid solutions initially and then polished successively with finer grades of emery paper. It was further polished using plain kerosene on the cloth to mirror bright finish [6].

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Fig. 1 Metal electrodes with terminals from the left graphite, brass, copper, zinc, iron, aluminium

Fig. 2 Graphite–Iron coupled galvanic cell

Different combination of surface-treated metal rods were subjected as anode and cathode, using seawater as multicomponent electrolyte which was collected from the Akkarai beach, whose pH was 8.2, in the room temperature of 32 °C, their electric potential were checked. The experiment setup shown in Fig. 2 was kept undisturbed for 4 h and the electric potential were compared. The two best coupled electrode combination gave better performance compared to other. Thus, those combinations were further proceeded for testing with seawater which was collected from different location at various depths. The cathode electrode was fixed to a single metal and the anode metal electrodes were changed and the testing was carried out to so, the selected electrodes were subjected to further analysis, sea water with different pH was used and tested for their change in voltage.

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Surface area is important parameter to be analysed, the exposure of surface area of the electrode to the electrolyte was varied and the electric potential was measured.

2.1 Weight-Loss Studies The weight-loss experiments were carried out under total immersion conditions in test solution maintained at room temperature. The experiments were carried out in a beaker containing 1000 ml solutions. After exposure, the specimens were removed, washed initially under running tap water, to remove the loosely adhering corrosion product and finally cleaned. Then the weight loss was determined by a sensitive analytical balance (0.1 g). Similar experiments were conducted to find the corrosion rate and percentage weight loss. In each case duplicate experiments were conducted and showed that the second results were within +1% of the first. Whenever the variations were very large, the data were confirmed by a third test. The percentage weight loss, %WL was calculated using the relation % weight loss  (1 − W 2/W 1) × 100,

(1)

where, W1 and W2 are the weight losses in the initial and final weight of electrode respectively [7].

2.2 Corrosion Rate The rate, or speed, is dependent upon environmental conditions as well as the type, and condition, of the metal [8]. Corrosion rate can be found using Corrosion Rate  87.6 × (W/(DAT)),

(2)

where, W D A T

weight loss in milligram metal density in g/cm3 Area of sample in cm2 Time of exposure of metal sample in hours.

3 Results and Discussion The measurement of electric potential of graphite electrode as fixed cathode and the variable electrodes like copper, aluminium, iron, graphite, brass and zinc. It is

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Fig. 3 Comparison of electric potential (V) for fixed cathode-graphite and variable anodes

observed that the graphite iron and graphite zinc combination gave better results; compare to others coupled electrode combinations. The response of graphite with iron and zinc electrode was about 1.0–1.1 V, for aluminium was around 0.8 V, and Copper and Brass resulted around 0.2–0.4 V in Fig. 3. The Graphite behaviour in electrochemistry is that it behaves electrochemically like a noble metal such as gold or platinum. This nobility results in an electrical potential difference which causes galvanic current to flow when graphite is coupled to a less noble metal or alloy in an electrolyte. The less noble metal or alloy corrodes due to galvanic action [9]. The measurement of electric potential of other combination of electrodes like fixing iron, zinc, brass, copper and aluminium as cathode and other electrodes like copper aluminium, iron, graphite, brass and zinc as variable anode, the potential did not reach 1.0 V in any case. Thus, these combinations of electrodes were not utilized further. Graphite–Zinc and Graphite–Iron combination gave better performance of 1.0–1.1 V among other combination. Thus, those combinations were tested again with seawater which was collected from different location like Akkarai, Mahabalipuram, Pondicherry, Cuddalore, Chennai port, Poompuhar. Figure 4 show the OCV and the Electric potential of Graphite–Zinc and Graphite–Iron in different location of Bay of Bengal like Akkarai, Mahabalipuram, Pondicherry, Cuddalore, Chennai, Poompuhar-1, Poompuhar-2.

Fig. 4 OCV and electric potential of graphite–zinc and graphite–iron in different location

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It is inferred from Fig. 4 that there is voltage drop from OCV in graphite–zinc combination. And the voltage is stabilized to 1.0 V, after 30 min and remains constant. In case, of Graphite–iron combination, it is observed that the voltage rise from the OCV after 30 min, and remains constant, about 1.1 V, which is near to the theoretical emf of 1.38 V. The rise in voltage is because of high ionic flow or high dissolution of ions. So Graphite–Iron combination is chosen to be the best combination.

3.1 Electrochemical Reaction in the Graphite–Iron Cell Half-cell Reaction occurred in Graphite–Iron cell [10], At Cathode C(s) + H2 O → CO(g) + 2H+ + 2 e− + 0.52 V

(3)

Fe2 O3 (s) + 3H2 O + 2e− → 2 Fe (OH)2(s) + 2 OH− − 0.86 V

(4)

At Anode

Overall Reaction C(S) + Fe2 O3(s) + 4 H2 O → CO(g) + 2Fe (OH)2(s) + 2H2 O + 1.38 V

(5)

It is known that when two dissimilar conducting materials in electrical contact with each other are exposed to an electrolyte, a current, called the galvanic current, flows from one to the other. Galvanic corrosion is that part of the corrosion that occurs at the anodic member of such a couple and is directly related to the galvanic current by Faraday’s law [11]. The half-cell reaction of two metal electrodes was expressed in the Eqs. (3) and (4), the anode side reaction, Fe metal ions from the iron electrodes were reacted with the dissolved oxygen present in the seawater electrolyte and forms the Fe2 O3 . These Fe2 O3 ions reacts with the water molecules and free electrons produced from the cathode and produces Fe (OH)2 precipitate . The movement of electrons from one electrode to another thus produces galvanic current.

3.2 Effect of pH Variation Seawater pH is typically limited to a range between 7.5 and 8.4 [12]. Table 1 exhibits the voltage measurement of graphite iron electrode after 1 h of deployment in the seawater collected from various locations of Bay of Bengal, at different pH. It is observed from Table 1 that the voltage rise is seen with rise in pH. Rise in pH is

Study on Suitable Electrode for Energy Harvesting … Table 1 Graphite–Iron voltage for different Ph Place Depth (m) OCV (V)

635

Voltage after 1 h (V)

pH

Kalpakkam

10

1.043

1.058

8.3

Mahabalipuram

15 26 5

0.969 1.046 1.060

1.009 0.984 1.083

8.2 7.9 8.1

Pondicherry

10 15 10

0.916 1.050 1.054

1.029 1.059 1.054

8.0 8.0 8.1

Chennai port

25 50 75 5 10 15 20 5

1.071 0.943 0.93 1.07 1.10 1.10 1.12 1.08

1.065 1.051 1.085 1.07 1.08 1.08 1.09 1.096

8.0 7.9 7.7 8.1 8.1 8.1 8.1 8.3

Poompuhar 1

10 16 5

1.08 1.08 1.03

1.097 1.091 1.119

8.1 8.1 8.4

Poompuhar 2

10 15 5

1.04 1.122 1.036

1.03 1.007 1.004

8.1 8.1 8.1

10 15 20

0.98 1.04 1.03

1.031 1.049 1.039

8.1 8.0 8.0

Cuddalore

because of more ionic movements, that is free ions presence is more in the surface region.

3.3 Effect of Surface Area Generally, increasing the surface area of the electrodes facing each other decreases resistance thus carries more current. The efficiency remains mostly same but the process proceeds at faster rate. From Table 2 it is inferred that the change in surface area of both the electrodes, do not have a significant effect on the electric potential of the galvanic cell.

636 Table 2 Surface area and electric potential effect

G. Nithya Sivakami et al. Surface area (cm2 )

Electric potential (V)

6.64 9.19 17.39 22.76 28.13

1.18 1.151 1.128 1.113 1.17

Fig. 5 Day-wise observance of corrosion effect on the cell

3.4 Corrosion Studies Corrosion Study observance, clear solution of seawater in which the electrode couple were subjected. First day, a minimal sign of rust on the electrode, no precipitate was observed on the solution. Second day, some signs of rust on the electrode were observed. But, the solution was clear and with a tinge of orange-yellow with no precipitate. Some particles in suspension but barely noticeable. On third day, partially covered with rust on the electrode. A sign of precipitate and solution was yellowish orange. Some particles in suspension which is very noticeable are seen. Fourth day almost half of the electrode was covered in rust. Some orange precipitate found in the beaker. Solution has a yellowish-orange tinge. Orange particles were in suspension. Fifth day, orange precipitate was evident and dominant at the bottom of the beaker. Solution has a definite yellowish-orange tinge. Solution was cloudy with orange particles in suspension have shown in Fig. 5. It is observed from the corrosion study that the graphite electrode does not exhibit any significant change in size or weight of the material deployed, whereas in the iron electrode, weight loss was observed and the effect of galvanic corrosion was observed on the surface of the electrode and little amount of rusted particles were loaded onto the graphite electrode. It is clear that only replacement of anode electrode is required.

Study on Suitable Electrode for Energy Harvesting … Table 3 Estimation of corrosion rate Time (h) Weight of iron electrode (g) – 24 48 72 96 120

75.401 74.532 74.114 74.100 74.076 74.048

637

Weight loss (g)

%Weight loss

Corrosion rate (mm/year)

– 869 1287 1301 1325 1353

– 1.153 1.706 1.725 1.757 1.794

– 9.4 6.9 4.7 3.5 2.9

Weight-Loss Studies Weight loss is one of the important parameter. It was found that 1.79% of weight loss for 5 days deployment of the cell in the electrolyte. Also, it is noticed from Table 3 that the % weight loss remains stable after 48 h of deployment, which shows that it is effective to utilize iron electrode in seawater-activated batteries. Since Graphite, electrode do not require any replacement, it is affordable to replace one of the electrode. Corrosion Rate From Table 3 the corrosion testing carried out for 5 days shows that the corrosion rate decreases with increase in time. This is because of the formation of product layer over the iron electrode layer. Also it is observed that the electric potential does not drop down on formation of adhesive layer. The electric potential remains within the range of 1.0–1.1 V, in electrolyte whose pH of 8.2.

4 Conclusion For the development of seawater-activated battery, parameter with respect to electrode like pH of the electrolyte, surface area of the electrode and the corrosion effect of the coupled electrode were studied. And, it is finalized the usage of Graphite and Iron as the electrodes in development of seawater-activated batteries. Future Work With the knowledge gained above, it is further decided to extend the work for development of sea water batteries using Graphite and Iron material as electrodes by performing the following: • Circuit analysis • Stack designing-flow pattern, compartment spacing, cell arrangements • Cell Construction and studies. Acknowledgements This part of work is supported by Underwater Acoustic Research lab, Department of ECE, SSN College of Engineering, Chennai.

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References 1. Mantia FL, Pasta M, Deshazer HD, Logan BE, Cui Y (2011) Batteries for efficient energy extraction from a water salinity difference. Amer Chem Soc 1810–1813. https://doi.org/10. 1021/nl200500s 2. Reinhart FM, Jenkins JF (1972) Corrosion of material in surface seawater after 12 and 18 months of exposure. Nat Tech Inf Service 3. La Violete PE (1967) Temperature, salinity, and density of the world’s seas: Bay-of Bengal and Andaman sea 4. Thorley RAW (2004) Reactions between sodium and various carbon bearing compounds, pp 13–16 5. Linden D, Reddy TB (2001) Handbook of batteries, 3rd edn 6. Ailor WH (1971) Hand book of corrosion testing and evaluation. Wiley, New York 7. Njoku CN, Onyelucheya OE (2015) Response surface optimization of the inhibition efficiency of Gongronema latifolium as an inhibitor for aluminium corrosion in HCl solutions. Int J Mat Chem 5(1):4–13 8. Rahmanto G, Nuryanto R (2002) Corrosion rate of copper and iron in seawater based on resistance measurement. J Coast Develop 5(2):67–74 9. Miller BA (1998) The galvanic corrosion of graphite epoxy composite materials coupled with alloys 10. Lide DR (2006) CRC handbook of chemistry and physics, 7th edn. CRC Press, Boca Raton, FL. ISBN 0-8493-0487-3 11. Zhang (2011) Galvanic corrosion, Wiley, pp 123–143 12. Chester J, Roy T (2012) Marine geochemistry, Blackwell Publishing. ISBN 978-1-118-34907-6

Surrogate-Based Optimization of a Biplane Wells Turbine Tapas K. Das

and Abdus Samad

Abstract Oscillating Water Column (OWC) is one of the most popular wave energy converters being used for the last two decades. The pneumatic energy from water waves inside the air chamber of OWC is converted into mechanical energy with the help of Wells turbine. Biplane Wells turbine has inherent advantage over the monoplane turbine in terms of starting characteristics and operating range. The main parameters affecting the performance of biplane Wells turbine are the gap between the planes and the offset angle between blades in two planes. Surrogate-based optimization represents the optimization methodologies that use surrogate modelling techniques to find out maxima or minima. Surrogate modelling techniques are very useful for design analysis that uses computationally expensive codes such as Computational Fluid Dynamics (CFD). In the present work, flow over a biplane Wells turbine is simulated using CFD and optimized using surrogate approach. Radial Basis Neural Network (RBNN) method is used to create the surrogate. Blade thickness and the offset angle defining the circumferential position of blades in two planes are considered as the two variables and the objective function is taken as efficiency of the turbine rotor. The comparison of performance between the reference blade and the optimized blade is presented in this article. Keywords Wells turbine · Biplane · Surrogate model · Radial basis function

Nomenclature ρ ω

Air density (kg/m3 ) Angular velocity (rad/s)

T. K. Das (B) · A. Samad Wave Energy and Fluids Engineering Lab, Ocean Engineering Department, Indian Institute of Technology Madras, Chennai 600036, TN, India e-mail: [email protected] A. Samad e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_48

639

640

c η ϕ R T CT P0 P0∗ Q ua ut

T. K. Das and A. Samad

Chord length (m) Efficiency Flow coefficient Rotor tip radius (m) Torque (N-m) Torque coefficient Total pressure drop (Pa) Pressure drop coefficient Volume flow rate (m3 /s) Inlet air velocity (m/s) Tip speed velocity (m/s)

Abbreviation OWC RMS SST RSM ANN KRG RBNN

Oscillating Water Column Root Mean Square Shear Stress Transport Response Surface Methodology Artificial Neural Network Kriging Radial Basis Neural Network

1 Introduction Among the various wave energy conversion devices available, Oscillating Water Column (OWC) is the most used and maximum number of prototypes available till date. The reason behind the popularity of OWC is the simplicity in design and less number of complicated mechanical parts. The OWC (Fig. 1) contains an air chamber where the piston-like motion of the trapped ocean water is converted to an oscillating air flow. This oscillating air flow is used to rotate a bidirectional turbine—a turbine which rotates in same direction irrespective of the direction of airflow. A generator connected with the turbine generates electricity. Both impulse and reaction turbines can be used in OWC and both have their own advantages and disadvantages. Wells turbine is a type of reaction turbine which has been researched extensively. Raghunathan [1] gave a detailed analysis of different parameters affecting the performance of Wells turbine. It was shown that a monoplane turbine’s performance is limited by the pressure drop across the rotor blade. A multiplane turbine can be used in wave energy device which produces pressure drop larger than the limit for single plane turbine. The main geometric parameters affecting the performance of a biplane turbine are the gap between the planes (gap to chord ratio) and the offset angle—the angle defining the circumferential position of blades in the two planes of

Surrogate-Based Optimization of a Biplane Wells Turbine

641

Fig. 1 Schematic diagram of an OWC

Fig. 2 Stagger angle between the planes

Plane 1 Plane 2

Offset angle

biplane Wells turbine (Fig. 2). Experimental studies [2–4] were carried out to see the effect of different parameters on the performance of biplane Wells turbine. Shaaban [5] carried out numerical analysis to study the effect of gap to chord ratio on the turbine performance. It was shown that the downstream rotor provides only 10–30% of the total torque of the turbine. Surrogate-based model also known as metamodel or low-fidelity model is an effective approach to design computationally expensive models such as Computational Fluid Dynamics (CFD) or experimental models. Surrogate-based models were mainly developed for use in aerospace systems where CFD simulations can become computationally expensive. Quiepo et al. [6], Forrester and Keane [7] have given comprehensive review about the recent advances and challenges of surrogate-based design and optimization. Among the different types of surrogate modelling techniques available, Response Surface Methodology (RSM), Artificial Neural Network (ANN), Kriging (KRG) and Radial Basis Neural Network (RBNN) method are the most popular ones used in engineering applications. Halder and Samad [8], Halder et al. [9] applied multiple surrogate-based design optimization to improve the efficiency and operating range of a monoplane Wells turbine. Jin et al. [10] carried out a comparative analysis of different surrogate modelling techniques based on overall performance, efficiency, simplicity, robustness and transparency. It was seen that RBNN excels in all the categories considered in [10].

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Based on the literature review, a biplane turbine with four blades in each plane having blade profile NACA0015 is considered as the reference geometry in the present work. A single objective optimization is carried out using RBNN surrogate modelling technique. Two design variables are considered: the maximum blade thickness and the offset angle. The objective function for this optimization problem is to maximize the efficiency.

2 Methods 2.1 Reference Geometry Figure 3 shows the reference biplane Wells turbine with four blades in each plane. The blades are having NACA0015 profile with a chord length of 0.125 m. The turbine has 1 mm tip gap between the blade tip and the blade casing. The overall solidity of the turbine is 0.64 (0.32 per plane). The blades are fixed at 45° offset angle between the planes. As the turbine has a symmetry around the rotational axis, only one-fourth of the full turbine is considered for numerical analysis. The computational domain consists of one blade from both the planes. Table 1 lists the geometric dimensions of the turbine. For the purpose of validation of the numerical results, the geometry is taken same as the one used in [2] for experimental study.

Oscillating air flow

Fig. 3 A biplane Wells turbine

Gap between planes

Offset angle Table 1 Geometric parameters

Parameter

Specification

Blade profile

NACA0015

Blade chord length

0.125 m

Hub radius Tip radius

0.2 m 0.294 m

Tip clearance

0.001 m

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643

2.2 Numerical Analysis Figure 4a shows the computational domain considered for analysis. The upstream side is taken as five times the chord length and the downstream side is ten times of chord length. The gap between the planes is 1.5 times the chord length. Figure 4b, c shows the unstructured mesh with prism layers near the boundary of blades. The unstructured mesh is created using ANSYS ICEM CFD v16.0. The prism layer has 12 layers and the distance of the first layer from the boundary of the blade is 0.000012 m. The height of the first layer is calculated keeping the Y + value less than 1. The fine boundary layers are used to capture the effect near blade wall more accurately. The finite volume based commercial code ANSYS CFX V16.0 is used for the numerical simulation. Reynold’s Averaged Navier–Stokes (RANS) equation is discretized using finite volume method to solve the continuity, momentum and energy equations. SST k- turbulence model is used to capture the near wall effects more accurately. The fluid (air) is incompressible and a steady flow is considered. A steady velocity is considered at the inlet and ambient pressure at the outlet. The periodic boundary condition is imposed on the circumferential side and the hub, casing and rotor blade surface have no-slip boundary condition. The convergence criteria is con-

(a) Upstream Blade 1.4C 5C Velocity

10C Downstream Blade

(b)

Periodic

(c)

Fig. 4 a Computational domain, b mesh in the hub, c mesh near blade surface

Pressure

644

Fig. 5 Grid independence test

Parameter

Description

Flow domain

Two blades (one blade/plane)

Mesh Fluid (air)

Unstructured Incompressible

Interface Inlet

Periodic Velocity

Outlet

Pressure

Residual criteria Mass imbalance

1 × 10−6 0.001 0.10

Torque coefficient C T

Table 2 Boundary conditions

T. K. Das and A. Samad

0.08

0.06

0.04 1.8x106 2.4x106 3.0x106 3.6x106 4.2x106

Number of elements

sidered as RMS residual less than 1 × 10−6 and mass imbalance less than 0.001. The rotational speed of both the rotor is fixed at 2500 rpm. Table 2 shows all the boundary conditions used to solve the equations. As the computational requirement is very high for this type of CFD simulations, the numerical simulation is done using a supercluster having a total computational power of 97 TFlops. The supercluster consists of IBM System with highly optimized servers populated with 2 X Intel E5-2670 8 C 2.6 GHz processor. Using this highperformance computing system, the average time for each simulation is 10–12 h. CFD simulations require an optimum number of mesh elements to reduce the computational time. To achieve an optimum number of elements for the present geometry, a grid independence test is carried out and the result is shown in Fig. 5. The number of elements is varied from 1.8 to 4.2 million. It can be seen that the torque coefficient does not vary after 2.4 million elements. So the optimum element number is taken as 2.4 million for this numerical study.

Surrogate-Based Optimization of a Biplane Wells Turbine Table 3 Design variables Design variables

645

Lower limit

Upper limit

Maximum blade thickness

12% of chord length

30% of chord length

Blade offset angle between planes

0°

45°

2.3 Optimization Method The first step in the optimization process is to select the design variables and decide the design space. In this case, two design variables are selected: the maximum blade thickness and the blade offset angle between the planes. The blade chord length is kept fixed. The range of design variables are shown in Table 3. The design space is created using the Design of Experiments (DOE) techniques described by Myers et al. [11]. In the present work, DOE is carried out using three-level full factorial method. Nine different design points are selected and the objective function is evaluated in these points using the numerical analysis mentioned before. The objective function values at these design points are used to construct the surrogate for the optimization process. Radial basis neural network is a type of neural network that uses radial basis function. RBNN consists of three layers: the first layer is the input layer, second layer is a hidden layer with radial basis function as activation functions and the output layer. The parameters used for fitting the surrogate are the spread constant and the error goal which is defined by the user. The MATLAB function newrb is used to design radial basis function neural network.

3 Result and Discussion As per the literature available on Wells turbine, the performance of the turbine is expressed using four nondimensional parameters, which are given as follows: i. The torque coefficient: CT 

T ρω2 R 5

(1)

ii. The pressure drop coefficient: P0∗  iii. The efficiency:

P0 ρω2 R 2

(2)

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Fig. 6 Validation with experimental results

0.8

Present result Experimental, Gato & Curran(1996)

0.7

CT , P*0 ,

0.6 0.5

P*0

0.4 0.3 0.2

CT

0.1 0.0

0.08

0.12

0.16

0.20

0.24

Flow coeffcient

η

Tω P0 Q

(3)

ua ut

(4)

iv. Flow coefficient: ϕ

The turbine is simulated at five different flow coefficient from 0.08 to 0.22. As the rotational speed is constant, the tip velocity remains constant for any change in flow coefficient. Only the inlet flow velocity changes with change in the flow coefficient. The numerical results are first validated with experimental results of Gato and Curran [2]. Figure 6 shows the present numerical results are in good match with experimental results and the deviation is within ±5% for all three parameters. Once the validation is done, the surrogate model is constructed from the sample points using the radial basis neural network method. Figure 7 shows the response surface created using the surrogate model. The axis of Fig. 7 is normalized, where zero is the lower limit and one is the upper limit for variables. The optimal point is found using sequential quadratic programming. The optimum configuration has a thickness of 17.5% of chord length and blade offset angle 43°. The maximum efficiency from the numerical optimization is found to be 62.9% which is 2.77% more than the reference geometry (Fig. 8). A numerical analysis is carried out at the optimum point and the result matches with that of the surrogate-based optimization result (Table 4).

Surrogate-Based Optimization of a Biplane Wells Turbine

647

0.65

Efficiency

0.6 0.55 0.5 0.45 0.4 1 1 0.5

0.5

Stagger angle 0

Thickness

0

Fig. 7 Surrogate predicted response surface 0.75

Efficiency

Fig. 8 Comparison of reference and optimized geometry

0.50

0.25

Reference Optimized

0.00 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32

Flow coeffcient

4 Conclusion A numerical study is carried out and optimum configuration for a biplane Wells turbine is obtained using surrogate-based optimization and CFD-based numerical analysis. The performance of optimum geometry is compared with the reference geometry. 2.77% increase in efficiency is obtained using the optimum rotor blade configuration. Also, it can be seen that there is not much variation in optimum geometry compared to the reference geometry. Other design variables and different surrogate-based techniques can be explored in future to have a better optimum configuration.

648 Table 4 Optimization results

T. K. Das and A. Samad Model

η (Surrogate)

η (CFD)

Reference Optimized

– 0.629

0.612 0.630

References 1. Raghunathan S (1995) The wells air turbine for wave energy conversion. Prog Aerosp Sci 31:335–386. https://doi.org/10.1016/0376-0421(95)00001-F 2. Gato LM, Curran R (1996) Performance of the biplane wells turbine. Trans ASME 118:210–215 3. Raghunathan S, Tan CP (1983) The performance of biplane wells turbine. J Energy 7:741–742 4. Raghunathan S, Setoguchi T, Kaneko K (1989) The effect of inlet conditions on the performance of wells turbine. J Energy Res Technol 111:37. https://doi.org/10.1115/1.3231399 5. Shaaban S (2012) Insight analysis of biplane wells turbine performance. Energy Convers Manag 59:50–57. https://doi.org/10.1016/j.enconman.2012.02.006 6. Queipo NV, Haftka RT, Shyy W, Goel T, Vaidyanathan R, Kevin Tucker P (2005) Surrogatebased analysis and optimization. Prog Aerosp Sci 41:1–28. https://doi.org/10.1016/j.paerosci. 2005.02.001 7. Forrester AIJ, Keane AJ (2009) Recent advances in surrogate-based optimization. Prog Aerosp Sci 45:50–79. https://doi.org/10.1016/j.paerosci.2008.11.001 8. Halder P, Samad A (2016) Optimal wells turbine speeds at different wave conditions. Int J Marine Energy 16:133–149. https://doi.org/10.1016/j.ijome.2016.05.008 9. Halder P, Samad A, Thevenin D (2017) Improved design of a wells turbine for higher operating range. Renew Energy 106:122–134. https://doi.org/10.1016/j.renene.2017.01.012 10. Jin R, Chen W, Simpson TW (2001) Comparative studies of metamodelling techniques under multiple modelling criteria. Struct Multidiscip Opt 23:1–13. https://doi.org/10.1007/s00158001-0160-4 11. Myers RH, Montgomery DC, Anderson-cook CM (2017) Response surface methodology. Metallurgia Italiana. https://doi.org/10.1017/cbo9781107415324.004

Tidal Energy Estimation of Potential Tidal Inlets Along the East Coast of India Vikas Mendi, N. Amaranatha Reddy, Jaya Kumar Seelam and Subba Rao

Abstract The power consumption is increasing with modernization of infrastructure and with the depleting fossil fuels. The need to look for alternate sources of energy generation has already reached a peak. The production of power from renewable energy sources is considered to be on a large scale in the near future because of the abundant sources across the country. One of the most reliable sources is the tidal energy as it can be extracted both by kinetic and potential means at the tidal inlets. The process of extracting tidal potential energy by storing the water during the high tide and release during low water is a well-established method. However, there are many parameters that are to be considered for the potential energy extraction. Two such important parameters, i.e. tidal range and basin area are considered in this study. The interrelationship between these two parameters and its overall influence on potential tidal energy estimation is studied. Along the four coastal states, excluding the Gulfs, around 250 tidal inlets have been identified (Vikas, M.Tech. thesis, 2015 [8]). Considering the standards of existing tidal power plants, tidal energy sites for energy extraction are estimated and will be presented in this paper. Keywords Tidal energy · Inlet · Basin area

V. Mendi (B) · N. Amaranatha Reddy · S. Rao National Institute of Technology Karnataka, Surathkal, Mangalore 575025, Karnataka, India e-mail: [email protected] N. Amaranatha Reddy e-mail: [email protected] S. Rao e-mail: [email protected] N. Amaranatha Reddy Madanapalle Institute of Technology and Science, Madanapalle, India J. K. Seelam CSIR-National Institute of Oceanography, Dona Paula, Goa, India © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_49

649

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1 Introduction Tidal energy is one of those forms of renewable energies which is gathering researchers attention in the recent past. This is due to the advantages of extracting energy from tides over other forms of energy. Tidal energy is considered as clean and non-depleting. The tide is a cyclic process that occurs over a 12-h duration mainly due to the attractive force of the moon. Like the traditional hydropower generated from dams, tidal energy also can be produced by storing the water that flows between consecutive high and low tides to attain required head. There have been discussions in the literature about the minimum height of the tide that can be considered suitable for energy extraction by construction of barrage. However, the head of water stored in the tidal basin is dependent on two other important factors, i.e. the basin area and the inlet throat width. The inlet throat width should be such that it facilitates the maximum amount of water to enter the tidal basin during the spring tide and also accommodates enough number of turbines for energy extraction. Basin area, of course, has to be large enough to store the incoming waters during the high tide. An estimation of tidal energy is done along the east coast of India to prove the potential of the tidal energy resource and address the future energy needs. Global Scenario of Tidal Energy Tidal energy globally is being harnessed from the Roman times. The phenomenon of tides was demonstrated in many ways by various scientists and researchers. However, Sir Isaac Newton explained the phenomenon in a most convincing way. The necessity to reduce CO2 emissions and a gradual increase in cost of fossil fuel have resulted in a significantly increased need for tidal energy [6]. Today, tidal energy is increasingly being considered as a potential source of renewable energy around the world [2]. Extreme tides are found in many locations across the globe. The highest tides around the world are shown in Fig. 1. The first major hydroelectric plant was put to operation in 1967 that used the energy of the tides to generate electricity. It produced about 540,000 kW of electricity [3]. Studies have shown that the European territorial waters have 106 locations for possible extraction of tidal energy that would provide electricity of 48 TW per year. It is estimated that around 50,000 MW of installed capacity is achievable along the coast of British Columbia alone. There are greater predictions of extracting energy of about 90,000 MW off the north-west coast of Russia and about 20,000 MW at the inlet of Mezen River and White Sea of Russia. Table 1 gives the highest available tidal levels in some of the regions that have a greater potential to establish tidal power stations [5]. Tidal power plants have already been set up at some of these locations and some are still in the planning phase. The main characteristics of four exiting tidal power plants that were constructed after World War II and still exist are given in Table 2 [5]. The oldest, existing and operating tidal power plant is the La Rance tidal power plant in France. Its capacity is 240 MW supported by 24 bulb units working in both flow directions extracting tidal energy. The basin area is 22 km2 .

Tidal Energy Estimation of Potential Tidal Inlets …

651

Fig. 1 High potential areas for tidal resources (Source http://westcoastpower.ca) Table 1 Highest tides of the global ocean [5] Site Country

Tidal elevation (m)

Bay of Fundy

Canada

16.2

Severn Estuary

England

14.5

Port of Ganville La Rance Puerto Rio Gallegos

France France Argentina

14.7 13.5 13.3

Bay of Mezen (White Sea)

Russia

10.0

Penzhinskaya Guba (Sea of Okhotsk)

Russia

13.4

Gujarat

India

11.0

2 Study Area Indian coastline has western and eastern coastal plains which possess distinct features. India has 7516 km of coastline including Andaman and Nicobar Islands. The study area considered for this work is the east coast of India comprising four maritime states viz. Tamil Nadu, Andhra Pradesh, Odisha and West Bengal. The east coast is a wide stretch of land width of plain varies from 100 and 130 km, stretches from Tamil Nadu in the South to West Bengal in the North. Figure 2 shows the study area considered in this study.

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Table 2 Existing tidal power plants [5] Site

Country

Bay area (km2 )

Avg. tide (m)

Installed power (MW)

La Rance Sihwa Annapolis

France South Korea Canada

22 30 15

8.55 5.6 6.4

240 254 18

Jiangxia

China

1.4

5.08

3.9

Kislaya Guba

Russia

1.1

2.3

0.4

Fig. 2 Study area showing maritime states of east India

Tidal Energy Estimation of Potential Tidal Inlets …

653

3 Methodology 3.1 Identification of Tidal Inlets The tidal inlets are identified in Google Earth along the east coast of India. A total of 252 identified inlets are listed in Table 3.

3.2 Calculation of Tidal Basin Area The basin area is one of the important parameters to consider while estimating the energy potential. The head available depends on the volume of water that is stored in the tidal basin. Basin areas for the tidal inlets along the east coast of India are listed in Table 3. Basin area is calculated by the Polygon tool in Google Earth and verified by online area calculation tool. Basin areas of some existing tidal power plants are listed in Table 4.

3.3 Calculation of Tidal Prism Tidal prism is obtained by first simulating for tidal range at the identified tidal inlets. MIKE21 flow model is used to obtain the tidal range. MIKE is from Danish Hydraulic Institute numerical model. The flow model FM is a powerful simulation tool of MIKE21 for two- and three-dimensional hydrological modelling developed by the Danish Hydraulic Institute. The 2D and 3D models are named as MIKE21 and MIKE3 that are based on finite volume method and use flexible mesh for simulations. This hydrological modelling software has proved successful in replicating the complex oceanographic, coastal and estuarine environments. The flow model (FM) houses Hydrodynamic Module which is based on the numerical solution of the two-dimensional shallow water equations—the depth-integrated incompressible Reynolds averaged Navier–Stokes equations shown below. ∂u ∂u ∂h ∂u +u +v − f v  −g ∂t ∂x ∂y ∂x ∂v ∂v ∂h ∂v +u +v − f u  −g ∂t ∂x ∂y ∂y   ∂h ∂h ∂h ∂u ∂v +u +v  −h + ∂t ∂x ∂y ∂x ∂y

Name

SRNP

Thottavilai

Manapad

Govindamal colony

Veerapandianpattinam

Mangaladevi

Punnaikayal

Veppalodai

Sippikulam

Vaippar

Velayudhapuram 2

Velayudhapuram 1

Vembar

Mookaiyur

Valinokkam

Sethu karai

Muthariyarnagar

Mandapam

Atrangarai

No.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

07.26

33 17.82

9°

14.43

22.66 42.40 57.81

08.59

27.09

15

9°

20

42.44

9° 17 10.54

9°

9°

40.49

14 55

16.55

55.95

79°

01

34.80

79° 08 46.08

78°

78°

54

78° 49 58.85

29

06.31

9° 11 03.77

78°

78°

22

78° 18 56.38

78°

17

78° 16 04.43

78°

14

78° 38 51.98

47.97

04

12

35.12

78° 07 46.10

78°

78°

07

9° 07 42.92

9°

9°

16.25

02

9° 01 27.78

00

8° 59 19.60

8°

57

8° 38 27.51

8°

8°

20.70

31

78° 07 35.97

8° 30 12.50

32.06

78° 07 22.98

78°

03

8° 22 48.48

8°

21.69

77° 48 03.67

8° 09 27.19

14

Longitude

Latitude

Table 3 Locations of identified tidal inlets and their basin areas

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

State

Ramanathapuram

Ramanathapuram

Ramanathapuram

Ramanathapuram

Ramanathapuram

Ramanathapuram

Tuticorin

Tuticorin

Tuticorin

Tuticorin

Tuticorin

Tuticorin

Tuticorin

Tuticorin

Tuticorin

Tuticorin

Tuticorin

Tirunelveli

Tirunelveli

District

1.15

1.08

1.05

1.03

0.96

0.91

0.88

0.86

0.86

0.85

0.85

0.85

0.84

0.84

0.84

0.84

0.84

0.85

0.85

Avg. tide (m)

(continued)

2.176459

2.22341

0.0449

0.73338

0.210741

0.834904

0.501879

0.180685

0.111256

0.495705

0.006704

0.222357

5.53929

0.044125

0.008378

0.0631

0.69242

0.26724

0.07861

Basin area (km2 )

654 V. Mendi et al.

Kaliyanagari

S.P.Pattinam 2

S.P.Pattinam 1

Muthukuda

Arsanagaripattinam

Embakkottai

Gopalapattinam

Sannathi

Kottaippattannam

Tandalai

Manamelkudi 2

Manamelkudi 1

30

31

32

33

34

35

36

37

38

39

Muthuramalingapattinam 9°

26

29

Velangudi

25

28

Pudupattinam

24

Odavayal

Alikkudi

23

27

Karankadu

22

45.98

15.22

40 13.72

9°

01.60

59

59.52

22.51

56.41 54.97

9°

40.59

9°

16.23

51.10

79° 15 11.75

40.52

10° 03 09.14

79°

13

79° 13 34.38

79°

11

79° 16 02.79

10°

25.38

05.77

79° 09 43.35

79°

09

10° 02 41.10

00

9° 58 16.40

56

9° 55 04.82

54

79° 07 25.48

23.50

9° 53 02.44

79°

07

79° 06 22.15

79°

05

79° 04 40.94

79°

02

79° 01 51.35

78°

78°

58

79° 07 45.21

15.95

05.81

78° 58 14.97

78°

57

9° 51 38.29

9°

50

9° 50 01.48

48

9° 46 08.24

45

9° 44 53.87

9°

9°

30.79

39

9° 38 43.48

9°

Thiruppalaikudi

21

31

78° 57 54.56

9° 23 32.78

Pudhuvalasai

20

Longitude

Latitude

Name

No.

Table 3 (continued)

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

State

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Ramanathapuram

Ramanathapuram

Ramanathapuram

Ramanathapuram

Ramanathapuram

Ramanathapuram

Ramanathapuram

Ramanathapuram

Ramanathapuram

District

1.28

1.00

0.87

1.35

1.38

1.64

1.38

1.40

1.39

1.40

1.40

1.42

1.43

1.44

1.44

1.41

1.41

1.39

1.32

1.19

Avg. tide (m)

(continued)

0.055572

0.024046

0.006069

0.026079

0.016009

0.077706

0.176455

0.111707

0.30565

0.164615

0.03392

0.028825

0.08309

0.02569

0.00916

0.020365

0.130146

0.441355

0.096108

0.003

Basin area (km2 )

Tidal Energy Estimation of Potential Tidal Inlets … 655

Name

Mumpalai 5

Mumpalai 4

Mumpalai 3

Mumpalai 2

Mumpalai 1

Kandanivayal

Subramanyapuram

Ravuttanvayal

Sembiyan 3

Sembiyan 2

Sembiyan 1

Manthirippattinam 2

Tiruvathevan 3

Tiruvathevan 2

Tiruvathevan 1

Palliya kulam

Manthiripattinam

Perumagalur

Adaikkathevan

No.

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

Table 3 (continued)

24.13

04 19.94 59.66

14

16.79

29.67

42.31 48.01

56.48

57.20 24.56

10°

12

14.54

10° 11 12.37

10°

10

10° 10 12.50

10°

09

22.27 42.56

79°

16

32.57

79° 15 10.46

79°

14

79° 14 19.90

79°

14

79° 14 28.12

13

43.06

10° 09 25.34

79°

79°

13

79° 13 46.05

79°

13

79° 13 42.00

79°

13

79° 14 15.08

79°

79°

14

79° 14 23.42

32.32

08

22.66

79° 14 53.26

79°

15

10° 09 14.22

10°

10°

10.64

08

10° 08 06.07

10°

07

10° 06 32.40

10°

06

10° 04 55.45

10°

10°

24.28

04

10° 04 18.44

10°

43.49

79° 15 13.89

10° 03 24.41 03

Longitude

Latitude

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

State

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

District

1.10

1.10

1.10

1.10

1.10

1.62

1.22

1.49

1.49

1.74

1.40

1.36

1.72

1.27

1.49

1.39

1.34

1.27

1.43

Avg. tide (m)

(continued)

0.139753

0.023325

0.008744

0.008888

0.002111

0.002582

0.008422

0.032301

0.02015

0.003587

0.001375

0.00213

0.069066

0.026935

0.011239

0.041276

0.050008

0.023356

0.053517

Basin area (km2 )

656 V. Mendi et al.

Keezhathottam

Thuraikkadu

Kodiyakadu

Kodikkarai

Vedaranyam

Madavilagam

Thopputhurai

Naluvethapathi

Vanvanmahadevi

Vettaikarairuppu

Pudupalli

67

68

69

70

71

72

73

74

75

76

Sarabendrarajanpattinam 10°

64

66

Manora

63

Kallivayal

Nayagathivayal

62

65

Marakkavalasai

61

40.22 01.58

32.70

26.87

10°

34

35.33

10° 33 27.11

10°

31

10° 29 31.52

10°

12.20

15.25 42.19

79°

51

27.44

79° 51 37.09

79°

51

79° 52 00.91

79°

52

79° 52 43.26

10° 22 30.40 24

80° 00 44.46

10° 20 04.06

40.93

79° 50 10.80

79°

45

10° 16 33.46

10°

40.33

79° 44 21.93

10° 18 45.00 16

79° 31 13.21

22.36

10° 17 40.96

79°

19

79° 18 25.85

79°

17

79° 22 02.80

56.66

03.09

79° 16 46.63

79°

16

10° 16 50.09

15

10° 15 29.74

10°

15

10° 14 32.71

10°

Ravuthanvayal

60

13

79° 17 05.02

10° 13 01.99

Villunivayal

59

Longitude

Latitude

Name

No.

Table 3 (continued)

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

State

Nagapattinam

Nagapattinam

Nagapattinam

Nagapattinam

Nagapattinam

Nagapattinam

Nagapattinam

Tiruvarur

Thanjavur

Pudukkottai

Nagapattinam

Nagapattinam

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

Pudukkottai

District

0.93

0.89

0.87

0.86

0.92

0.93

0.89

0.75

0.98

0.87

1.08

1.11

1.01

1.10

1.10

1.10

1.10

1.10

Avg. tide (m)

(continued)

0.014538

0.228025

0.250514

0.039556

2.719439

2.459958

0.015415

0.036212

0.132571

62.69245

20.83383

0.511646

0.019621

0.097401

0.002505

0.009299

0.003711

0.019497

Basin area (km2 )

Tidal Energy Estimation of Potential Tidal Inlets … 657

Name

Vizhunthamavadi

Tirupoondi

Velankanni

Nagapattinam

Thethinagar

Keezhaiyur 2

Keezhaiyur 1

Bharathi nagar

Akkampettai

Chandirapady

Kittiyandiyur

Veepanchery

Vanagiri

Pompuhar

Thirumullaivasal

Chinnakottaimedu

Pazhaiyar

Chinna vaaikaal

Ariyakoshti

No.

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

Table 3 (continued)

34.43

49 16.12 45.54

19.90

05

51

05.00

06.94

10.39 12.61

51

26.83

20.24

79° 46 48.83

56.10

11° 30 10.19

79°

49

79° 48 20.90

11°

31.50

11° 27 25.78

21

79° 50 31.36

29.31

11° 18 09.29

79°

51

79° 51 27.05

79°

79°

51

79° 51 13.56

79°

51

79° 51 12.90

79°

51

79° 51 07.36

79°

79°

51

79° 50 58.76

11°

08.77

19.66

79° 51 12.59

79°

51

11° 14 40.63

08

11° 06 38.56

11°

11°

13.62

01

10° 59 42.07

10°

57

10° 54 49.43

10°

53

10° 50 39.23

10°

10°

51.95

45

10° 40 40.76

10°

00.67

79° 51 24.50

10° 35 37.18 38

Longitude

Latitude

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

State

Cuddalore

Cuddalore

Nagapattinam

Nagapattinam

Nagapattinam

Nagapattinam

Nagapattinam

Nagapattinam

Nagapattinam

Nagapattinam

Nagapattinam

Nagapattinam

Nagapattinam

Nagapattinam

Nagapattinam

Nagapattinam

Nagapattinam

Nagapattinam

Nagapattinam

District

0.90

0.90

0.90

0.90

0.91

0.85

0.78

0.75

0.72

0.60

0.50

0.40

0.87

0.87

0.96

0.97

0.99

0.99

0.95

Avg. tide (m)

(continued)

0.025025

0.020924

4.64861

5.667055

11.13194

0.162057

2.662857

0.170666

0.112545

0.485465

0.860868

0.110315

0.015446

0.715906

0.271065

1.405773

0.83687

0.755958

0.01872

Basin area (km2 )

658 V. Mendi et al.

Name

Pudukuppam

Samiyaar

Cuddalore

Devanampattinam

Pudukuppam

Subauppalavadi

Aladimedu

Chinna veerampattinam

Puducherry

Muthaialpet

Vembalur

Odiyur

KPK

Sudurangapattinam

Kalpakkam

Kokkilamedu

Padur

No.

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

Table 3 (continued)

11° 16.26 19.96 39.54

21.48 53.21 44.04

12°

14.78

12°

33.84

12°

48

12.49

12° 34 34.00

30

12° 27 57.17

26

26.14 14.06

80°

14

56.52

80° 11 31.23

80°

10

80° 09 15.82

80°

08

80° 02 57.24

45.15

12° 19 23.34

79°

50

79° 49 50.89

79°

49

79° 49 20.75

79°

47

79° 47 36.99

79°

47

80° 02 54.61

47.45

52.18

79° 47 09.08

79°

45

12° 15 49.43

11°

57

11° 54 22.36

11°

52

11° 49 59.41

11°

46

11° 45 16.02

11°

44

11° 42 24.08

25.80

79° 46 34.96

11° 31 49.33 32

Longitude

Latitude

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

Tamil Nadu

State

Kancheepuram

Kancheepuram

Kancheepuram

Kancheepuram

Kancheepuram

Kancheepuram

Kancheepuram

Viluppuram

Puducherry

Cuddalore

Cuddalore

Cuddalore

Cuddalore

Cuddalore

Cuddalore

Cuddalore

Cuddalore

District

1.24

1.12

1.06

1.05

1.07

1.09

1.04

0.99

0.97

0.96

0.94

0.94

0.96

0.93

0.94

0.92

0.91

Avg. tide (m)

(continued)

3.513357

0.411493

1.565036

3.0822

2.775697

0.564603

29.92771

0.83948

7.567384

5.484487

0.00395

0.486699

2.720001

0.84595

1.692434

1.822467

3.31308

Basin area (km2 )

Tidal Energy Estimation of Potential Tidal Inlets … 659

Name

Srinivasapuram

Sathya Nagar

Athipatti

Karimanal

Shar

Chinnathota

Nalagamula

Konduru

Swanamukhi River

Kothapatnam

Srinivasa

Gunnampadia 2

Gunnampadia 1

No.

113

114

115

116

117

118

119

120

121

122

123

124

125

Table 3 (continued)

80° 18 58.11 80° 15 04.34 80° 14 54.28 80° 13 44.53 80° 09 15.61 80° 09 02.09 80° 07 47.80 80° 07 37.31 80° 07 40.83 80° 07 45.06

13° 27 59.83

13° 45 57.13

13° 49 04.26

13° 51 35.89

14° 01 45.12

14° 04 29.03

14° 07 32.16

14° 09 11.30

14° 11 21.95

14° 12 18.68

37.21

80° 20 19.79

80°

18

13° 14 01.72

13°

01.42

80° 17 21.52

13° 00 49.43 04

Longitude

Latitude

Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh

Tamil Nadu

Tamil Nadu

Tamil Nadu

State

Nellore

Nellore

Nellore

Nellore

Nellore

Nellore

Nellore

Nellore

Nellore

Nellore

Tiruvallur

Chennai

Chennai

District

1.19

1.20

1.20

1.20

1.20

1.18

1.19

1.19

1.19

1.22

1.22

1.22

1.22

Avg. tide (m)

(continued)

0.33146

12.58404

0.004552

0.002544

0.011132

0.010262

1.185671

1.417396

6.440022

0.008452

108.8603

0.108836

348.5286

Basin area (km2 )

660 V. Mendi et al.

Name

Gopalapuram 2

Gopalpuram 1

Nelaturu

Pathapalem

Koruturu

Ramudupalem

Utukuru

Ramathirtham

Isakapalle

Juvvaladinne

Ramayapatnam 2

Ramayapatnam 1

No.

126

127

128

129

130

131

132

133

134

135

136

137

Table 3 (continued) Longitude 80° 08 07.21 80° 08 15.43 80° 09 26.20 80° 10 37.10 80° 10 59.90 80° 11 04.38 80° 12 51.64 80° 09 43.47 80° 07 36.58 80° 06 01.91 80° 04 57.49 80° 02 56.41

Latitude

14° 13 12.14

14° 14 42.97

14° 19 09.88

14° 22 22.87

14° 28 26.58

14° 31 58.26

14° 35 24.43

14° 38 37.61

14° 44 23.28

14° 49 08.44

15° 02 44.09

15° 04 11.35

Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh

State

Prakasam

Prakasam

Nellore

Nellore

Nellore

Nellore

Nellore

Nellore

Nellore

Nellore

Nellore

Nellore

District

1.27

1.26

1.25

1.22

1.22

1.20

1.20

1.20

1.21

1.20

1.20

0.80

Avg. tide (m)

(continued)

1.371686

0.159462

3.150112

0.416098

0.194231

1.448175

2.6781

0.080784

6.4272

0.640105

0.071745

0.186187

Basin area (km2 )

Tidal Energy Estimation of Potential Tidal Inlets … 661

Name

Karedu

Pakala

Anantavaram 2

Anantavaram 1

Peddapattapalam

Motumala

Chintayigari palem

Kanuparthi

Peddaganjam

Pallepalem

Pullaripalem 3

No.

138

139

140

141

142

143

144

145

146

147

148

Table 3 (continued) Longitude 80° 05 11.59 80° 05 22.53 80° 06 16.17 80° 06 46.04 80° 06 55.49 80° 13 27.95 80° 14 20.39 80° 14 30.17 80° 15 48.42 80° 16 37.29 80° 18 42.28

Latitude

15° 11 19.72

15° 16 56.64

15° 18 47.12

15° 19 23.45

15° 21 10.58

15° 30 05.83

15° 32 41.39

15° 36 09.79

15° 38 00.38

15° 39 22.25

15° 43 07.86

Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh

State

Guntur

Prakasam

Prakasam

Prakasam

Prakasam

Prakasam

Prakasam

Prakasam

Prakasam

Prakasam

Prakasam

District

1.31

1.30

1.30

1.30

1.31

1.31

1.30

0.83

1.31

1.27

1.27

Avg. tide (m)

(continued)

0.518215

0.011288

0.018746

0.012705

3.13434

0.221384

0.576638

1.8506

2.087093

0.001635

0.823175

Basin area (km2 )

662 V. Mendi et al.

Name

Pullaripalem 2

Pullaripalem 1

Katari palem

Krupa nagar

Pandurangapuram

East Gollapallem

Gokarnamatam

Dindiadavala

Haripuram

LVD

Elachetladibba

RKP

No.

149

150

151

152

153

154

155

156

157

158

159

160

Table 3 (continued) Longitude 80° 19 15.33 80° 19 51.67 80° 22 58.52 80° 26 00.35 80° 32 40.18 80° 38 19.72 80° 41 51.21 80° 46 02.41 80° 49 54.57 80° 55 48.36 81° 04 00.91 81° 06 09.92

Latitude

15° 43 27.37

15° 43 43.90

15° 44 42.18

15° 46 35.94

15° 48 22.46

15° 51 13.72

15° 52 35.29

15° 52 52.03

15° 51 45.61

15° 42 42.08

15° 43 24.53

15° 54 34.96

Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh

State

Krishna

Guntur

Guntur

Guntur

Guntur

Prakasam

Prakasam

Prakasam

Prakasam

Prakasam

Krishna

Prakasam

District

1.27

1.26

1.26

1.27

1.28

1.28

1.29

1.29

1.29

1.30

1.30

1.30

Avg. tide (m)

(continued)

12.15045

0.145102

0.017576

2.119758

105.9531

105.9531

1.299581

0.517818

1.167374

2.808696

0.270737

0.030257

Basin area (km2 )

Tidal Energy Estimation of Potential Tidal Inlets … 663

Name

Ramakrishnapuram 2

Ramakrishnapuram 1

Palakayatippa

Machilipatnam

Polatitippa

Chlilkalapudi

Kara agraham

Gokavaram

Tallapalem

Kanuru

Kruthivennu

Peda Gollapalem

No.

161

162

163

164

165

166

167

168

169

170

171

172

Table 3 (continued) Longitude 81° 06 13.53 81° 07 50.47 81° 10 24.88 81° 11 10.10 81° 12 05.76 81° 12 24.18 81° 14 13.68 81° 14 54.15 81° 15 58.00 81° 23 46.99 81° 29 23.23 81° 32 39.44

Latitude

15° 56 47.11

15° 56 52.91

15° 58 25.50

16° 04 46.67

16° 06 13.64

16° 08 38.65

16° 10 46.49

16° 14 21.34

16° 15 19.48

16° 16 43.68

16° 20 37.93

16° 21 19.62

Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh

State

Krishna

East Godavari

Krishna

Krishna

Krishna

Krishna

Krishna

Krishna

Krishna

Krishna

Krishna

Krishna

District

1.32

1.30

1.27

1.27

1.26

1.26

1.26

1.26

1.25

1.26

1.26

1.26

Avg. tide (m)

(continued)

21.50382

33.05684

7.845563

4.37122

6.753883

0.908234

0.057091

0.280135

0.107469

2.830025

0.146708

0.075524

Basin area (km2 )

664 V. Mendi et al.

Name

Chinna Gollapalem

Marritippa

Odalaravu

Komaragiri patanam

Gachakayala pora

Kothapalem

Gadimoga

Sasikanth Nagar

Nemam

Mulapeta 2

Mulapeta 1

Pentakota

No.

173

174

175

176

177

178

179

180

181

182

183

184

Table 3 (continued) Longitude 81° 43 06.80 81° 57 10.98 82° 02 01.04 82° 08 38.60 82° 16 51.49 82° 20 22.34 82° 20 58.07 82° 18 07.94 82° 18 49.23 82° 21 44.42 82° 36 02.01 82° 42 11.08

Latitude

16° 20 55.90

16° 19 09.08

16° 24 20.81

16° 26 27.49

16° 29 55.72

16° 35 42.11

16° 43 58.91

16° 59 09.56

17° 02 17.02

17° 05 21.55

17° 06 04.68

17° 17 28.00

Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh

State

East Godavari

East Godavari

East Godavari

East Godavari

East Godavari

East Godavari

East Godavari

East Godavari

East Godavari

East Godavari

Krishna

Krishna

District

1.48

1.47

1.47

1.47

1.46

1.46

1.46

1.46

1.42

1.40

1.35

1.33

Avg. tide (m)

(continued)

0.151525

0.096904

0.702994

0.444866

0.604239

0.400473

0.069306

0.487501

145.1667

16.83648

0.261633

0.526506

Basin area (km2 )

Tidal Energy Estimation of Potential Tidal Inlets … 665

Name

Rajanagaram

Boyapadu

Dhandawaka

Bangarammapalem

Pudimadaka

Chippada

Dosuru

Cheepurupalle

Peddapalem

Vishaka Port

MVP sector

Musalayyapalem

No.

185

186

187

188

189

190

191

192

193

194

195

196

Table 3 (continued) Longitude 82° 36 40.49 82° 44 37.68 82° 52 12.09 82° 59 37.95 83° 00 27.91 83° 03 31.61 83° 05 31.40 83° 10 13.77 83° 17 33.97 83° 20 35.91 83° 21 44.28 83° 23 20.98

Latitude

17° 17 07.19

17° 20 35.05

17° 21 47.66

17° 25 05.41

17° 28 32.66

17° 29 59.42

17° 31 23.52

17° 32 19.03

17° 34 05.48

17° 41 17.41

17° 44 01.72

17° 45 47.52

Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh

State

Vishakapatanam

Vishakapatanam

Vishakapatanam

Vishakapatanam

Vishakapatanam

Vishakapatanam

Krishna

Vishakapatanam

Vishakapatanam

Vishakapatanam

Vishakapatanam

Vishakapatanam

District

1.63

1.61

1.59

1.59

1.57

1.56

1.53

1.52

1.51

1.51

1.51

1.49

Avg. tide (m)

(continued)

0.007163

1.437398

0.007415

0.00378

0.007529

3.422777

0.022434

0.282695

0.015564

0.021679

0.09583

1.913039

Basin area (km2 )

666 V. Mendi et al.

Name

Pedda Rushikonda

Kummaripalem

Kancheru

Konada

Kollaya valasa 2

Kollaya valasa 1

Pathiwada

Chintapalli

NJR puram

Tekkai

Kuppili

Bontala koduru

No.

197

198

199

200

201

202

203

204

205

206

207

208

Table 3 (continued) Longitude 83° 27 19.63 83° 33 05.72 83° 34 14.44 83° 36 25.93 83° 36 45.31 83° 37 33.68 83° 39 25.24 83° 40 46.92 83° 42 19.66 83° 48 24.23 83° 56 45.45 84° 00 28.91

Latitude

17° 47 25.58

17° 54 01.94

17° 58 34.36

18° 00 47.02

18° 02 22.63

18° 02 35.16

18° 03 03.17

18° 04 23.20

18° 05 19.07

18° 06 16.96

18° 09 17.17

18° 12 48.10

Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh

State

Srikakulam

Srikakulam

Srikakulam

Srikakulam

Vizianagaram

Vizianagaram

Vizianagaram

Vizianagaram

Vizianagaram

Vizianagaram

Vishakapatanam

Vishakapatanam

District

1.76

1.75

1.74

1.72

1.69

1.67

1.67

1.67

1.65

1.65

1.65

1.64

Avg. tide (m)

(continued)

2.316625

0.140581

0.35246

1.576308

0.498835

0.015237

0.331492

0.00899

0.013825

0.007173

0.00716

0.785717

Basin area (km2 )

Tidal Energy Estimation of Potential Tidal Inlets … 667

Name

Vastavalasa

Seepanapeta

Kalingapatanam

Siddibeharakothuru

Malagam

Devunalthada

Vajrapukothuru

Metturu

Pithali

Uppalam

Borivenka

Pukkalapalyam

No.

209

210

211

212

213

214

215

216

217

218

219

220

Table 3 (continued) Longitude 84° 05 19.85 84° 08 11.50 84° 12 59.53 84° 14 12.08 84° 21 22.45 84° 27 17.06 84° 30 42.22 84° 34 33.78 84° 35 23.30 84° 41 03.22 84° 42 28.98 84° 44 42.58

Latitude

18° 14 49.52

18° 17 21.41

18° 20 41.14

18° 26 22.85

18° 27 30.60

18° 33 50.33

18° 41 42.58

18° 45 27.65

18° 50 48.19

18° 52 18.52

18° 58 14.70

19° 00 03.78

Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh Andhra Pradesh

State

Srikakulam

Srikakulam

Srikakulam

Srikakulam

Srikakulam

Srikakulam

Srikakulam

Srikakulam

Srikakulam

Srikakulam

Srikakulam

Srikakulam

District

1.90

1.87

1.86

1.86

0.97

1.84

1.83

1.82

1.82

1.80

1.78

1.78

Avg. tide (m)

(continued)

0.062765

2.141476

0.493907

0.104145

1.37642

0.461171

0.08042

0.00416

2.264468

2.508056

0.004138

0.195178

Basin area (km2 )

668 V. Mendi et al.

Name

Donkuru

Sonpur

Alladpur

Dhepanuapada

Venketraipur

Pallibandha

Anandapur

Baliapanda

Bhimapur

Sahukhanata

Tandahar

Dhanuhar Belari

Saharabedi

Nuagan

Kaudia

No.

221

222

223

224

225

226

227

228

229

230

231

232

233

234

235

Table 3 (continued)

53.75

15 24.92

19°

09.48

38.63

57 29.02

20° 17 36.17

20°

12

20° 02 47.51

19°

19°

11.05

54

19° 50 55.03

49

19° 46 56.96

19°

40

19° 22 23.92

19°

19° 04

14.92 11.82 49.31

25

40.67

13.36

30.41

86° 43 31.01

86°

42

86° 33 53.54

86°

86°

22

86° 13 44.43

86°

02

85° 54 58.26

85°

47

85° 31 23.98

85°

84°

03.26

84° 50 10.08

19° 08 49.02 55

84° 48 14.39

19° 06 59.72 15.61

84° 47 16.76

19° 03 02.52

11

Longitude

Latitude

Odisha

Odisha

Odisha

Odisha

Odisha

Odisha

Odisha

Odisha

Odisha

Odisha

Odisha

Odisha

Odisha

Andhra Pradesh Odisha

State

Jagatsinghpur

Jagatsinghpur

Jagatsinghpur

Jagatsinghpur

Jagatsinghpur

Jagatsinghpur

Jagatsinghpur

Puri

Khordha

Ganjam

Ganjam

Ganjam

Ganjam

Ganjam

Srikakulam

District

2.28

2.16

2.10

2.05

2.07

2.06

2.05

2.03

1.97

1.92

1.95

1.93

1.92

1.90

1.90

Avg. tide (m)

(continued)

34.76744

15.60578

4.661037

45.60841

3.24139

2.68565

2.21264

0.433643

671.5256

3.622675

0.531728

0.330663

0.412248

13.793050

0.907548

Basin area (km2 )

Tidal Energy Estimation of Potential Tidal Inlets … 669

Name

Baligarh

Banapada

Joginatha

Krishnapriyapur

Amarnagar

Pirikhi

Huladigudi

Jambhirei

Chandrabali

Begundiha

Tajpur

Serpujalpai

Nijkashba

Gagra char

Jadu bari chak

Haldia

Durgachak

No.

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

Table 3 (continued)

38.89

41.39

41

21°

19.98

22°

22°

00.95 19.32

01 02

21° 56 30.91

54

21° 47 31.88

21°

21°

55.14

38 22.42 00.28

88°

88° 11

11 45.07

45.07

88° 03 09.51

88°

01

88° 00 05.27

87°

53

87° 45 32.41

87° 38 27.31

05.64

21° 38 01.57

87°

22

87° 32 50.10

21°

49.38

21° 33 58.93

32

87° 12 26.38

03

38.81

21° 30 54.72

87°

86°

57

87° 07 19.40

43.97

46

22.12

86° 51 13.05

86°

45

21° 28 29.46

20°

20°

14.82

35

20° 30 25.24

20°

14.99

86° 44 24.47

20° 23 40.31 28

Longitude

Latitude

West Bengal

West Bengal

West Bengal

West Bengal

West Bengal

West Bengal

West Bengal

West Bengal

Odisha

Odisha

Odisha

Odisha

Odisha

Odisha

Odisha

Odisha

Odisha

State

Parganas

Parganas

Midnapur

Midnapur

Midnapur

Midnapur

Midnapur

Midnapur

Balasore

Balasore

Balasore

Balasore

Bhadrak

Kendrapara

Kendrapara

Kendrapara

Kendrapara

District

2.60

3.30

2.84

2.36

1.73

1.70

1.78

1.69

3.41

3.80

3.98

4.05

3.95

2.89

2.41

2.33

2.36

Avg. tide (m)

233.5836

21.85207

0.07405

0.249623

5.523177

1.2799

0.88938

1.242805

21.15097

0.108049

3.546401

6.233297

47.46539

0.531458

5.873865

0.686253

6.569228

Basin area (km2 )

670 V. Mendi et al.

Tidal Energy Estimation of Potential Tidal Inlets …

671

Table 4 Existing tidal power plants [5] Site

Country

Basin area (km2 )

Avg. tide (m)

La Rance Sihwa Annapolis

France South Korea Canada

22 30 15

8.55 5.6 6.4

Jiangxia

China

1.4

5.08

Kislaya Guba

Russia

1.1

2.3

Fig. 3 Basins with wide (left) and narrow (right) throat width

The simulated tidal ranges for the identified tidal inlets are listed in Table 3. The tidal prism is nothing but tidal range times the basin area. The variation of tidal prism for the inlets along the east coast of India from south to north is shown in Fig. 3.

3.4 Potential Energy Calculation The potential energy is a function of tidal prism of the basin. Potential energy obtained due to the stored water can be calculated as [5, 7]. E

1 Aρgh 2 2

(1)

h is the mean tidal range, A is the basin or lagoon area, ρ is the average density of water  1025 kg per cubic meter (density of seawater actually varies between 1021 and 1030 kg/m3 ) g is the acceleration due to the Earth’s gravity  9.81 m/s2 . From Eq. 1, it can be seen that the potential energy varies with square of tidal range. So, a barrage should be placed in such a location where it is possible to achieve maximum storage head. Black and Veatch [1] suggest that the ideal water depths to achieve the best possible power output at few potential sites around the UK range

672

V. Mendi et al.

between 25 and 40 m and the recommended diameter of the rotors to range between 10 and 20 m [4].

4 Results and Discussion The estimation of potential tidal energy involved two important parameters; tidal range and the basin area. Maximum productivity of the tidal energy is obtained at the places where both tidal range and basin area are large enough as it facilitates greater head. It is also a fact that the shape of the tidal basin considered is important because it helps to capture the water flowing in. Even if the basin has considerably large area and if it is connected through a very narrow channel and long, the basin cannot be filled during the spring tidal condition as shown in Fig. 3. As discussed above, larger tidal prism aids the storage of large volumes of water facilitating greater head. Figure 4 shows the variation of tidal prism from south to north along the east coast of India. From Table 4, it can be observed that the energy is being extracted from basins having areas of 1.1 km2 and average tide as less as 2.3 m. From Table 3, 82 locations can be identified.

Fig. 4 Variation of tidal prism along the east coast of India

Tidal Energy Estimation of Potential Tidal Inlets …

673

Fig. 5 Potential energy generated

The potential energy that can be extracted at each of the inlets is shown in Fig. 5. It can be clearly observed from Fig. 5, the energy extraction potential is more towards the north. If all the inlets are considered for energy extraction, then the total potential energy that can be generated is found to be 94249 MW along the east coast of India. However, from Table 4, we can observe that the least tidal prism is 2.53 Mm3 . And from Fig. 4, it is evident that there are 16 inlets in Tamil Nadu, 27 in Andhra Pradesh, 16 in Odisha and 3 in West Bengal (62 inlets in total) whose tidal prism exceeds 2.53 Mm3 .

5 Conclusions • A total of 252 tidal inlets are identified along the east coast of India. Out of which, 62 are found suitable for energy extraction.

674

V. Mendi et al.

• The threshold set for the parameter tidal prism in the selection of suitable tidal inlets for potential energy extraction is considered from the standards of the existing tidal power plants. • It can be observed that all the four states, i.e. Tamil Nadu, Andhra Pradesh, Odisha and West Bengal under consideration have tidal inlets which have very low tidal prism and also high tidal prism. • In this study, only tidal prism is considered. Consideration of cross-sectional area, width at the mouth of the inlet and at the location of tidal turbines would give a better understanding of the estimation of tidal energy.

References 1. Black and Veatch (2005) Tidal stream energy resource and technology summary report submitted to Carbon Trust. www.carbontrust.com. Accessed 8 Dec 2016 2. Bryden IG, Scott JC (2007) How much energy can be extracted from moving water with a free surface: a question of importance in the field of tidal current energy? J Renew Energy 32:1961–1966 3. Charlier RH, Finkl CW (2009) Text book on ocean energy: tide and tidal power 4. Frost C, Morris CE, Mason-Jones A, O’Doherty DM, O’Doherty T (2015) The effect of tidal flow directionality on tidal turbine performance characteristics. Renew Energy 78:609–620 5. Gorlov AM (2001) Tidal energy, Northeastern University, Boston Massachusetts, USA, pp 2955–2960 6. Nicholls-Lee RF, Turnock SR (2008) Tidal energy extraction: renewable, sustainable and predictable. Sci Prog 91(1):81–111 7. Tousif SMR, Taslim SMB (2011) Tidal power: an effective method of generating power. Int J Sci Eng Res 2(5) 8. Vikas M (2015) Classification of tidal inlets along the Indian coast. M.Tech. thesis, Department of Applied Mechanics and Hydraulics, National Institute of Technology Karnataka, Surathkal

Optimal Design of a Marine Current Turbine Using CFD and FEA Thandayutham Karthikeyan, Lava Kush Mishra and Abdus Samad

Abstract Ocean currents that are produced due to motion of tides can be utilized in power extraction by using suitable turbines. The turbine should be structurally and hydrodynamically strong. In this paper, a 0.8 m horizontal axis marine current turbine (MCT) with three blades is analyzed. A 3D CAD model of a turbine is optimized using CFD and FEA tools. The performance of the turbine is based on the coefficient of power; however, the turbine should resist the loads acting on it. The fatigue load damages the turbine which is mainly due to wave loads and it must be evaluated to avoid the cost of replacing a new turbine. Only a turbine with high power coefficient and good material strength will result in a favorable design. The parameters like pitch angles, number of blades, and turbine material are modified to study the performance and structural stability of the turbine. The detailed CFD study including boundary conditions and methodology has contributed to get an insight of the flow physics. The best suitable pitch angle and number of rotor blades for the turbine are analyzed and discussed. The optimized turbine has two rotor blades with a pitch angle of 19.5° and has achieved a significant 25% increase in CP . Later, different materials are chosen to identify the variation in stress and tip deflection of the turbine blades. This will direct toward a safe design of the turbine blades. Keywords Marine energy · Marine current turbine · CFD and FEA analysis Surrogate models

T. Karthikeyan · L. K. Mishra · A. Samad (B) Wave Energy and Fluids Engineering Lab, Department of Ocean Engineering, IIT Madras, Chennai 600036, TN, India e-mail: [email protected] T. Karthikeyan e-mail: [email protected] L. K. Mishra e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_50

675

676

T. Karthikeyan et al.

Nomenclature Abbreviation BEM CAD CFD FEA GA KRG PRESS RANS RBF RSA TSR WAS

Blade element momentum Computer-aided designing Computational fluid dynamics Finite element analysis Genetic algorithm Kriging Predicted error sum of square Reynolds-averaged Navier–Stokes Radial basis function Response surface approximation Tip speed ratio Weighted average surrogate

Symbols A a a Cd Cl CP CT c D e˜ F H h Q R r T t UT Vrel α ρ 

Rotor area (m2 ) Axial induction factor Tangential induction factor Drag coefficient Lift coefficient Power coefficient Thrust coefficient Chord (m) Turbine tip diameter (m) PRESS vector Objective function Total depth of water (m) Installation depth from ocean surface (m) Torque (N-m) Rotor radius (m) Local radius (m) Thrust (N) Thickness (m) Free stream velocity (m/s) Relative velocity (m/s) Angle of attack Density (kg/m3 ) Angular velocity of rotor (rad/s)

Optimal Design of a Marine Current Turbine Using CFD and FEA

φ ϕ

677

Local blade pitch angle Angle between the plane of rotation

Subscripts ERR OPT RMS SUR

Error Optimal Root mean square Surrogate

1 Introduction Tidal energy is the resource to be exploited for the sustainable generation of electricity. The factors like fluid properties and predictability make the generation of electricity from marine currents to be highly appealing compared to other renewables. An MCT which can operate at around 2 m/s in seawater can results in four times higher energy per year/m2 compared to similar wind turbine [1]. This leads to a significant improvement in power generation which is in high demand. A 1/30th scaled down axial flow turbine with a diameter of 0.8 m is taken for primary test in recirculating water channel. The performance of the turbine and wake characteristics was determined over a range of rotor thrust coefficients and flow speeds. Blockage effects and surface turbulence effects were studied by increasing flow speeds [2]. The experiments show that the hydro-spinnal turbine presents a relatively low power coefficient compared to that of other competitive turbines. This helps us to understand the advantages of the common horizontal axis MCT, which are dominant in tidal energy production [3]. A 3D numerical model of an actuator disk, where the water flows over it can, represents a running tidal turbine. It is placed in a channel of different aspect ratio and blockages. The importance of this work is to understand the effects of turbulent mixing behind the disk. Also, the effects of aspect ratio and channel blockage on the prediction of the hydrodynamic limit are analyzed [4]. This acts as preliminary approach which imitates the working of a turbine. CFD simulations are performed for different turbines which vary on blockage ratio to achieve its maximum power coefficient. In addition, the maximum power coefficients for both rotors operating in an unblocked domain compare favorably with actual scale [5]. The blade shape is deemed to be the most important parameter affecting turbine performance. The other primary parameters are number of rotor blades and pitch angle. It is demonstrated that positive pitch angles feature better results than negative angles. Considering the number of blades, the fewer blades have higher rotational speed. This behavior is due to the reduced overall drag of the blades. It is understood that twisted blades lead to self-starting of the turbine, whereas the straight-bladed turbine did not self-start at low flow rates [6, 7]. To design tidal power devices, the

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local blockage is considered as it operates in a blocked condition on tidal channels due to its geometry. The rotor design with the highest blockage achieves highest power coefficient. To reach maximum efficiency, the rotor with lower blade twist and greater solidity are designed for operating at high blockage [8]. It is also important to choose the solidity of the turbine to use in specific application. The hydrodynamic performance can be maximized for turbines with lower values of blade pitch angles and chord lengths and it is considered for the current work. A higher blade pitch angle and lower tip speed ratio are required to maximize the structural stability of the turbine [9, 10]. However, the present work considers the parameters like the blade pitch angle and number of rotor blades which dominates the power production from a turbine. Mostly, the optimization studies were focused on maximizing the power coefficient of the turbines. Other study includes genetic algorithm for constrained optimization and found it to be better than the methods followed by classical optimization [11–13]. This paper discusses the improvement of power coefficient of a MCT using surrogate-based optimization. The predictions by the surrogate models are significant which could develop a new methodology for optimizing the turbine. The change in performance and the fluid flow physics due to the parameter changes are discussed in detail with necessary figures. It is also vital to understand the structural stability of the turbine which will help to predict the life period. A finite element analysis will help us to understand the material strength and also helps us to compare the stability of the optimized turbine and the reference time. It is important for a turbine to balance the hydrodynamic effects and structural stability. The selection of material for the turbine should be cost-effective from the selection of raw materials till the manufacturing [14].

2 Numerical Methodologies 2.1 Computational Fluid Dynamics The 3D model of the turbine is created and to reduce the simulation time, periodic boundary conditions are used for present simulation which is shown in Fig. 1. A three blade 0.8 m horizontal axis marine current turbine with 25° pitch angle is numerically validated. The blades were modeled from the various NACA profiles like 63–812, 63–815, 63–818, 63–821, and 638–24 for 17 stations [15, 16]. The periodic conditions are given on the surfaces which measures 2.5 D. The angle between the periodic boundary surfaces is 120° for three rotor blades. Similarly, for two and four rotor blades, the angles are 180° and 90°, respectively. To understand the near wall fluid conditions, prism-layered mesh is used on the walls of turbine blades which is given in Fig. 2. The grid independent study identifies that 10 million mesh elements are best suitable for further simulations and analysis [17]. The RANS equation with a two equation turbulence closure model is chosen for the current

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Fig. 1 Periodic fluid domain extraction

Outlet

Inlet

7D

2.5D 2.5D

3D

Fig. 2 Mesh on turbine wall

analysis. The K-ω SST turbulence model with a y+ value closer to 1 is maintained to solve RANS equation [18]. The time-averaged representations of the continuity and momentum equations are known as RANS and it governs the fluid flow which are solved using ANSYS CFX. They are in Eqs. (1) and (2), respectively, for a steady incompressible flow, ∇ · ui  0    ∂    ∂ ∂   ∂ui ∂uj −pδij + μ +ρ −ui uj ui uj  ρ + ∂xj ∂xj ∂xj ∂xi ∂xj

(1) (2)

The current work optimizes power coefficient of an axial turbine. An MCT’s performance is governed by the tip speed ratio [19], which is shown in Eq. (3). The same can improve the outputs mentioned below in Eqs. (4) and (5).

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R UT Q Power coefficient : cP  0.5ρπR2 U3T T Thrust coefficient : cT  0.5ρπAU2T Tip speed ratio :

TSR 

(3) (4) (5)

2.2 FEA The structural stability of turbine must be considered to develop an optimal design. An elliptical tube is taken for purpose of numerical validation. Instead of distributed load, multiple point loads can be used for elliptical tube model. The major diameter is 0.25 m and minor diameter is 0.0625 m with a shell structure. Ratio of minor diameter to major diameter is 0.25. The thickness of the shell is taken as 0.005 m, which is 2% of the major diameter and it is fixed along the span. The spanwise length of the tube is 1.8 m, similar to a cantilever beam fixed at one end. A uniformly distributed load of 500 N/m was applied along the span of the tube. The elliptical tube has 19 stations along its span and loads are applied at each station. Material used for this model is fiberglass composite material. This material has Young’s modulus E  20 GPa and density ρ  1,850 kg/m3 and tetrahedron mesh elements are used for simulation which is shown in Fig. 3 [20]. Table 1 has the grid-independent study for FEA. Hence, 57,672 number of elements were chosen for validation which has a maximum tip deflection of 25.095 mm. Table 2 shows the comparative results of the present FEA, analytical and literature model which is also considered as a numerical validation. The material chosen should have high strength and must be resistive to corrosion to work in marine environment [21]. Aluminum alloy and stainless steel are good in terms of resistance to corrosion and high strength [22].

Fig. 3 FEA mesh for the marine current turbine

Optimal Design of a Marine Current Turbine Using CFD and FEA Table 1 Grid-independent study for FEA

Table 2 Validation of elliptical tube

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No of elements

Tip deflection (mm)

28,749

25.081

57,672

25.095

84,219

25.095

Analysis

Von-Mises stress (MPa)

Tip deflection (mm)

FEA Literature [21]

20.191 22.487

25.095 25.021

Analytical [21]

19.601

25.404

The tangential and normal force components using lift and drag force are manually calculated using axial velocity (1 − a)Vo and tangential velocity (1 + a )ωr. The lift and drag coefficients are used to find the lift and drag force per length from the equations given below. The calculation of lift and drag forces for the marine current turbine are available in literatures [23, 24]. 1 2 ρV cCl 2 rel 1 Drag force, D  ρV2rel cCd 2 Normal force, PN  L cosϕ + D sinϕ Lift force, L 

Tangential force, PT  L sinϕ − D cosϕ

(6) (7) (8) (9)

3 Numerical Optimization The optimization process involves a methodology to select the best alternatives available from the given designs. A full factorial sampling scheme is used for selecting design points. The chosen objective function is the coefficient of power which is mainly selected for marine current turbine. The maximization of objective function is proven to be dominant to enhance turbine’s performance [25]. The surrogates are adaptive methods and cannot generate the initial data, however, replicates the end results of high-fidelity CFD simulations. Surrogates depend on specific problems and thus it is important to work on various surrogates for better prediction. Multiple surrogates use the same initial data to produce different optimal points which is better than using a single surrogate [26]. This improves the possibility of finding the best alternative and the robustness of surrogate increases. The procedure for optimization is given in Fig. 4. From a parametric study, the design space is initiated and is shown in Table 3. The CFD analysis calculates the objective function and the search algorithm identifies the optimal point after constructing the surrogate model [27].

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Problem setup (Objective function & design variable)

Optimal design Yes

Design of experiments (Selection of design points)

No Optimal point

Numerical analysis

Search for optimal point

Construction of surrogate

Fig. 4 Optimization methodology Table 3 Design space for optimization

Variable

Lower

Upper

Pitch angle

15°

25°

Number of blades

2

4

3.1 Response Surface Approximation Model The response surface approximation model is a collection of statistical and mathematical techniques for building empirical model. It is aimed to reduce the expensive analysis methods in designing the optimal points. Using design of experiments, the objective optimizes an output variable which is influenced by various input variables [28]. The changes are made in a series of tests called runs to identify the changes in the response. The second-order response surface model with strong applicability is generally used.

3.2 Radial Basis Function The Radial Basis Function (RBF) ideology is derived from the function approximation theory. Their main features are two-layer feed-forward networks and the hidden nodes implement a set of radial basis functions. Human nervous system functions are simulated through a numerical approach which is called as a radial basis function. A hidden layer and a linear output layer combine to give a network of two layers in RBF. The parameter sets and difference of their coordinates determine the distance between two points [29].

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3.3 Kriging Model Kriging is based on the interpolation and highly utilized in concoction with methods that are gradient free. The sum of the mean and deviation terms is defined as the Kriging surrogate model [30]. The trend that is approximate for real function is represented by the mean. The quantified error term value is a difference between approximated surrogate-predicted function and real function.

3.4 Weighted Average Surrogate The weighted average surrogate model is utilized in the current investigation. Weights are decided based on high error producing surrogates that have low weights. In this work, predicted error sum of squares that is the measure of goodness which helps to acquire global weight. Next construction of RSA, Kriging and RBF surrogate models with the help of objective function values at design points. GA-sequential quadratic programming search algorithm is used to obtain the optimal points from initial population generated by the surrogates [31]. Weighted average surrogate estimates a weighted function (yWAS ), which is a weighted average of multiple surrogates. yWAS  ωKRG yKRG + ωRSA yRSA + ωRBF yRBF

(10)

where ωKRG , ωRSA , and ωRBF are the weights of the corresponding surrogates, and the sum of the weights is equal to one [32]. The weights of the surrogates are estimated from the PRESS and are calculated as ω∗i  ωi

N

ω∗i

(11)

i1

1

Eavg  Ei N i1  γ ω∗i  Ei + αEavg N

(12) (13)

where Ei is the PRESS calculated error and N is the number of surrogates. The predicted error sum of squares through the k-fold cross validation strategy finds the root mean square error. Here, e˜ is the PRESS vector and the number of points is p. The error is calculated as  (14) PRESSRMS  e˜ e˜ T /p

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4 Results and Discussion The 25° pitch angle turbine with three blades is numerically validated with its experimental data. The TSR versus coefficient of power curve ensures the validation and is shown in Fig. 5. It is to be noticed that relative error between the curves is 7.04% and is acceptable. This difference is due to approximations which were carried out during the numerical simulation. The values are plotted from TSR  3–8 and the peak CP value falls between TSR  4 and 6.5. The 25° pitch angle turbine was experimented and has the highest CP of 0.375 at TSR  5.5, however, CFD predicted CP was 0.346. The free stream velocity was fixed to 1.54 m/s and is used from the experimental data [33]. The CFD results from the various turbine configurations are the input data for the optimization techniques which predicts the optimal turbine. The 20° pitch angle turbine produces higher CP values irrespective to any number of blades which must be noted. However, the performance of two blades is higher throughout the working range and the peak CP value is 0.454. The change in positive pitch angle will achieve higher lift and can rotate the turbine with minimum input energy. It is found that by changing only the pitch angle from 25° to 20°, turbine’s CP increases by 25%. The increase in torque increases the CP of the turbine which will increase the output power. The CP increases when there is an increase in number of rotor blades; however, the overall drag is also increased [34]. This affects the fluid flow at the downstream of the turbine and reduces the CP values. The comparison of CP and different blade pitch angle for the turbine with two blades are shown in Fig. 6. The optimized two blade rotor with 19.5° pitch angle achieves the highest CP value of 0.566. The PRESS errors and weights for the surrogates used are shown in Table 4. However, there is a difference between the simulated values and surrogate-predicted values. The FERR plays a vital role in identifying the optimal point. It is calculated to find the error between the objective function that is obtained by the surrogates and the CFD simulations which are shown in Table 5. FSUR , FCFD , Opt , and FERR are the objective function achieved by the surrogate (FSUR ), CFD for optimized blade (FCFD , Opt ), and error between surrogate predicted and optimized design (FERR ), respectively.

Fig. 5 Validation curve

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Fig. 6 Comparison of optimized model

Table 4 PRESS and weights

Table 5 Design optimization results

Model

PRESS

Weights

RBF RSA KRG

0.115 0.046 0.048

0.226 0.389 0.383

Model

FSUR

FCFD, Opt

FERR

REF RBF RSA KRG WAS

0.351 0.630 0.561 0.566 0.566

– 0.591 0.590 0.569 0.583

– 0.061 0.051 0.005 0.030

It is found that the optimized turbine achieves higher tip velocity compared to the reference model due to a change in the local pitch angle near the tip. Figure 7 represents the total pressure contours of the two blade optimized turbines and three blade reference turbines. The pressure on the suction side pressure of the blades is found to be varying for both the cases; however, it is more gradual for the optimized turbine. The pressure near the tip of the optimized turbine is very low at the leading edge compared to the reference model. This explains that the tip velocity of the optimized turbine is higher and can perform well at higher tip speed ratio. This difference in pressure is due to continuous change in pitch angle from the root to the tip of the turbine which increases the lift characteristics of the blade. In general, the blades with less number of blades are preferable for high tip speed ratio which reduces the turbulence effect in the downstream of the turbine. Figure 8 helps to visualize the recirculation region that is formed at the root of the reference turbine which reduces the CP . The same is neglected in the optimized turbine due to reduction in turbulence effects. It is important to note that the intensity of eddy is higher for the reference model compared to optimized model. The Von-Mises stress and tip deflection for the reference model and optimized turbine is given in Table 6. It is clear that the optimized turbine which has better hydrodynamic effects is also structurally stable than the reference turbine. The opti-

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Fig. 7 Total pressure contours: a reference model, b optimized model

(a)

(b)

Fig. 8 Stream lines: a reference model, b optimized model

mized turbine as a whole system which has only two blades will counter lesser loads compared to the reference model. The contours of Von-Mises stress and tip deflections for the reference an optimized turbine are given in Figs. 9, 10, 11 and 12.

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Table 6 FEA analysis of marine current turbine for different materials Material Reference model Optimized model Von-Mises stress (MPa)

Tip deflection (mm)

Von-Mises stress (MPa)

Tip deflection (mm)

Aluminum alloy

145.48

23.656

141.55

22.948

Stainless steel

145.48

8.706

141.56

8.445

Fig. 9 Von-Mises stress for a reference turbine and b optimized turbine using aluminum alloy

Fig. 10 Von-Mises stress for a reference turbine and b optimized turbine using stainless steel

Fig. 11 Tip deflection for a reference turbine and b optimized turbine using aluminum alloy

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Fig. 12 Tip deflection for a reference turbine and b optimized turbine using stainless steel

5 Conclusion Design optimization of a marine turbine is reported in this paper. The power coefficient of the turbine was maximized by altering the pitch angle and number of blades using CFD analysis and surrogates-based optimization. FEA is also a powerful tool to predict the structural strength which is used in this present work. The Von-Mises stress and tip deflection are calculated for the reference and optimized turbine design. The stainless steel is found to be structurally stable than aluminum alloy. The conclusions are given as follows: • The optimized design has a pitch angle of 19.5° and has two blades, whereas the reference design has 3 blades and a pitch angle of 25°. • The CP values were high at TSR  5.5 for all the cases; however, the optimized turbine reached a maximum value of 0.566 which is significant. • By changing only the blade pitch angle from 25° to 20°, CP  0.454 can be achieved. The CP of the optimized turbine has increased by 25% compared to the turbine with 20° blade pitch angle. • Kriging gave the best prediction and produced a satisfactory result. The multiple surrogates with CFD can be used for the marine energy applications which are quick and cost-effective to predict the performance of the turbine. • From the above analysis, it can be shown that optimized model is having less stress and tip deflection compared to reference model. Stainless steel predicts less deflection and Von-Mises stress which could be an alternate material for the turbine blades. The maximum Von-Mises stress for stainless steel is 141.55 MPa and tip deflection is 8.445 mm for optimized blade model.

References 1. Bahaj AS, Myers LE (2003) Fundamentals applicable to the utilization of marine current turbines for energy production. Renew Energy 28(14):2205–2211

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2. Myers LE, Bahaj AS (2007) Wake studies of a 1/30th scale horizontal axis marine current turbine. Ocean Eng 34(5/6):758–762 3. Rosli R, Norman R, Atlar M (2016) Experimental investigations of the Hydro-Spina turbine performance. Renew Energy 99:1227–1234 4. Nishino T, Willden RHJ (2012) Effects of 3-D channel blockage and turbulent wake mixing on the limit of power extraction by tidal turbines. Int J Heat Fluid Flow 37:123–135 5. Wimshurst A, Willden RHJ (2016) Computational analysis of blockage designed tidal turbine rotors. Progress in Renewable Energies Offshore, Taylor & Francis Group, pp 587–597 6. Amet E, Maitre T, Pellone C, Achard JL (2009) 2D numerical simulations of blade vortex interactions in a darrieus turbine. J Fluids Eng 131(11):1–15 7. Priegue L, Stoesser T, Runge S (2015) Effect of blade parameters on the performance of a cross flow turbine. In: Proceedings of the 36th IAHR world congress, 28th June to 3rd July, The Netherlands 8. Schluntz J, Willden RHJ (2015) The effect of blockage on tidal turbine rotor design and performance. Renew Energy 81:432–441 9. Mukherji SS, Kolkar N, Banerjee A, Mishra R (2011) Numerical investigation and evaluation of optimum hydrodynamic performance of a horizontal axis hydrokinetic turbine. J Renew Sustain Energy 3(063105):1–17 10. Kolekar N, Banerjee A (2013) A coupled hydro-structural design optimization for hydrokinetic turbines. J Renew Sustain Energy 5(053146):1–22 11. Selig MS, Carroll VLC (1996) Application of a genetic algorithm to wind turbine design. J Energy Res Technol 118(1):22–28 12. Belessis MA, Stamos DG (1996) Investigation of the capabilities of a genetic optimization algorithm in designing wind turbine rotors. In: Proceedings of European union wind energy conference and exhibition, May 20–24, Goteborg, Sweden 13. Fuglsang P, Madsen HA (1999) Optimization method for wind turbine rotors. J Wind Eng Ind Aerodyn 80(1/2):191–206 14. McEwen LN, Evans R, Meunier M (2012) Cost effective tidal turbine blades. In: 4th international conference on ocean energy, 17th October, Dublin 15. Bahaj AS, Molland AF, Chaplin JR, Battern WMJ (2007) Power and thrust measurements of marine current turbine under various hydrodynamic flow conditions in a cavitation tunnel and a towing tank. Renew Energy 32(3):407–426 16. Blackmore T, Myers LE, Bahaj AS (2016) Effects of turbulence on tidal turbines: Implications to performance, blade loads and condition monitoring. Int J Marine Energy 14:1–26 17. Karthikeyan T, Avital EJ, Venkatesan N, Samad A (2017) Design and analysis of marine current turbine. In: Proceedings of ASME 2017 gas turbine India conference and exhibition, 7th and 8th December, Bangalore, India 18. Menter FR (2014) Two- equation eddy- viscosity turbulence models for engineering applications. AIAA J 32(8):1598–1605 19. Bai X, Avital EJ, Munjiza A, Williams JJR (2014) Numerical simulation of a marine current turbine in free surface flow. Renew Energy 63:715–723 20. Danao LA, Abuan B, Howell R (2016) Design analysis of a horizontal axis tidal turbine. In: 3rd Asian wave and tidal conference, 24–28th October, Marina Bay Sands, Singapore 21. Grogan DM, Leen SB, Kennedy CR, Bradaigh CMO (2013) Design of composite tidal turbine blades. Renew Energy 57:151–162 22. Thakker A, Jarvis J, Buggy M, Sahed A (2008) A novel approach to materials selection strategy case study: wave energy extraction impulse turbine. Mater Des 29:1973–1980 23. Hansen MOL (2008) Aerodynamics of wind turbines – Second edition. Earthscan publication, The United Kingdom 24. Batten WMJ, Bahaj AS, Molland AF, Chaplin JR (2008) The prediction of the hydrodynamic performance of marine current turbines. Renew Energy 33:1085–1096 25. Zhu GJ, Guo PC, Luo XQ, Feng JJ (2012) Multiple objective optimization of the horizontal-axis marine current turbine based on NSGA-II algorithm. Earth Environ Sci 15:1–8

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26. Badhurshah R, Samad A (2015) Multiple surrogate based optimization of a bidirectional impulse turbine for wave energy conversion. Renew Energy 74:749–760 27. Koo GW, Lee SM, Kim KY (2014) Shape optimization of inlet part of a printed circuit heat exchanger using surrogate modeling. Appl Therm Eng 72(1):90–96 28. Jiang Y, Lin H, Yue G, Zheng Q, Xu X (2017) Aero-thermal optimization on multi-rows film cooling of a realistic marine high pressure turbine vane. Appl Therm Eng 111:537–549 29. Tsoukalas I, Kossieris P, Efstratiadis A, Makropoulos C (2016) Surrogate-enhanced evolutionary annealing simplex algorithm for effective and efficient optimization of water resources problems on a budget. Environ Model Softw 77:122–142 30. Lee H, Jo Y, Lee DJ, Choi S (2016) Surrogate model based design optimization of multiple wing sails considering flow interaction effect. J Propul Power 24(2):422–436 31. Samad A, Kim KY (2008) Multiple surrogate modeling for axial compressor blade shape optimization. Struct Multidisciplinary Optim 39(4):439–457 32. Jiang Y, Lin H, Yue G, Zheng Q, Xu X (2017) Aero-thermal optimization on multi-rows film cooling of a realistic marine high pressure turbine vane. Appl Therm Eng 111:537–549 33. Batten WMJ, Bahaj AS, Molland AF, Chaplin JR (2007) Experimentally validated numerical method for the hydrodynamic design of horizontal axis tidal turbines. Ocean Eng 34(7):1013–1020 34. Delafin PL, Nishino T, Wang L, Kolios A (2016) Effect of the number of blades and solidity on the performance of a vertical axis wind turbine. J Phys: Conf Ser 753:1–8

Offshore Energy for the Remote Islands of Lakshadweep K. Srilakshmi , Satya Kiran Raju Alluri and Manu

Abstract Conjoining the available energy with renewable energy will allow us to utilize the renewable energy sector efficiently by reducing the current prices of electricity. Keeping this in mind, the island administration wants to shift towards renewable energy as the present diesel-electric system is posing a severe threat to its fragile environment of the island. Wind resource assessment was carried out and observed that wind energy has potential for energy generation. In the present paper, an attempt is made to study suitable substructure concepts along with detailed installation methodology for Lakshadweep. As these islands do not have the facility to handle more than 2 tons. It would be challenging to arrive at site-specific installation methodology for an offshore wind turbine. The aerodynamics loads are estimated by open source code ‘FAST’ and the hydrodynamic loads by Morison’s equation. These loads are transferred to structure and then to the soil, where its interaction is modelled as three nonlinear orthogonal springs. The behaviour of structure under combined loads is analysed using Finite Element Method. It is proposed to construct the gravity-based foundation onshore in lagoon side of the island, launched into the sea using hydraulic jacks, tow using tug and ballast at the proposed location. So, it is essential to identify the natural frequencies and Response Amplitude Operations (RAO) to understand the behaviour of foundation during towing. The draft of foundation is estimated under static condition and RAO’s are obtained using panel method. Keywords Offshore wind · Wind resource assessment · Aerodynamic loads Hydrodynamic loads K. Srilakshmi (B) · Manu National Institute of Technology Karnataka, Surathkal, Mangalore 575025, Karnataka, India e-mail: [email protected]; [email protected] Manu e-mail: [email protected] S. K. R. Alluri National Institute of Ocean Technology, Chennai 600100, Tamil Nadu, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_51

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1 Introduction

'000 KWh

At present, there is a dearth of energy and energy resources in Lakshadweep islands. With the increased electricity consumption, the Lakshadweep island authorities have shown their keen interest to utilize renewable energy sources along with the present system [1, 2]. The power generation at present in Lakshadweep islands is shown in Fig. 1. Energy plays a vital part for functioning of society which includes residential, commercial, institutional and industrial activities. It augments the development and economic growth of a region. The excess harnessing of conventional non-renewable energy is resulting in depletion of natural energy reserves, degradation of environment and ecological imbalances. Renewable energy has grabbed a lot of attention among researchers, industries and governments during the past few years. Presently, the focus is to identify alternative renewable energies like wind, solar, wave, etc. Among the above, wind energy has already got a wide range of acceptance in many countries and their focus is to develop uninterrupted wind energy which is possible by offshore wind farms because of the availability of continuous offshore wind. Offshore wind farms consist of several staggered wind turbines supported on offshore platforms and connected to a substation via underwater electric cables. The design of this platform is governed by environmental conditions and geotechnical aspects. The support platform costs about 24% [3] of the total system cost and needs to be optimized to increase commercial viability of offshore wind projects. The substructure concepts used to support offshore wind turbine includes monopiles, gravity base structures, jackets, tripods, tripiles and floating platforms. The share of various foundations types used across the world for offshore wind turbines are given in Fig. 2 [4]. The choice of foundation depends on water depth, environmental and geotechnical conditions. Monopiles and gravity-based foundations are generally adopted for shallow water depth below 30 m. As the water depth increases, these 20500 20000 19500 19000 18500 18000 17500 17000 16500 16000 15500 15000 1996-97

97-98

98-99 YEAR

Fig. 1 Power generation in Lakshadweep islands

99-00

00-01

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Fig. 2 Share of various foundations for offshore wind farms

foundations yield larger lateral deflection and rotations at nacelle level. So, braced frame structure like jacket and tripod are used in transition water depths of 30 to 50 m. In ultradeep water (>50 m) floating compliant structures are adopted [5].

1.1 Problems with Present Electric System As these islands are remotely located, they depend on electricity generated through diesel systems. About 7.0 million litres of high-speed diesel is required to meet the energy requirements of island. The required diesel is transported from Calicut to jetty at island using barrels on barge from Calicut. The barrels which are at island jetties will be carried to stockyards. This process is very cumbersome, exorbitant and is creating a lot of damage to the fragile environment of the islands because of the poor handling and storage of diesel barrels. Because of the diesel spillage at stockyards, water is also getting polluted. Apart from this because of the emissions of diesel generators a lot of noise and air pollution is also there.

2 Wind Resource Assessment Ministry of New and Renewable Energy Sources has carried out wind resource assessment at two islands Agatti and Minicoy. The annual wind energy potential in various islands are mentioned in Table 1. Study indicates that between May and November the highest wind speeds of about 8–9 m/s, remaining months have hourly wind speeds greater than 2.8 m/s [1, 6]. Therefore, wind energy has potential for energy generation in Lakshadweep. As these islands are small and fully covered with coconut trees, offshore wind would be an ideal solution.

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Table 1 Wind energy potential in each island of Lakshadweep (Source Ministry of NonConventional Energy Sources) Sl. no. Island Annual electricity generation potential (in Thousand kWh) 1

Minicoy

1239.50

2 3 4 5

Kavaratti Amini Andrott Kalpeni

1239.30 929.50 1239.30 929.50

6

Agatti

7 8 9 10 11

Kadmat Kiltan Chetlat Bitra Bangaram

929.50 1239.30 433.70 309.80 62.00 124.00

Total

8675.40

Monthly wind data at Agatti Island is collected. The collected raw data is processed to remove all uncertainties. The summary of uncertainty elements associated with the wind speed and the corrected values as per IEC are listed below [7]: 1. Measurement uncertainty—As the buoy is in critical environment a minimum of 2% is selected. 2. Future wind resource—A total of 7.14% is obtained at Agatti island by summing up uncertainty in future wind measurement and uncertainty due to long-term climate change. 3. Wind shear—Uncertainty associated with wind shear is considered using the following Eq. 1.  σ  100[

Hh H2

α

− 1]

(1)

σ is uncertainty, Hh is hub height, H2 is height of measured wind and α is uncertainty in wind shear. A total of 7.65% is obtained at Agatti island by considering the above uncertainties. These uncertainties are applied for measured wind speeds at Agatti.

2.1 Plant Load Factor PLF gives the average capacity exploitation. It is used to check the output of a power plant with the rated output it could produce. Annual Power production per annum is

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Table 2 Exceedance values without uncertainties

Island

P50 (KW)

P75 (KW)

P90 (KW)

Agatti

996.0865

60.4465

−781.6586

Table 3 Exceedance values with uncertainties

Island

P50 (KW)

P75 (KW)

P90 (KW)

Agatti

757.4857

2.5858

−676.8477

estimated by considering the power curves and corrected wind speeds by applying uncertainties. In this paper, it is assumed that the annual energy production falls into normal distribution and the calculations are done based on it. P50 , P75 and P90 are calculated. The 50, 75 and 90% exceedance values were estimated for 5 MW NREL baseline offshore wind turbine for Agatti island are shown in Tables 2 and 3.

3 Methodology The optimum substructure configuration for offshore wind turbine can be arrived only by considering the in-place behaviour of structure along with suitable installation methodology. The structure has to be analysed for combined aerodynamic and hydrodynamic forces to understand the in-place behaviour. Then the structure should be designed to safely transfer the forces into the soil by satisfying serviceability and strength aspects. The detailed design methodology is given in Fig. 3. The aerodynamic loads are estimated using open source tool ‘FAST’ based on Blade Element Momentum Theory. The wave kinematics is obtained using suitable wave theory and the hydrodynamic forces are estimated using Morison’s equation. The soil interaction is modelled as springs with suitable stiffness. The structural behaviour of entire system is analysed using finite element method and members are designed. The gravity-based foundation is checked against stability due to sliding, overturning and bearing. It is proposed to transport the gravity foundation through flotation and ballast at proposed location. The draft of foundation is estimated using static stability conditions and the Response Amplitude Operators are estimated for dynamic stability.

4 Structural Analysis and Design of Substructure 4.1 Aerodynamic Loads on Turbine The behaviour of NREL 5 MW turbine has to be studied under various design conditions. International Electrotechnical Commission [8] has provided models for the

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Fig. 3 Methodology for identification of optimal substructure configuration

various wind conditions during these design conditions and these models have to be established for various wind speeds. The obtained wind time history from these models can be converted to thrust force on turbine using open sources tool FAST. This tool works under beam element momentum theory. The Blade Element theory assumes the rotor blade sections as infinitesimally small thickness like a two-dimensional aerofoil’s. Aerodynamic forces for each segment are estimated considering local flow conditions and the overall forces are obtained by integrating all the sections. The Momentum theory assumes loss of momentum which is used in calculating induced velocities is due to the amount of the work done by airflow through rotor on the blade elements in both axial and tangential directions. These induced velocities

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from momentum theory are used by Blade element theory for calculation of thrust forces on turbine. The thrust force time history obtained from FAST is converted to equivalent static load for all the load conditions as per IEC. The equivalent static load can be obtained by multiplying the maximum dynamic load in time history with the dynamic amplification factor. The dynamic amplification factor depends on the spacing of natural frequency of structure and the dominant frequency of force time history and estimated using the Eq. 2. The natural frequency of structure is obtained using Eigenvalue analysis and the dominant frequency of force is obtained using Fast Fourier Transform. The damping in the structure is considered 2%. It is observed that Maximum Aerodynamic loads of 1.22 MN was obtained for extreme operating gust rated case and this is used for design of substructure. 1 DAF   2 1 − r 2 + (2ζ r)2

(2)

where r is the ratio of forcing frequency to the natural frequency of structure and ζ is the damping ratio.

4.2 Hydrodynamic Loads on Substructure The substructure has to be designed for a designed wave height of 4 m and period of 12 s. The hydrodynamic forces for this wave conditions are estimated using Morison’s equation, which is applicable for members with diameter smaller than 0.2 times of wavelength [9]. Considering the general dimensions of substructure for fixed offshore wind turbines, Morison’s expression is commonly used. It is a semi-empirical formula which assumes the total force as a sum of inertia component due to the fluid acceleration and a drag component due to fluid velocity. The wave kinematics such as velocity and acceleration required by Morison’s equation can be obtained by considering different wave theories. The choice of wave theory depends on wave height (H), wave period (T) and water depth (d). Chart based on experimental results are available to guide the use of wave theory based on two non-dimensional parameters (H/gT2) and (d/gT2). Based on this chart stokes second-order [10] wave theory is used. The currents mostly exist in the same direction of wave and it will be the critical case for design. Surface current of 1.5 m/s with one-seventh power profile [11] variation is considered for design of substructure. The current velocity exert drag force on the structure and cannot be algebraically added to wave forces because of nonlinear term in the Morison’s drag equation. So, The total drag force due to wave and current is obtained by considering vector sum of current velocity and water particle velocity. The combined drag and inertia force (including wave and current) varies with time and will be maximum only at one occasion. In order to find the

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maximum force, phase angle is varied from 0° to 360° with an increment of 10° and the base shear for each case is estimated. It is observed that maximum base shear is at 300° phase and this case is used for design of substructure. The methodology adopted for substructure development is shown in Fig. 4. The details of substructure and environmental parameters are given in Table 4 and Table 5 respectively.

External Condition

Loads

Wind

Aerodynamic

Waves

Hydrodynamic

Soil

Soil Structure Interaction

Blade and Tower Substructure Foundation

Fig. 4 Methodology followed for substructure development Table 4 Substructure concepts—gravity based foundation [12] Wind turbine

Rated power (MW) Hub height (m)

Gravity-based foundation

5 90

Tower diameter (m)

6

Rotor diameter (m)

126

Water depth (m)

6

Diameter (m)

20

Height (m)

10

Weight (tons)

1226

Table 5 Estimated loads for given environmental parameters Load Value Equipment load (turbine nacelle + rotor assembly)

350 T

Aerodynamic load-turbine

1220 KN

Wind load-tower Hydrodynamic load

445.13 KN 1278 KN

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Fig. 5 Solid and FEM models for gravity-based foundation

4.3 Structural Analysis of Gravity-Based Foundation The gravity-based is modelled using three noded plates as shown in Fig. 5 and rigid links are used to transfer the loads at base of monopile to inner shaft of gravity base foundation. The gravity foundation mainly consists of five components base plate, outer shaft, inner shaft, inclined shaft and stiffeners (Fig. 5). The base plate of the foundation is 20 m diameter, with two concentric shafts. The inner shaft has a radius of 3 and 13 m height, which holds the monopole. The outer shaft has a radius of 10 m and its height being 6 m. An inclined slab connects the top of the inner and the outer shaft. There are six stiffeners to connect the inner and outer shaft and to increase the stiffness. The modelled structure is designed for bending moments in orthogonal directions and the reinforcement is proved as per IS 456. The grade of concrete and steel for design are M40 and Fe415, respectively. The configuration of the foundation is also checked for stability against sliding and overturning and bearing with a Factor of Safety of 22, 31 and 3, respectively.

5 Installation Methodology A brief installation procedure of gravity-based foundation is shown in Fig. 6.

5.1 Gravity-Based Foundation The installation methodology for gravity-based foundation is shown in Fig. 6. The gravity-based foundation is constructed on a steel platform nearby the fishing harbour.

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Construction of Foundation near port

Sea Bed preparation at Site

Launching of Foundation into water by hydraulic jacks

Foundation launched into sea for towing

Foundation towed to the site

Foundation positioned and lowered

Fig. 6 Installation methodology for a gravity-based foundation

The monopole is then installed through inner ring of foundation. In the second stage, the landside edge of the platform is raised by hydraulic jacks. The gravity-based foundation is slid into the water. Due to buoyancy effects, the structure will float. The gravity-based foundation is then towed to the required position using a tug. Before lowering the foundation, the seabed has to be levelled using gravel bed. The foundation is then positioned using tugs and then lowered by ballasting water into it. The hollow chambers inside the foundation are filled with plain cement concrete to increase the stability of the foundation. The static stability of foundation is carried out and the draft is estimated to be 2.83 m from the bottom. As the foundation needs to be towed for long distance, it is essential to identify the natural frequencies and Response Amplitude Operations (RAO). Natural frequencies and RAO’s are computed for three translation modes

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HEAVE RAO

PITCH RAO

2.5

1.2

2

1 RAO

0.8 RAO

701

0.6

1.5 1

0.4 0.2

0.5

0 0

5

10

15

20

0

TIME PERIOD(S)

0

5

10 15 TIME PERIOD(S)

20

Fig. 7 Heave and pitch RAO’s for gravity foundation

and three rotation modes. These RAO’s are extracted using MAXSURF MOTIONS and are given in Fig. 7. It can be observed that the natural frequency is far away from the encounter frequency of waves (5–30 s).

6 Commercial Viability A typical wind farm with 50 units was considered for costing. The installation of the gravity-based foundation involves local construction within the fishing harbour and its towing to the site through open sea (Table 6).

7 Conclusion The energy demand in Lakshadweep islands cannot be met through conventional sources alone and hence the government decided to encourage renewable sources of energy. Offshore wind energy will be a visionary solution for the Lakshadweep Islands. Aerodynamic and hydrodynamic loads have to be calculated for an offshore wind turbine. Aerodynamic loads are estimated using beam element momentum theory for various load conditions specified in IEC 61400 standard and converted to equivalent static force using dynamic amplification factor. Maximum equivalent static loads of 1.22 MN was observed from extreme operating gust rated case. The hydrodynamic loads are estimated using Morison’s equation and suitable wave theory. The monopole and tower are modelled as beam elements and the gravity structure is modelled using three noded plates. The soil–structure interaction is modelled using springs with suitable stiffness. Eigenvalue analysis results indicate natural frequency of 1 s for gravity-based foundation. It can be observed that natural frequencies are well separated from regu-

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Table 6 Preliminary cost estimate for gravity foundations S. no. Item Units Unit price

Qty

Cost (Crs.)

1

Structural steel

tons

140,000

147

2.06

2

M 40 grade m3 for RCC Steel for RCC tons

12,000

533

0.64

80,000

79.95

0.64

500

3043

0.15

1

0.30

736

0.04

1

0.50

3 4

5

6

7

m3

Sand for filling inside foundation Towing per unit foundation for 100 km Dredging for 1.5 m and levelling the ground

m3

Dredging per unit existing fishing harbour to required draft of 4 m and for other infrastructure Total cost of gravity-based foundation

3,000,000

500

5,000,000

4.33

lar wave periods (6–30 s) and operating frequency of wind turbine (5 s). So, it can be concluded that the substructure is safe against resonance due to waves and turbine rotation. Static analysis for extreme event shows tip deflection of 42.35 cm; a utilization factor of 0.46 for gravity-based foundation. All these analyses are performed using SACS software and designed based on API standards. The stability of gravity foundation is also checked against sliding, overturning, soil bearing and static flotation stability. The concrete design is carried out as per IS 456 and steel is provided appropriately. The static draft obtained is 2.83 m. The RAO’s of the foundation are estimated using MAXSURF MOTIONS and it is observed that natural frequencies are well separated from regular wave frequencies 5–30 s. In case of gravity-based foundation installation methodology considering marine spread in India is identified. In this method, the foundation is cast on shore and towed to required location and lowered.

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References 1. Tata Energy Research Institute (2001). http://www.globalislands.net/userfiles/_india_ lakshadweep1.pdf. Accessed 18 Aug 2016 2. MNRE (2015) https://mnre.gov.in/file-manager/…/National-Offshore-Wind-Energy-Policy. pdf. Accessed 30 Aug 2016 3. Zhang J et al (2010) Response surface based cost model for onshore wind farms using extended radial basis functions. In: Proceedings of the ASME IDETC 2010, Montreal, Quebec, Canada, 15–18 Aug 2010 4. EWEA (2015) https://www.ewea.org/…/statistics/EWEA-European-Offshore-Statistics-H12015.pdf. Accessed 8 Sep 2016 5. Wen Chen I et al (2016) Design and analysis of jacket substructures for offshore wind turbines. https://doi.org/10.3390/en9040264 6. Mani A, Rangarajan S (1996) Wind energy resource survey in India-IV . Allied Publishers Limited, New Delhi 7. NYSERDA (2010) https://www.nyserda.ny.gov/About/…/Research-and-Development…/ Wind-Reports. Accessed 25 Aug 2016 8. IEC (2009) Wind turbines: design requirements for offshore wind turbines, IEC 61400-3:2009 9. Techet AH (2004) Morrison’s equation, Massachusetts institute of technology, 13.42 04/01/04 10. Schaffer HA (1996) Second-order wavemaker theory for irregular waves, Pergamon. Ocean Eng 23(1):47–48 11. Bryden IG et al (2007) Tidal current resource assessment. Proc Inst Mech Eng Part A J Power Energy 221(2):125–135. https://doi.org/10.1243/09576509JPE238 12. Jonkman J et al (2009) Definition of a 5 MW wind turbine for offshore system development, NREL technical report. NREL/TP-500-38060, National Renewable Energy Laboratory (NREL), Golden, CO, USA, Feb 2009

Control-Oriented Wave to Wire Model of Oscillating Water Column R. Suchithra

and Abdus Samad

Abstract The interest in wave energy converters (WECs) is increasing, the study of grid connection of WEC along with the control system has become inevitable. WEC such as an oscillating water column (OWC) device involves conversions in various physical domains, thus a model describing the conversions at each stage and coupling between them should be accurate yet simple enough to reduce the computation time involved. The already existing models do not include all the components of wave to wire conversion. This paper presents a wave to wire model for control system studies. The model reduction technique is used to create a dynamically equivalent model for any large systems have more interconnecting stages. The dynamics involved in conversion stages are hydrodynamic and aerodynamic coupling at the capture chamber, aerodynamic and thermodynamic coupling inside the capture chamber, aerodynamic and rotor dynamic coupling in air turbine; and rotor dynamics and generator dynamics in the turbine generator coupling. Thus, a wave to wire model is represented to capture all the dynamics involved. It is observed that the model retains its fundamental physics, improves the computation time and reduces the number of unknowns to describe the state-space of OWC system. The accuracy and efficiency of the model is investigated through various static and dynamic analyses and found acceptable for OWC-WEC control system studies. Keywords Oscillating water column · Wave to wire model · Model reduction Wells turbine · Doubly fed induction generator

R. Suchithra (B) · A. Samad Wave Energy and Fluids Engineering Lab, Ocean Engineering Department, Indian Institute of Technology Madras, Chennai 600036, TN, India e-mail: [email protected] A. Samad e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_52

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Nomenclature Abbreviation DFIG OWC PTO ROM WEC

Doubly fed induction generator Oscillating water column Power take-off Reduced-order model Wave energy converter

Symbols a Vc B bt C Ca Cd Cs Ct d Dt D  E dq Fa F FK F Δpair g h H ha0 idq J k K Kt L lr M Rc R

Wave amplitude Volume of the air chamber Damping coefficient Rotor blade height Hydrostatic stiffness Input power coefficient Discharge coefficient Speed of sound Torque coefficient Draft of the OWC Diameter of the turbine System drag Transient voltage Added mass force Froude–Krylov force Air force on water column Acceleration due to gravity Water depth Wave height Height of the water column Direct quadrature axis current Moment of inertia of motor generator set Wave number Stiffness coefficient Turbine constant Wavelength Chord length of rotor Water column mass Radius of the water column Resistance

Control-Oriented Wave to Wire Model of Oscillating Water Column

rt Ti Te To Tt Ur vdq vx X  X z Z zt γ Δp ζ η θr ρa ρs u´ φ φt ω ωr ωs m Ma Nr p pc q

707

Mean radius of the turbine Time period Electromagnetic torque Transient open circuit time constant Turbine torque Circumferential velocity Direct quadrature axis voltage Mean axial velocity Reactance Transient impedance Internal free surface elevation Impedance Number of blades Heat capacity ratio of air Pressure drop between the chamber and atmosphere Damping coefficient Water surface elevation Torsional displacement of the rotor Density of air Density of water Water particle velocity Phase angle of the wave Flow coefficient Wave angular frequency Rotor angular frequency Generator angular frequency Mass of air inside the chamber Added mass Rotor speed Number of generator poles Chamber pressure Volume flow rate

1 Introduction Ocean waves contain enormous potential as a source of renewable energy. The estimated power of wave energy around the world is around 2–3 TW [1]. A major part of the worldwide energy crisis could be met by trapping the immense power of ocean waves. Among the wave energy converters (WECs), the oscillating water column (OWC) based WEC is the most exploited technology. The OWC device captures the energy from the oscillating nature of waves, and the concept is quite different from available WECs. The oscillating wave creates an oscillating air column, which drives a turbine. As there is no direct contact of power

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take-off devices with the waves, and this concept can be conceived in any offshore and shoreline structures. The OWC system is making progress with a few commercially available plants and prototype models [2]. Various OWC models show the impact of its geometrical design on the performance of the device. An equal attention should be given to the effect of PTO and auxiliary devices on the overall performance of OWCWEC. Challenges in OWC system include natural environment, device constraints, mismatch of wave frequency to resonant frequency and variation in wave conditions and air velocity. Due to all these challenges, the overall system performance is significantly affected. From power system point of view, the grid integration of a typical OWCWEC suffers from power fluctuation, synchronization issues, weak AC grid with small-circuit ratio and disturbances in system inertia. The mathematical model of OWC device is necessary to study its overall performance for various sea states. A wave to wire model will be helpful in that case. The model should capture all the necessary dynamics of the WEC. The solution for many of the problems associated with an OWC device is to control the operation of the plant. As waves vary in height and period, a good control scheme can be helpful in improving the efficiency of a wave energy converter. For power system studies and control application, the model need not be a high-fidelity model. Thus, a reduced-order model (ROM) of OWCbased WEC is sufficient to study the dynamics involved from wave to wire (Fig. 1) (Table 1). As a complete model of OWC-WEC is necessary to understand the dynamics involved in each conversion stage, This paper describes the development of, fully coupled, bidirectional, time-domain wave to wire ROM of a OWC-based WEC, containing a Wells turbine coupled to a doubly fed induction generator (DFIG). Furthermore, a wave to wire ROM is considered and outputs of each stage are analyzed with theoretical predictions. A state-space equation is formulated which explains

Fig. 1 Basic block diagram of wave to wire model

Control-Oriented Wave to Wire Model of Oscillating Water Column Table 1 Wave to wire models or historical developments Author Applications

709

Inference

Iturrioz et al. [3]

Radiation, hydrostatic, excitation and viscous forces are considered

Model does not include the effect of air turbine and generator

Brendmo et al. [4]

A mechanical mass–spring equivalent model of the OWC system with excitation and diffraction forces Wave to wire full order model including the radiation force, diffraction force and air compressibility is taken into account The nonlinear damping of the turbine is calculated with the wave to wire model Hydrodynamics between the waves and chamber

This model does not accounts for dynamics of turbine and generator connected to an OWC device This model does not clearly state the dynamics of internal surface elevation

Alberdi et al. [5]

Anand et al. [6]

Xie et al. [7]

Dynamics inside the capture chamber is not modelled The model does not capture the necessary dynamics involved in all the conversion stages

all the dynamics involved in the wave to wire conversion. The rest of the paper is structured as follows: In Sect. 2, model of capture chamber hydrodynamics and aerodynamics are developed. Turbine aerodynamics is modelled in Sect. 3. The ROM of generator is developed in Sect. 4. Results for different wave climate are analyzed in Sect. 5. Finally, concluding remarks are made in Sect. 6.

2 Capture Chamber Model The OWC-WEC consists of two blocks: collecting chamber and PTO system. The collecting chamber takes power from waves and transfers to the air in the chamber [8]. The chamber has an opening below the mean sea level. When a wave approaches the device, water enters the chamber, and forces the air to escape through the turbine annuli.

2.1 Wave Hydrodynamics A wave can be described by its length, height and water depth. The other parameters such as water particle velocity and acceleration can be derived from the above parameters. Water surface elevation varies sinusoidally with time and is a function of

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wavenumber and frequency as given in Eq. (1). Wave motion near the shore has elliptic oscillations with a certain speed in a certain direction [9]. Equation (2) represents the water particle velocity. ηi (t)  ai cos(ωi t + φi )

(1)

Water particle velocity and acceleration at arbitrary depth h is described as vi (t)  −

ai ωi sinh ki (z + h) sin(ωi t + φi ) sinh ki h

(2)

2.2 Capture Chamber Hydrodynamics and Aerodynamics This part describes the behaviour of water surface elevation by the external excitation from the waves through simulations. Equation (3) is the time-domain motion of an oscillating water column [10]. M z¨ + B z˙ + C z  F(t)

(3)

where M  ρs π Rc2 (d + z)  B  0.2 C(M + Ma ) C  ρs gπ Rc2 2 Ma  ρs π Rc3 3 2.2.1

Force Calculation

The total force acting on the water column includes the added force F a (t), the Froude–Krylov force F FK (t) and force due to the changing air pressure inside the chamber F δair (t). Thus, the expression for excitation force is F(t)  Fa (t) + FF K (t) + Fδair (t)

(4)

Fa (t)  Ma (ν˙ − z¨ )

(5)

The excitation force is equivalent to Froude–Krylov force with the assumption that diffraction component in the excitation force is negligible and can be ignored, as the OWC device is sufficiently small and does not affect the pressure field. This force in the vertical direction is simplified as the ‘linear wave theory’. This theory predicts that only the variation of η(t) is sufficient to describe the heave motion of internal

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water surface elevation inside the chamber, the wave motion are incompressible and irrotational. The force F FK (t) can be expressed as FF K (t)  π R 2 ρs gai

cosh ki (h − d) cos(ωi t + φi ) cosh ki h

(6)

The air force is calculated by Fδair (t)  − p(t)π R 2

(7)

A force created due to pressurization and depressurization of air pocket inside the capture chamber, couples the aerodynamics and thermodynamics problems of OWC device, this force in turn affect the dynamics of internal water surface elevation. Equation (8) shows the dynamics of chamber pressure [11]. dpc C 2 dm γ pc d Vc  s − dt Vc dt Vc dt

(8)

where Vc  π R 2 (h a0 − z).

3 Aerodynamics of Wells Turbine Wells turbine is one of the most economical turbine for wave energy conversion. The operating range of the turbine depends on its geometry. Turbine characteristics under steady flow condition are considered as initial condition in this work. The input to the turbine is an oscillating pressure drop across the turbine. Modelling of turbines is done using the Eqs. (9) and (10). The characteristic curves used for modelling are obtained from the work of Setoguchi et al. [12]. pq(t)   Ca    2 ρa νx + Ur2 bt lt n t νx /2 Tt   Ct    2 ρa νx + Ur2 bt lt n t rt /2

(9) (10)

An OWC-WEC uses the fast rotational speeds generated by the air turbine for driving a generator for electricity conversion. Numerical simulations carried out on Wells turbine shows its operating speed for different wave conditions [13]. However, the limits on turbine rotation are also dependent on the type of generator used. Thus, a variable speed generator is prescribed for wave energy conversion, such that the turbine rotation can be tuned to wave climate. For a Wells turbine, the mass flow is calculated using the Eq. (11), which relates the turbine geometry and differential pressure with the turbine rotational speed. This

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relation is important in order to analyze the damping imposed by a turbine on the operation in different sea state [14]. dm K t D p − dt Nr

(11)

where K t is a constant associated with the specific turbine design, for a given turbine operating at a constant speed, the mass flow is linearly dependent on the pressure difference. This approximation is used by Nunes et al. [15].

4 ROM of DFIG ROM is a model reduction technique to obtain the dynamics of the machine by simplifying the set of differential equations describing the machine. The grid transient in the network usually creates high-frequency terms, which are not of particular interest in electromechanical transient studies. The ROM can be written as a simple Thevenin’s equivalent voltage source otherwise called as transient voltage equation. The equation is rearranged in terms of stator, rotor voltages and transient impedance. In this formation, the stator flux is no longer a state variable. The transformations are done in synchronous reference frame. Equations (13) and (14) shows the transient voltage for direct and quadrature axis, respectively.   

    d Ed 1 Xs − X  Xs − X    − 1 + X  2 E d + sωs To + Rs  2 Eq Z Z dt To  



   Xs − X Xm 1  Xs − X vqr + X  2 vds − Rs  2 vqs − To ωs (12) Z Z To Xr   

    d Eq 1 Xs − X  Xs − X    − 1 + X  2 E q − sωs To + Rs  2 Ed Z Z dt To  



   Xs − X Xm 1  Xs − X vdr + R s  2 vds + X  2 vqs + To ωs (13) Z Z To Xr J

1 dθ ∂ 2θ + θ  Tt − Te +D 2 ∂t dt K

(14)

The input variables of the system are the air velocity and pressure drop across the turbine, which are both time variant. The dynamic equation for the wave energy plant is the torque balance as given in Eq. (14), which is a second-order equation representing a simple mass, spring and damper; excitation given to the mechanical system, its value is equal to the difference of turbine torque and electromagnetic torque.

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This input–output system gives a good approximation of the complete OWC device. With this formulation, any linear or nonlinear control algorithm can be implemented. Provided the conditions such as approximation error is minimum, preservation of stability and passivity of the original system, and the model should be computationally effective. The control system is not simulated, as it is not the purpose of the paper to study how it works.

5 Results and Discussion In this work, a MATLAB code for solving the OWC subsystems in the time domain was developed. The differential equations were solved in the ode45 solver. Figure 2 shows the non-dimensional internal water surface elevation for normalized time. The results of z also follow the same trend as with the work of Iturrioz et al. [3], their model was developed based on Cummins equation [16], which is approximated by means of a state-space system that comes from solving state-space system of radiation force convolution integral. Figure 3 shows the time series of differential pressure with respect to atmospheric pressure inside the chamber. The chamber creates an oscillating pressure, as a result, a bidirectional airflow is created, which is a driving force to the turbine. A speed control can be helpful in tuning the turbine according to the variation of the differential pressure. Variation of pressure drop for different wave height is necessary to evaluate the operating range of OWC device for various wave climate. The differential pressure drop variation along with turbine rotational speed can be used to track the maximum power that can be absorbed for a given sea state. A maximum power point tracking algorithm can be helpful in such analysis (Fig. 4). The efficiency of the OWC device is greatly dependent on the coupling of the turbine with the generator. The damping depends on the geometry, size and rotational speed of the turbine. Figure 5 shows the damping variations for different wave periods. The effect of turbine damping on the OWC duct plays a significant role in the energy conversion process. This damping of the turbine can be altered to a desired value by changing the rotational speed of the generator hereby modifying the turbine speed. The damping of the turbine is dependent on incoming wave frequency and

Fig. 2 Time series internal chamber dynamics for different wave heights

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Fig. 3 Differential pressure variations for different wave heights

Fig. 4 Rotor speed variations for different wave heights

Fig. 5 Damping coefficient for different wave period

rotational speed of turbine. As wave frequency not controllable, thus damping can be changed by rotational speed control. The maximum peak power reached is around 2.5 kW. The results in Fig. 6 show the time series of transient voltages at different time instances for H  0.5 m and T i  5 s. For t  0–10 s.

Control-Oriented Wave to Wire Model of Oscillating Water Column

(a)

715

(b)

Fig. 6 Direct and quadrature axis transient voltage for an instance of a 0–10 s, b 1–1.5 s

6 Conclusion A reduced-order wave to wire model of an OWC-WEC in time domain is presented in this study. The ROM reduces the dimensions of the system and extracts a dynamic model relevant to control systems. The proposed model sufficiently captures all the necessary dynamics involved in wave to wire conversion of OWC-based WEC. The time-domain model incorporates a turbine model and its control system. This paper evaluates the capture chamber dynamics to evaluate the pressure drop and flow velocities for different wave conditions with a turbine fitted in the outlet of the chamber. The model is helpful in defining each stage of conversion in an OWC device clearly. It gives a coherent picture of the dynamics of internal surface elevation for various wave conditions and its effect on other dynamically coupled devices. When the turbine starts rotating, the damping associated with the coupled system, changes and affects the internal dynamics of the chamber. The generator dynamics is modelled using a third-order model of DFIG. The stator flux oscillations are removed. The model is adequate for transient and steady-state operation. The model allows one to deal with the machine with only three differential equations in the electrical part. The initial transients of state variable of DFIG captured in this model. Thus, the time-domain model of OWC device is suitable for control system applications.

References 1. Falnes J (2007) A review of wave-energy extraction. Mar Struct 20:185–201. https://doi.org/ 10.1016/j.marstruc.2007.09.001 2. Heath TV (2012) A review of oscillating water columns. Philos Trans R Soc A Math Phys Eng Sci 370:235–245. https://doi.org/10.1098/rsta.2011.0164 3. Iturrioz A, Guanche R, Armesto JA, Alves MA, Vidal C, Losada IJ (2014) Time-domain modeling of a fixed detached oscillating water column towards a floating multi-chamber device. Ocean Eng 76:65–74. https://doi.org/10.1016/j.oceaneng.2013.11.023 4. Brendmo A, Falnes J, Lillebekken PM (1996) Linear modelling of oscillating water columns including viscous loss. Appl Ocean Res 18:65–75. https://doi.org/10.1016/01411187(96)00011-9

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5. Alberdi M, Amundarain M, Garrido AJ, Garrido I, Casquero O, De la Sen M (2011) Complementary control of oscillating water column-based wave energy conversion plants to improve the instantaneous power output. IEEE Trans Energy Convers 26:1021–1032. https://doi.org/ 10.1109/TEC.2011.2167332 6. Anand S, Jayashankar V, Nagata S, Toyota K, Takao M, Setoguchi T (2007) Performance estimation of bi-directional turbines in wave energy plants. J Therm Sci 16:346–352. https:// doi.org/10.1007/s11630-007-0346-1 7. Xie J, Zuo L (2013) Dynamics and control of ocean wave energy converters. Int J Dyn Control 1:262–276. https://doi.org/10.1007/s40435-013-0025-x 8. Drew B, Plummer AR, Sahinkaya MN (2009) A review of wave energy converter technology. Proc IMech Part A J Power Energy 223:887–902. https://doi.org/10.1243/09576509JPE782 9. Dean RG, Dalrymple RA (1989) Water wave mechanics for engineers and scientists. World Scientific Publishing Co., Pte. Ltd., Singapore 10. Gervelas R, Trarieux F, Patel M (2011) A time-domain simulator for an oscillating water column in irregular waves at model scale. Ocean Eng 38:1007–1013. https://doi.org/10.1016/ j.oceaneng.2011.04.006 11. Falcão AFO, Henriques JCC, Cândido JJ (2012) Dynamics and optimization of the OWC spar buoy wave energy converter. Renew Energy 48:369–381. https://doi.org/10.1016/j.renene. 2012.05.009 12. Setoguchi T, Santhakumar S, Maeda H, Takao M, Kaneko K (2001) A review of impulse turbines for wave energy conversion. Renew Energy 23:261–292. https://doi.org/10.1016/S09601481(00)00175-0 13. Halder P, Samad A (2016) Optimal Wells turbine speeds at different wave conditions. Int J Mar Energy 16:133–149. https://doi.org/10.1016/j.ijome.2016.05.008 14. Falcão AFO, Rodrigues RJ (2002) Stochastic modelling of OWC wave power plant performance. Appl Ocean Res 24:59–71. https://doi.org/10.1016/S0141-1187(02)00022-6 15. Nunes G, Valério D, Beirão P, Sá da Costa J (2011) Modelling and control of a wave energy converter. Renew Energy 36:1913–1921. https://doi.org/10.1016/j.renene.2010.12.018 16. Cummins WE (1962) The impulse response function and ship motions. Schiffstechnik 101–109

Hysteresis Behavior for Wave Energy Conversion Device Under Alternative Axial Flow Conditions Paresh Halder , Tapas K. Das , Abdus Samad and Mohaned H. Mohamed

Abstract Wells turbine is an axial flow air turbine extensively used in the oscillating water column (OWC) of ocean energy harvesting device. The turbine has low aerodynamic efficiency at higher flow rate and poor starting characteristics. In this paper, the characteristics of the hysteresis behavior of a Wells turbine for a wave energy conversion device under alternative axial flow conditions are reported. The numerical work is carried out by solving the three-dimensional unsteady Reynolds Average Navier–Stokes equations (URANS) with two-equation eddy viscosity model. It is noticed that the unsteady numerical results are associated with two hysteresis loop. In the clockwise hysteresis loop, larger flow separation can be noticed on the blade suction side due to stronger vortex while flow separation decreases due to weaker vortex during counterclockwise hysteresis loop. Also, the effect of the blade sweep and blade profile thickness on the hysteresis behavior of the wave energy conversion device are reported. Keywords Wells turbine · Wave energy conversion · Unsteady Hysteretic behavior

P. Halder (B) · T. K. Das (B) · A. Samad (B) Wave Energy and Fluids Engineering Laboratory (WEFEL), Ocean Engineering Department, Indian Institute of Technology Madras, Chennai 600036, TN, India e-mail: [email protected] T. K. Das e-mail: [email protected] A. Samad e-mail: [email protected] M. H. Mohamed (B) Faculty of Engineering-Mattaria, Mechanical Power Engineering Department, Helwan University, P.O. 11718 Cairo, Egypt e-mail: [email protected] M. H. Mohamed Mechanical Engineering Department, College of Engineering and Islamic Architecture, Umm al-Qura University, P.O. 5555 Makkah, Kingdom of Saudi Arabia © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_53

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1 Introduction The wave energy converters (WECs) are still in their nascent stage and efforts are going on to push it to its adolescent stage. Among ample concepts to harvest marine energy, the wave energy has tremendous potential. Several countries have installed a WEC device called oscillating water column (OWC), and it is the most common device for WEC. The OWC consists of an air chamber where the air oscillates due to the action of waves. The pneumatic energy of the air converts to mechanical energy by the turbine and a generator converts this mechanical energy to electrical energy. A typical reaction turbine is Wells turbine (Fig. 1) and it has a narrow operating range while peak efficiency is high. It consists of several symmetrical airfoil blades systematically arranged around a hub and the turbine has 90° stagger angle. The turbine is a unidirectional rotating and axial flow type. Several researchers have reported the steady and unsteady behavior of Wells turbine both numerically and experimentally [1–5]. Halder et al. [6–8] optimized the blade sweep, profile shape on the performance of Wells turbine. The results indicated that the blade sweep and profile shape enhance the performance. Kim et al. [9] numerically studied the hysteresis characteristic of Wells turbine based on four different parameters. The blade thickness and the angle of attack have a more dominant effect on the turbine performance compared to the setting angle and the gap-to-chord ratio. The starting and running characteristics of Wells turbine based on different parameters such as blade solidity, setting angle, tip-tochord ratio are reported in [10, 11]. Different types of OWC devices and optimization techniques discussed in Das et al. [12] indicates that optimized geometry enhances the performance of Wells turbine. Thakker and Abdulhadi [13, 14] numerically studied the effect of blade profile under unidirectional and sinusoidal flow conditions. Kinoue et al. [15, 16] numerically explained the hysteresis loop occurring in accelerating and decelerating loop during sinusoidal flow. The clockwise and anticlockwise hysteresis loop during acceleration and deceleration loop affects the flow separation in suction surface (SS) of the Wells turbine.

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In view of the above literature, there is a lack of understanding of hysteresis behavior of a Wells turbine. The blade profile and sweep alteration affect the turbine performance. Therefore, a numerical simulation of the optimized blade geometry under unsteady flow condition can give an insight into the flow physics of hysteresis behavior. Hence, both steady and unsteady flow simulations for optimized blade geometry of Wells turbine have been carried out in this work. The two optimum design variable such as blade profile thickness and sweep parameters are taken from the previous work [7]. The details of the optimization procedure are also discussed in the previous work [7].

2 Numerical Approach The present work reports an optimized Wells turbine blade geometry, which was taken from previous work of Halder and Samad [7]. A CAD model was prepared for the flow domain or computational domain and CFD toolbar ANSYS CFX® v14.5 [17] was used for numerical simulation. The numerical simulations are solved by 3D unsteady Reynolds averaged Navier–Stokes (URANS) equations with two equations turbulence k–w SST model. The governing equations were continuity, momentum, and high resolution and first-order schemes were implemented in the computations. The turbine has eight rotor blades, which rotate axis-symmetrically at a constant angular velocity of 209.44 rad/s. A single rotor blade having the NACA0015 airfoil was simulated and periodic boundary conditions in the tangential directions were applied. The sinusoidal velocity profile is introduced at the velocity inlet to generate the wave while outlet boundary conditions are imposed as opening conditions. The details of the mesh information and boundary conditions are provided in the previous work [7]. The grid independence study was reported in the previous work [7].

3 Result and Discussion The computational results are validated with the existing literature as discussed in the previous work Halder and Samad [7]. The validations are compared in terms of nondimensional performance parameter: flow coefficient (U*), pressure coefficient (Δp*), torque coefficient (T*), and efficiency (η). The results show that the CFDproduced results are well accurate. Figure 2 illustrates the numerical results of pressure drop coefficient (P*), torque (T*) for both unsteady and steady behaviors at a wider flow coefficient for the sinusoidal flow. The continuous and dash lines are the steady and the unsteady result, respectively. The results showed that the clockwise hysterics loop support the steady results for both cases. However, the result does not match closely during decelerating flow. The flow coefficient varies 0.0–0.4 for sinusoidal flow. In Fig. (3b), blade stalls at U  0.275 (Optimum design ‘A’) and 0.225 (Optimum design “E”) for steady and

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U  0.325 (Optimum design “A”) and U*  0.220 (Optimum design “E”) for the unsteady cases. After the stall, the torque varies randomly as shown in Fig. 3b. However, the calculated pressure has counterclockwise and clockwise hysteresis loop in the unstalled and stalled condition, respectively. It can be seen that the hysteresis mechanism helps in the dynamic stall of the aerofoil. Similar hysteresis behavior was also reported in other literature [18, 19]. Figure 4 represents the pressure variation at mid-span of the flow passage for different flow coefficient during accelerating and decelerating flow. By comparing Fig. 5a, b, it is shown that the pressure is almost the same in both cases for a given flow coefficient. At flow coefficient U*  0.325, it is observed that the lower pressure occurred at the blade suction side near the leading during accelerating flow compared to deceleration flow for optimum design “A” which implies that flow attached the suction side during decelerating flow. Figure 5 shows the circumferential velocity distribution at the mid-span of the flow passage for optimum blade A and E. By comparing Fig. 4a, b, it can be observed that higher flow separation is noticed near the blade trailing edge during accelerating flow while flow attached to the blade surface during decelerating flow. However, for optimum blade A, the flow separation on the SS is less compared to the optimum

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blade E for both accelerating and decelerating flow. As a result, the optimum blade A has higher torque coefficient in the hysteresis loop compared to the optimum blade E.

4 Conclusion In the present investigation, two different optimize blade are investigated using unsteady 3D RANS equations with two-equation turbulence closer model. Sinusoidal flow is used to get the hysterics behavior. The numerical results are well matched during accelerating flow for both cases. However, after deep stall condition, the torque varies randomly for optimized blade A. The main inference is as follows: (i) The calculated results show two different hysteresis loops: stalled conditions are found during accelerating flow while unstalled conditions are noticed during decelerating flow. (ii) The deep stall is a notice at flow coefficient U  0.325 and 0.220 for optimized blade A and E during accelerating flow.

References 1. Brito-Melo A, Gato LMC, Sarmento AJNA (2002) Analysis of Wells turbine design parameters by numerical simulation of the OWC performance. Ocean Eng 29:1463–1477. https://doi.org/ 10.1016/S0029-8018(01)00099-3 2. Raghunathan S (1995) The Wells air turbine for wave energy conversion. Prog Aerosp Sci 31:335–386. https://doi.org/10.1016/0376-0421(95)00001-F 3. Torresi M, Camporeale SM, Strippoli PD, Pascazio G (2008) Accurate numerical simulation of a high solidity Wells turbine. Renew Energy 33:735–747. https://doi.org/10.1016/j.renene. 2007.04.006 4. Halder P, Samad A, Kim J-H, Choi Y-S (2015) High performance ocean energy harvesting turbine design–a new casing treatment scheme. Energy 86:219–231. https://doi.org/10.1016/j. energy.2015.03.131 5. Taha Z, Sugiyono Sawada T (2010) A comparison of computational and experimental results of Wells turbine performance for wave energy conversion. Appl Ocean Res 32:83–90. https:// doi.org/10.1016/j.apor.2010.04.002 6. Halder P, Samad A, Thévenin D (2017) Improved design of a Wells turbine for higher operating range. Renew Energy 106:122–134. https://doi.org/10.1016/j.renene.2017.01.012 7. Halder P, Samad A (2016) Torque and efficiency maximization for a wave energy harvesting turbine: an approach to modify multiple design variables. Int J Energy Res 1–15. https://doi. org/10.1002/er.3694 8. Halder P, Rhee SH, Samad A (2016) Numerical optimization of Wells turbine for wave energy extraction. Int J Naval Architect Ocean Eng. https://doi.org/10.1016/j.ijnaoe.2016.06.008 9. Kim T, Lee, Yeon- Won, Ill-Kyoo Park, Toshiaki Setoguchi C-SK (2002) Numerical analysis for unsteady flow characteristics of the Wells turbine. In: Proceedings of the twelfth international offshore and polar engineering conference. Kitakyushu, Japan, May 26–31, 2002, pp 694–699 10. Kim T-H, Takao M, Setoguchi T et al (2001) Performance comparison of turbines for wave power conversion. Int J Therm Sci 40:681–689. https://doi.org/10.1016/S12900729(01)01257-1

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11. Inoue M, Kaneko K, Setoguchi T, Shimamoto K (1986) Studies on Wells turbine for wave power generator. Japan Soc Mech Eng 29:1177–1182 12. Das TK, Halder P, Samad A (2017) Optimal design of air turbines for oscillating water column wave energy systems: a review. Int J Ocean Climate Syst 8:37–49. https://doi.org/10.1177/ 1759313117693639 13. Thakker A, Abdulhadi R (2007) Effect of blade profile on the performance of Wells turbine under unidirectional sinusoidal and real sea flow conditions. Int J Rotat Mach 2007:1–8. https://doi.org/10.1155/2007/51598 14. Thakker A, Abdulhadi R (2008) The performance of Wells turbine under bi-directional airflow. Renew Energy 33:2467–2474. https://doi.org/10.1016/j.renene.2008.02.013 15. Kinoue Y, Setoguchi T, Kim T-H et al (2003) Mechanism of hysteretic characteristics of Wells turbine. Trans ASME 125:302–307. https://doi.org/10.1299/kikaib.69.610 16. Kinoue Y, Setoguchi T, Kim TH et al (2005) Hysteretic characteristics of the Wells turbine in a deep stall condition. Proc Institution Mech Eng, Part M J Eng Maritime Environ 218:167–173. https://doi.org/10.1243/1475090041737967 17. Curran R, Gato LMC (1997) The energy conversion performance of several types of Wells turbine designs. Proc Institution Mech Eng, Part M J Eng Maritime Environ 211:133–145. https://doi.org/10.1243/0957650971537051 18. Kinoue Y, Setoguchi T, Kim TH et al (2004) Hysteretic characteristics of the Wells turbine in a deep stall condition. Proc Institution Mech Eng, Part M J Eng Maritime Environ 218:167–173. https://doi.org/10.1243/1475090041737967 19. Kinoue Y, Mamun M, Setoguchi T, Kaneko K (2004) Hysteretic characteristics of monoplane and biplane Wells turbine for wave power conversion. Int J Sustain Energ 26:51–60. https:// doi.org/10.1016/j.enconman.2003.08.021

Ocean Current Measurements and Energy Potential in the Islands of Andaman Biren Pattanaik, D. Nagasamy, YVN Rao, Balaji Chandrakanth, Nitinesh Awasthi, Abhijeet Sajjan, D. Leo, Prasad Dudhgaonkar and Purnima Jalihal

Abstract The hydrokinetic energy potential of at Indian oceans remains largely untapped. The attempts toward utilizing this resource have made recently in India. However, those were mostly limited to academic studies. The current speeds along the Indian coastline are lesser as compared to other locations in the world. However, few places in India like the Gulf of Khambhat, Sundarbans, and Andaman and Nicobar Islands have currents due to tides. To initiate technology development to develop the hydrokinetic turbines and electric generator suitable for Indian sea climate, surveying of such location is essential. Early in 2008, when NIOT was executing the freshwater transportation project between islands, the current was visibly observed at Macpherson Strait in Andaman Island. Hence, the detailed current measurement exercise was carried out at the nearby Viper Island and Macpherson Strait. Even though the surface current was high on Viper Island, the current measured at 1–2 m below the sea water level was as low as 0.5 m/s (since it is a closed channel), whereas in Macpherson Strait it was observed as high as 2 m/s. In this location, the in-house developed prototype of φ 0.8 × 1 m straight bladed turbine was tested in floating configuration. In this trial, the current measurement was carried out over a period of time. The occurrences of current were plotted from these measured current data. From these occurrence data, the maximum available annual hydrokinetic energy is in the order of 4.8 MWh/m2 at this location. This paper focuses the suitable locations for ocean current turbine installations and current availability on Viper Island and Macpherson Strait of Andaman, India. Keywords Ocean current energy · Tidal · Current · Ocean current turbines Ocean current resource assessment · Acoustic Doppler current profiler

B. Pattanaik (B) · D. Nagasamy · Y. Rao · B. Chandrakanth · N. Awasthi · A. Sajjan · D. Leo P. Dudhgaonkar · P. Jalihal National Institute of Ocean Technology, Pallikaranai, Chennai 600100, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_54

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1 Introduction The primary sources of power generation in India are coal, hydro, nuclear power plant, etc. In case of Andaman and Nicobar group of islands the primary energy source is a diesel-based power plant. Energy is a key issue for sustainable development in any country. The grid extension to the islands is difficult to fuel transportation, and logistics are still challenging and proven to be costly. The ocean energy is vastly spread around the Indian coast and unharnessed. Hydrokinetic energy has still been an untouched potential and it requires further experimental measurements. In this work, measurement of the hydrokinetic currents at various locations of the Andaman Islands is presented. Also, hydrokinetic power module was designed and developed by NIOT and also the power module was demonstrated in an ocean current. As a part of the first phase, the current measurements were carried out near Viper Islands and also at the Macpherson Strait of Andaman as shown in Fig. 1. This paper discusses measurement methodology, ocean current measurement, and demonstration of the hydrokinetic power module in Indian Ocean current and hydrokinetic energy potential in that location.

Fig. 1 Current measurement locations in Andaman Islands

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2 Measurement Methodology The selection of the measurement methodology plays a vital role in drawing conclusions from the causes and factors affecting the phenomenon. Since the potential area remains to be vast, it was decided to prioritize, select locations based on the topographical data that are available and measurements were carried out at select locations based on that data. Multiple locations were simultaneously tested to find the significance of the currents measured and the data were recorded. The data was processed in the shore station, and the potential locations addressing the constraints that include logistics, safety, accessibility, service requirement, etc., were identified. Since the locations were measured for a short span, it was decided to conduct the measurement over two full tide cycles, i.e., spring and neap tides and all the data were recorded. The data were analyzed to study the hydrokinetic potential available at the select location and was plotted accordingly. It was interesting to observe that the variations were large over the duration and thereby to study its significance, it was planned to conduct a case study to visualize the potential in terms of power. This detailed methodology is as shown in the flowchart given below as shown in Fig. 2.

3 Current Measurements Current measurements were carried out near Viper Islands, and also at the Macpherson Strait of Andaman as shown in Fig. 1. As the location is in form of an open channel where water flow reversible with each tidal variation. The second reason for choosing this was as it is near to Port Blair, where logistics and operation of hydrokinetic power module are easier.

3.1 Viper Island Current Measurement As a part of preliminary investigations around the Port Blair region, few locations were identified based on the topography, since the driving force of the current stream is primarily due to the current variations at the Andaman Islands. As seen in Fig. 1, the marked location “A” experiences the seawater stream travel in and out during the tidal variations. Figure 3a shows the hydrokinetic current profile measured at Viper Island (11° 39 50.6 N, 92° 41 42.9 E) with mounting instrument’s image. It was very interesting to observe that the surface currents measured were well above in the range of 1.5 m/s, and the currents at depths beyond 2 m were to be around 0.3 m/s as shown in Fig. 3b. Acoustic Doppler current profiler (ADCP) was used for this measurement exercise, since the measurement location experiences large range current and large depth

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Fig. 2 Flowchart of measurement methodology

range profitability. It is to be noted that the water region in southwest direction is enclosed by land, and there were not much appreciable currents at that location. It was decided to carry out further measurements at locations connected to both sides of the sea like a flow channel, where the hydrokinetic energy capture can be more due to the tidal variation. The Macpherson Strait, marked “B” as shown in Fig. 1, was selected for the current measurement with the above said boundary conditions.

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Fig. 3 a Picture of ocean current measurement at Viper, and b ocean current profile with depth

3.2 Current Measurement in Macpherson Strait The Macpherson Strait is an open channel with both sides connected to the ocean and also near to Port Blair, and also logistics and operation are easier. Few solar lightbased check post is available surrounding Macpherson Strait and is not sufficient due to dense forest. The bathymetry was carried out at the Macpherson Strait to find shallow water where ocean currents were available. The three locations with ocean current potential were earmarked during the survey. The details were described below.

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Bathymetric survey was conducted along the Macpherson Strait using the single beam echo sounders with positioning aided by differential global positioning system (DGPS) for accurate predictions of locations with hydrokinetic potentials. The tide gauge also deployed for making tidal corrections. Bathymetry data recorded were reduced to mean sea level with the tidal corrections. The final bathymetry was prepared using an MIKE 21 tool and plotted accordingly as shown in Fig. 4 and from the figure it was observed that the maximum depth was ranging from 45 to 50 m.

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The maximum magnitude of current was observed during the spring tide of about 0.8 m/s recorded at a location indicated in Fig. 5. The current reading is in respect with the 30 min average current speeds recorded using the single point current meter as shown in Fig. 6. The velocity gradient was higher across the depth profile as shown in Fig. 5.

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The measured current profile with 1 minute average current speeds is plotted in Fig. 8. The surface current at this location was around 1 m/s initially and gradually increased to 2.5 m/s at a depth of 5 m. The current profiler measured the current speeds of above 2 m/s constantly at the depths beyond 5 m, and this indicated that the site has a very high energy potential as shown in Fig. 7.

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Fig. 6 Average current recorded in the Macpherson Strait at 11° 30.930590 N, 92° 38.553910 E from 23.02.2016 to 24.02.2016

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Initial surveys revealed that the shallow water locations ( 2. The flow profiles of the cylinders in this arrangement are shown in Fig. 13 for various S/D values. As in the previous case, vortices are shed which are disturbed and can be visualized for lower S/D. Bistable flow quoted by a multitudinous amount of research cannot be concluded for the same reason that the two cylinders oscillate at different shedding frequency due to the fact that their diameters are different. It is discernible that vortex for the riser is shed faster at S/D = 4 when compared to S/D = 0.75 owing to lower St on the riser. For the riser positioned closely with the jacket leg the variation of C p is prominent compared to other cases as shown in Fig. 14. This profound variation attributes to the location of the riser in both proximity and wake region of the jacket leg. From the time-averaged pressure coefficient for the riser as shown in Fig. 14, the C p for lower spacing ratio exhibits maximum fluctuations, due to the interference effects.

3.4 Staggered Arrangement (α  225°) The position of the riser is at the angle (α)  225°, in which case the riser becomes the upstream cylinder and the jacket leg is the downstream, unlike other cases. Similar to the earlier cases the mean C d , St and C p are computed for the jacket leg and the riser. Figure 15a manifests that mean drag coefficient on a jacket leg is less at lower S/D and rises to its isolated value at S/D = 3. Similarly the mean C d of riser where it has a peak at S/D = 0.75 and with spacing, it decreases and reaches its isolated mean C d value at S/D = 1.5. The flow patterns for staggered configuration are shown in Fig. 16 for different spacing ratios. At lower spacing ratio the upstream cylinder influences the forces acting on the larger diameter, thereby exhibiting a higher drag force for the riser. The pressure coefficient of the riser is exhibited in Fig. 17, which illustrates similar trend as the stationary case.

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3.5 Base Shear Ratios To further elucidate the effect of the various configurations in the aspects of drag force we present a new parameter called as base shear ratio (F*). The base shear ratio is defined as the ratio of net drag force of riser and jacket leg combined to the isolated case of the jacket leg and the riser as shown in Eq. (7). The values of F* is computed and the values are presented with respect to spacing ratio as shown in Fig. 18. Base shear ratio, F ∗ 

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one another forming as a single body for low S/D values and generates a higher base shear ratio. The base shear ratios exhibit lower values for staggered configuration cases for both the angles. In the tandem case, due to the shielding arrangement of the jacket leg, the base shear ratio is minimum compared to other configurations. Like the tandem configuration, for staggered configuration, the values are lesser compared to the side-by-side configuration due to partially shielding effect. Maximum force is being observed in side-by-side arrangement at S/D = 0.75.

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S/D = 0.75

S/D = 1

S/D =1.5

S/D = 2

S/D = 2.5

S/D = 3

Fig. 16 Instantaneous wake patterns for the jacket leg and the riser in staggered arrangement (α = 225°) for various spacing ratios (S/D)

4 Conclusion Flow past two circular cylinders with two different diameters are investigated by adopting RANS approach using k-ω turbulence model for the tandem, side-by-side and staggered configurations and the various spacing ratio (S/D). The numerical investigations are carried out at Re = 9.0 × 104 , and this study will have implications where the jacket leg and the riser in the offshore field lie close to each other, also in the cases of bridge piers. The numerical study is carried out by performing a systematic convergence study for wall function, domain and grid convergence for a single stationary cylinder. Appropriate domain and grid numbers are considered for further study based on the convergence study. The value of the wall function considered in the study is 20. Similar computational domain and wall function are considered for two cylinders with different diameters. Form the study we observe that at the tandem position the riser is shielded by the jacket leg, thereby reducing the hydrodynamic forces acting on the jacket leg

Hydrodynamic Study of Flow Past Cylinders … Fig. 17 Time-averaged pressure coefficient (C p ) variation along a riser for various S/D in staggered arrangement (α = 225°)

853

3 S/D=0.75 S/D=1.5 S/D=3.0 S/D=4.0 Riser - isolated case

2 X

Cp

1

X

0

X X

X

-1 X

-2

-3 0

45

90

135

180

Angle in degrees

Fig. 18 Base shear ratios variation along S/D

1.6 Side-by-side - 0 Tandem - 90

º

º º

Staggered - 45 º Staggered - 225 1350

1.4

F*

1.2

1

0.8

0.6

0.4 0.5

1

1.5

2

2.5

3

3.5

4

4.5

S/D

acting like a wake stabilizer. For the case of side-by-side, if the riser and the jacket leg are too close each other, the riser lies in the proximity region. Both the cylinders will behave like a single body with the flow in between them coming out as jet flow termed as “gap-flow jets/base bleed” for S/D < 2. Similar observations are not observed in the present case since the diameters of the riser is four times lesser than the jacket leg. In the staggered arrangement (α = 45°), the position of the riser lies both in proximity and wake region of the jacket leg. The St, drag and pressure forces of both the cylinders are observed to be strongly dependent upon one another for

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lower spacing ratios. From the study, it is observed that the cylinders of two different diameters exhibit lower hydrodynamic forces at the tandem arrangement.

References 1. Alam MM, Zhou Y (2007) Flow around two side-by-side closely spaced circular cylinders. J Fluids and Structures 23:799–805 2. Baxendale AJ, Grant I, Barnes FH (1985) The flow past two cylinders having different diameters. Aeronaut J 125–134 3. Bearman PW (1967) The effect of base bleed on the flow behind a two-dimensional model with a blunt trailing edge. Aeronaut Q 18:207–224 4. Biermann D, Herrnstein WH (1934) The interference between struts in various combinations. NACA Report No. 468 5. Bokaian A, Geoola F (1984) Wake displacement as cause of lift force on cylinder pair. ASCE J Eng Mech 111:92–99 6. Gerrard JH (1978) The wakes of cylindrical bluff bodies at low Reynolds number. Philos Trans R Soc Lond A 288:351–382 7. Gu ZF, Sun TF (1999) On interference between two circular cylinders in staggered arrangement at high subcritical Reynolds numbers. J Wind Eng Ind Aerodyn 80:287–309 8. Hiwada M, Taguchi T, Mabuchi I, Kumada M (1979) Fluid flow and heat transfer around two circular cylinders of different diameters in cross-flow. Bull JSME 22:715–723 9. Huhe-Aode Tatsuno M, Taneda S (1985) Visual studies of wake structure behind two cylinders in tandem arrangement. Rep Res Inst Appl Mech (Kyushu University, Japan) 32(99):1–20 10. Igarashi T (1982) Characteristics of a flow around two circular cylinders of different diameters arranged in tandem. Bull JSME 25:349–357 11. Ko NWM, Wong PTY, Leung RCK (1996) Interaction of flow structures within bistable flow behind two circular cylinders of different diameters. Exp Thermal Fluid Sci 12:33–44 12. Lam KM, Wong PTY, Ko NWM (1993) Interaction of flows behind two circular cylinders of different diameters in side-by-side arrangement. Exp Thermal Fluid Sci 7:189–201 13. Lee T, Basu S (1997) Nonintrusive measurements of the boundary layer developing on a single and two circular cylinders. Exp Fluids 23:187–192 14. Li J, Chambarel A, Donneaud M, Martin R (1991) Numerical study of laminar flow past one and two circular cylinders. Comput Fluids 19:155–170 15. Ljungkrona L, Norberg C, Sunden B (1991) Free-stream turbulence and tube spacing effects on surface pressure fluctuations for two tubes in an in-line arrangement. J Fluids Struct 5:701–727 16. Meneghini JR, Saltara F, Siqueira CLR, Ferrari JA Jr (2001) Numerical simulation of flow interference between two circular cylinders in tandem and side-by-side arrangements. J Fluids Struct 15:327–350 17. Mittal S, Kumar V, Raghuvanshi A (1997) Unsteady incompressible flows past two cylinders in tandem and staggered arrangements. Int J Numer Methods Fluids 25:1315–1344 18. Morkovin MV (1964) Flow around circular cylinder-a kaleidoscope of challenging fluid phenomena. In: Hansen AG (ed) Proceedings of the symposium on fully separated flows, ASME fluids engineering division conference, Philadelphia, USA, May 19. Nepf HM (1999) Drag, turbulence and diffusion in flow through emergent vegetation. Water Resour Res 35(2):479–489 20. Noarayanan LK, Murali K, Sundar V (2012) Performance of flexible emergent vegetation in staggered configuration as a mitigation measure for extreme coastal disasters. Nat Hazards 52(1) 21. Ohya YO, Okajima A, Hayashi M (1989) Wake interference and vortex shedding. In: Cheremisinoff NP (ed), Encyclopedia of fluid mechanics: aerodynamics and compressible flow, vol 8. Gulf Publishing Company, Houston, USA, pp 322–389

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22. Roshko A (1961) Experiments on the flow past a circular cylinder at very high Reynolds number. J Fluid Mech 10(3):345–356. ISSN 0022-1120 23. Sharman B, Lien FS, Davidson L, Norberg C (2005) Numerical prediction of low Reynolds number flows over two tandem circular cylinders. Int J Numer Meth Fluids 47:423–447 24. Sumner D (2010) Two circular cylinders in cross-flow: A review. J Fluids Struct 26:849–899 25. Suzuki N, Sato H, Iuchi M, Yamamoto S (1971) Aerodynamic forces acting on circular cylinders arranged in a longitudinal row. In: International wind conference wind effects on buildings and structures, Tokyo, Part II, pp 20-1–20-10 26. Williamson CHK (1985) Evolution of a single wake behind a pair of bluff bodies. J Fluid Mech 159:1–18 27. Williamson CHK (1996) Vortex dynamics in the cylinder wake. Annu Rev Fluid Mech 28:477–539 28. Wood CJ (1967) Visualization of an incompressible wake with base bleed. J Fluid Mech 29:259–272 29. Xu J, Zhu R-Q (2009) Numerical simulation of VIV for an elastic cylinder mounded on the spring supports with low mass ratio, J Marine Sci Appl 8:237–245 30. Zdravkovich MM (1977) Review of flow interference between two circular cylinders in various arrangements. ASME J Fluids Eng 99:618–633 31. Zdravkovich MM (1987) The effects of interference between circular cylinders in cross flow. J Fluids and Struct 1:239–261

Experimental Study on Heave and Yaw Motions of a 1:30 Spar Support for Offshore Wind Turbines Carlo Ruzzo, Nilanjan Saha and Felice Arena

Abstract Floating offshore wind turbines are envisaged to undergo a significant development in the near future, due to their advantages with respect to the onshore or nearshore counterparts, in terms of greater available wind power, reduction of the land occupation and minimization of the visual impact of the turbines. Although many numerical codes have been developed for the representation of the dynamic behaviour of such structures, few experimental data have been collected up to now. These data would be useful for the validation of the codes and to give practical indications for the design of floating offshore wind turbines. This paper reports some results based on experimental data collected during an at-sea experiment on a 1:30 model of the OC3-Hywind spar support for floating offshore wind turbines, in parked rotor conditions. The experiment was carried out at the Natural Ocean Engineering Laboratory (NOEL) of Reggio Calabria (Italy), between July 2015 and March 2016. Heave and yaw representative response spectra of the structure, obtained for local wind-generated waves, are shown, and the corresponding damping estimations are performed. The results obtained could be useful for design purposes and motivate further elaborations of the experimental data collected during the experiment, to be realized in the near future. Keywords Floating offshore wind turbines · Spar · Motion spectra · Heave · Yaw Hydrodynamic damping

C. Ruzzo · N. Saha · F. Arena (B) Natural Ocean Engineering Laboratory – DICEAM, Mediterranea University, Reggio Calabria, Italy e-mail: [email protected] C. Ruzzo e-mail: [email protected] N. Saha e-mail: [email protected] N. Saha Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai 600036, India © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_63

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1 Introduction Floating offshore wind turbines are envisaged for huge development in the near future, as emerging solutions for renewable energy exploitation in open seas [1]. With respect to onshore and bottom-fixed offshore wind turbines, they would present some advantages, including availability of stronger and steadier winds offshore, reduction of the land occupation and minimization of visual and environmental impacts. The investigation of the coupled dynamic behaviour of these concepts is however a complex and multidisciplinary task [2–4], involving the coupled representation of aerodynamics, hydrodynamics, turbine control system, mooring system, etc. To this aim, several numerical codes have been developed and code-to-code validation has been attempted [5–8]. However, there is an increasing need for experimental data, necessary for the field validation of the numerical codes. Concerning spar buoy, which is the floating support concept considered in this study, few grid-connected prototypes have been recently installed and tested in Norway [9] and in Japan [10]; however, the measured data have not been released for public use. Consequently, there is a significant need for scaled experimental activities, usually performed in wave tanks or ocean basins, which are crucial for the understanding of the hydrodynamic characteristics of such structures. Several activities have been conducted up to now and have provided useful results in terms of model identification and validation of the numerical codes. Some of the relevant ones are reported in the following. Shin [11] tested a 1:128 model of a spar floating wind turbine under different environmental conditions and compared the experimental RAOs and significant motions obtained with the corresponding output of the numerical codes FAST and MOSES. Sethumaran and Venugopal [12] tested a 1:100 model of a stepped spar with different mooring configurations and compared only the hydrodynamic results obtained with the output of the numerical code Orcaflex. Duan et al. [13] tested a 1:50 spar model and obtained response spectra for various load combinations, providing useful information of the coupled dynamic behaviour of the spar wind turbines. Relevant obstacles to the wave tank testing of scale models of offshore wind turbines are the relevant costs and the scaling effects, caused by the relatively small size of the models [14]. To face these issues, Ruzzo et al. [15–17] carried out intermediate-scale open-sea experiments on a 1:30 floating spar support for offshore wind turbines in parked rotor conditions, installed at sea at the Natural Ocean Engineering Laboratory (NOEL) of Reggio Calabria (Italy). More details are available with respect to experimental modelling in Ruzzo [18]. This model is scaled from the OC3-Hywind spar buoy, which is the reference spar floating offshore wind turbine [19], except for the mooring system, whose design is driven by the local inclined and irregular seabed. This paper presents results from the experiment, i.e. heave and yaw response spectra, highlighting the couplings with the other degrees of freedom and providing an alternative estimation of the corresponding hydrodynamic damping coefficients. The results presented in this paper have been obtained under irregular wind-generated sea states and hence can be directly used for design purposes.

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2 Set-up of the Experiment This section describes the setting up of the field experimental test. The characteristics of the model and of the installation site are briefly reproduced [18], and the procedure used for the selection of the wind-generated sea states is illustrated.

2.1 Description of the Model The 1:30 spar model is shown in Fig. 1. It is made up of a steel tapered hull, moored to the local inclined seabed through three delta-connected steel catenary lines of different lengths to account for the bathymetry effects [20, 21]. The turbine tower is represented by an aluminium tube, while the rotor-nacelle assembly is portrayed in parked rotor conditions by a lumped mass at the top of the tower [22]. The model is equipped with a Differential Global Positioning System (DGPS) and an Attitude and Heading Reference System (AHRS) inertial platform, both placed at the top of the aluminium tower. The former measures the motions in the three translational degrees of freedom, with respect to a base GPS antenna installed onshore, while the latter measures the three rotational ones. The description of the arrangement of the experiment, along with the detailed characteristics of the model, is reported in [15]. Table 1 reports the characteristics pertinent to the present study.

Fig. 1 Underwater view of the 1:30 spar model. Source [23]

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Table 1 Characteristics of the 1:30 spar model Symbol Units

Value

Hull diameter

D

[m]

0.217 (above taper) 0.313 (below taper)

Draft

h

[m]

3.884

Centre of gravity position

zG

[m]

−2.496

Total mass

m

[kg]

297.0

m2 ]

995.0

Mass moments of inertia about x-y axes

I xx , I yy

[kg

Mass moment of inertia about z axis Water depth

I zz

[kg m2 ]

4.870

d

[m]

2.75 (landside anchor) 6.90 (model) 10.4 (seaside anchor)

Fairleads position

zF

[m]

−2.224

Mooring line length

L

[m]

13.3 (landside) 16.5 (seaside)

Line mass per unit length

p

[kg m−1 ]

0.159

2.2 Wave Characteristics The open-sea experiment was conducted in the Natural Ocean Engineering Laboratory (NOEL) of Reggio Calabria (Italy). Thanks to the local geographic and environmental conditions [23], wind-generated sea states with JONSWAP-like spectra and relatively small size (H s  0.20–0.40 m, T p  1.8–2.6 s) occur with a certain regularity. This makes the site particularly suitable for scaled experiments on floating structures, since such sea states are intermediate-scale models (Froude scale) of strong ocean or Mediterranean storms, which usually represent the design sea states (for example, from [24], the return value of significant wave height, for R  100 years, in the Mediterranean Sea ranges between 5.8 and 12.1 m) of the full-scale structures. During the experiment, 1281 sea states and the corresponding structure motions in the six degrees of freedom have been collected overall. Each of them is 5-min long and has a sample rate of 10 Hz. The measuring of the sea states has been achieved through ultrasonic probes and pressure transducers placed on a measuring station few metres far from the spar structure, in an undisturbed wave field. Among the recorded sea states, wind-generated spectra have been identified as the ones fulfilling both the following requirements: • Narrow-bandedness parameter (as defined in [25]) of the wave head of pressure spectrum ψ* greater than 0.65;

Experimental Study on Heave and Yaw Motions … 0.16

E /H [ms/rad] ph s

Fig. 2 A subset of 10 wind-generated wave heads of pressure spectra recorded during the experiment, normalized with respect to Hs

861

0.12

0.08

0.04

0.00

0

1

2

3

4

5

[rad/s]

• Significant wave height H s and peak period T p within the range of JONSWAP spectrum (as defined in [26]). The first requirement has been used to exclude broadbanded spectra, which typically indicate sea states made up of wind-generated waves superimposed to swells. The second requirement has been instead used to exclude pure swells, whose spectra are narrowbanded but present a relatively high peak period, with respect to the significant wave height. The resulting set of selected sea states has been then further filtered, considering the additional requirement of significant wave height H s < 0.50 m. Sea states exceeding this threshold would indeed represent full-scale conditions with H s > 15 m, which may exceed the realistic ultimate conditions of the platform and may induce significant nonlinear effects. Overall, 62 wind-generated sea states have been selected following the above procedure and this dataset will be used for the elaborations reported in this paper. The wave head of pressure spectra of a subset of 10 samples, normalized with respect to H s , are shown in Fig. 2.

3 Heave and Yaw Analysis This section presents some results on heave and yaw motions. The response spectra are shown and some averaging procedures are presented to rule out uncertainty associated with the waves. Then, some natural frequency and damping estimations are performed, using the averaged spectra.

3.1 Response Spectra Analysis The measurements of the spar translational motions are the instantaneous distances between the fixed base antenna B and the moving on-board antenna T, which is placed at the top of the tower. Surge, sway and heave, which are conventionally referred to the centre of gravity G of the platform, must be obtained by applying the rotation

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0.025

u

3

s

E /H [ms/rad]

Fig. 3 Heave spectra corresponding to the subset of 10 sea states reported in Fig. 2, normalized with respect to H s

0.000

0

1

2

3

4

5

3

4

5

[rad/s]

700

2

E /Hs [º s/radm]

Fig. 4 Yaw spectra corresponding to the subset of 10 sea states reported in Fig. 2, normalized with respect to H s

350

0

0

1

2 [rad/s]

matrix of the Euler angles to the measurement in the time domain. In particular, the vertical motion of the platform centre of gravity Δu3 during the experiment has been calculated as u 3G  u 3T − cos u 4 cos u 5 (z T − z G ),

(1)

where Δu3T being the vertical component of the differential measurement between the on-board and the base antennas, u4 the roll angle of the platform and u5 its pitch angle. Heave motion u3 has been then calculated as u 3  u 3G − mean(u 3G ).

(2)

The response spectra of the model in heave and yaw have been calculated for each of the 62 records. Those corresponding to the subset of 10 sample sea states of Fig. 2, normalized with respect to the significant wave height H s , are shown in Figs. 3 and 4. Although individual response spectra are different between each other, it can be observed that each of them has a wave frequency component, dependent on the wave spectrum itself, and some natural frequency components, including the peaks due to the coupling with the other degrees of freedom. To better analyse these response spectra, two averaging methods are proposed in this paper. Given a set of records, the first one reports the mean of the top third spectral ordinates for each frequency,

Experimental Study on Heave and Yaw Motions … 0.012

Mean average Top third average Eu /Hs [ms/rad] 3

Fig. 5 Averaged heave response spectra, normalized with respect to H s , for the whole set of 62 wind-generated sea states

863

0.008

0.004

0.000 0

1

2

3

4

5

[rad/s]

150 Mean average Top third average 100

2

E /Hs [º s/radm]

Fig. 6 Averaged yaw response spectra, normalized with respect to H s , for the whole set of 62 wind-generated sea states

50

0

0

1

3

2

4

5

[rad/s]

while the second one their mean value. The averaged response spectra in heave and yaw, normalized with respect to significant wave height H s , have been obtained for the whole set of 62 wind-generated sea states and are shown in Figs. 5 and 6. The heave averaged spectra clearly shows three regions. The first one, for extremely low frequencies, is very narrow and coincides with the slow drift motions, which may be induced by wind, currents and/or tidal. The second region is associated to the heave natural frequency of the spar but does not clearly show a peak. It can be concluded that such frequency is between 0.77 and 1.06 rad/s. Although more data would be needed for a better identification of the peak, it is interesting to note that a slight reduction of the heave natural frequency is likely to take place under wind-generated wave conditions, with respect to the expected value for the 1:30 model, which should be about 1.05 rad/s [17]. This may be due to the partial submergence of the aluminium tower during the harsh wind-generated sea states. The diameter of this tower is indeed 0.10 m, resulting in a slight reduction of the heave stiffness of the spar when it submerges. The third region is finally associated to the wave frequency range. Similar considerations may be drawn regarding the yaw averaged spectra, with the difference that the peak of the second region is clearly identified, at the frequency of 0.94 rad/s. This peak is due to the coupling between yaw and roll/pitch motions of the spar and hence corresponds with the roll natural frequency of the platform.

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The response spectra obtained may be used for design purposes, since they correspond to the 1:30 model response under wind-generated waves and parked rotor conditions and may be easily scaled up to 1:1, using Froude scaling laws.

3.2 Hydrodynamic Damping Estimation Accurate estimation of the hydrodynamic damping is a challenge. This is primarily due to the fact that the equations of motions involve convolution integrals. However, in case the response process is Gaussian, one can use the linear equations implying that the wave steepness is small and the response is proportional to the amplitude of the incident waves. In this paper, the higher order viscous forces are neglected, and the linear equations are employed [27]. One may use each of the time series to generate a response spectrum and then use the spectrum for damping calculation. In this work, to weed out the uncertainty, the collection of spectra is averaged, and the averaged spectra are used in further calculation. Averaged response spectra could be used both for the quantitative estimation of the response under given environmental conditions, and to draw some information about the dynamic characteristics of the model. The dynamic identification of the 1:30 model installed at NOEL has been attempted in [17], where the Response Amplitude Operators (RAOs) of the model had been estimated by calculating the averaged transfer function between wave and response spectra. However, such a method is viable only in the frequency range where wave energy content is not negligible. Consequently, it cannot be used for the identification of the motions in the horizontal plane (surge, sway and yaw), whose natural frequencies are smaller than the peak frequencies of the incoming sea states. An alternative method is proposed here, based on the direct damping estimation from the averaged response spectra peaks. Let us consider a linearized equation of motion of the spar platform as ¨ + Cu(t) ˙ + Ku(t)  f(t), Mu(t)

(3)

where M, C and K are the linearized mass, damping and stiffness matrices, respectively; u is the response vector; and f is the external force vector. While sufficiently accurate estimations of mass and stiffness may be achieved during the design stage of the platform, experimental data are precious for the estimation of its overall hydrodynamic damping properties. For instance, Jonkman [19] suggested to consider nonlinear drag and linear radiation damping, augmented by a constant damping matrix, obtained by fitting the numerical response of the structure during free decay tests to the experimental one. Ruzzo et al. [17] showed that Jonkman’s predictions tend to underestimate the total hydrodynamic damping of the structure and proposed some alternative coefficients obtained by fitting numerical RAOs to the experimental ones estimated the during open-sea intermediate-scale experiment, but only for heave, roll and pitch degrees of freedom. The method proposed herein is more general, since it

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allows to estimate the damping coefficients for all the six degrees of freedom of the structure. The projection of Eq. (3) on the i-th degree of freedom may be written as 6 

Mi j u¨ j (t) + Ci j u˙ j (t) + K i j u j (t)  f j (t),

(4)

j1

and each element C ij may be obtained as reported in Eq. (5), from the corresponding mass and stiffness elements M ij and K ij , which are usually known, and the damping ratio ξ ij , which may be directly estimated from the averaged response spectra: Ci j  2ξi j



K i j Mi j .

(5)

The estimation of the damping ratios from the response spectra may be achieved through the classical methods of structure dynamics as the half-bandwidth or the logarithmic decrement methods. With respect to the two degrees of freedom considered in this paper, i.e. heave and yaw, only three damping ratios may be estimated, namely, ξ33 , ξ 46 and ξ 56 . The first one can be obtained by considering the peak of the heave averaged response spectrum corresponding to the heave natural frequency, while the other two should be obtained from the peak of the yaw response spectrum corresponding to the roll-pitch natural frequency. Since the structure is axisymmetric, it is not possible to distinguish between the two contributions of roll and pitch separately, and hence, the damping ratio has been considered the same for both. The damping ratios obtained considering the peaks of the top third and the mean averaged response spectra have been estimated using the logarithmic decrement method, are reported in Table 2. The damping ratios obtained for the top third and the mean response spectra are quite similar to each other, which is an important clue to establish the robustness of the proposed approach. To this aim, further studies are required, including the estimation of the damping ratios for all the degrees of freedom of the model, and the validation against individual sea states to assess whether averaged response spectra may be representative of the real damping properties of the model, and which of them should be used for practical applications.

Table 2 Damping ratios estimated from the averaged response spectra ξ 33 ξ 46

ξ 56

Top third averaged spectra (%)

12.53

8.28

8.28

Mean averaged spectra (%)

11.77

8.39

8.39

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4 Concluding Remarks This paper analyses the experimental data of heave and yaw motions of a 1:30 model of a spar supported offshore wind turbine, installed in the Natural Ocean Engineering Laboratory (NOEL) of Reggio Calabria (Italy) [23]. The experimental data simulates the parked rotor conditions of the turbine with the rotor-nacelle assembly being represented through a lumped mass at the top of the turbine tower [22]. In order to characterize the most relevant environmental conditions for design purposes, the experimental data have been filtered and only the records corresponding to incoming wind-generated sea states with significant wave height smaller than 0.50 m have been selected, thus obtaining a dataset of 62 5-min long spar motion records. These data have been then used to obtain the averaged heave and yaw response spectra of the model, which have been calculated considering the top third and the mean averages of the spectral ordinates for each frequency. These averaged response spectra are useful for direct application for design purposes, since they may be easily scaled up to the full-scale, providing the expected response spectra of the platform to any given design sea state [cf. 24]. In addition, they can be used for identification purposes for Gaussian sea states, particularly to achieve an estimation of the total linearized hydrodynamic damping matrix. To this aim, a new approach has been introduced in this paper, based on the application of traditional damping identification techniques to the averaged spectral peaks. Three damping ratios, corresponding to heave-heave, roll-yaw and pitch-yaw terms, have been estimated which may be important in estimation of short-term extreme responses [28]. Future work is also currently undergoing to extend the results to all the six degrees of freedom of the structure and to validate the proposed identification method along with studies on instability [29]. Acknowledgements The research leading to these results has received funding from the European Research Project “Large Multipurpose Platforms for Exploiting Renewable Energy in Open Seas—Acronym: PLENOSE”, Grant Agreement No. PIRSES-GA-2013-612581, on the Seventh Framework Programme of the European Union, SP3 People, “Support for training and career development of researchers (Marie Curie)”, “International Research Staff Exchange Scheme (IRSES)”, call FP7-PEOPLE-2013-IRSES.

References 1. Carbon Trust (2015) Floating offshore wind: market and technology review. Information: https://www.carbontrust.com/media/670664/floating-offshore-wind-market-technologyreview.pdf 2. Naess A, Moan T (2012) Stochastic dynamics of marine structures. Cambridge University Press, UK 3. Kim MH (2012) SPAR platforms: technology and analysis methods. American Society of Civil Engineers 4. Failla G, Arena F (2015) New perspectives in offshore wind energy. Philos Trans R Soc A: Math Phys Eng Sci 373(2035). https://doi.org/10.1098/rsta.2014.0228

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5. Jonkman J, Musial W (2010) Offshore code comparison collaboration (OC3) for IEA Task 23 offshore wind technology and deployment. Technical Report NREL/TP-5000-48191. National Renewable Energy Laboratory (NREL). Information: https://www.nrel.gov/docs/ fy11osti/48191.pdf 6. Robertson AN, Wendt F, Jonkman JM, Popko W, Daker H, Guyedon S, Qvist J, Vittori F, Azcona J, Uzunoglu E, Guedes Soares C, Harries R, Yde A, Galinos C, Hermans K, de Vaal JB, Bozonnet P, Bouy L, Bayati I, Bergua R, Galvan J, Mendikoa I (2017) OC5 Project Phase II: validation of global loads of the DeepCwind floating semisubmersible wind turbine. Energy Procedia 137:38–57 7. Browning JR, Jonkman J, Robertson A, Goupee AJ (2014) Calibration and validation of a spar-type floating offshore wind turbine model using the FAST dynamic simulation tool. In: The science of making torque from wind 2012. J Phys Conf Ser 555:012015. https://doi.org/ 10.1088/1742-6596/555/1/012015 8. Karimirad M, Messonnier Q, Gao Z, Moan T (2011) Hydroelastic code-to-code comparison for a tension leg spar-type floating wind turbine. Marine Struct 24(4):412–435 9. Hywind Demo Project. Information: https://www.statoil.com 10. Ishida S, Kokubun K, Nimura T, Utsunomiya T, Sato I, Yoshida S (2013) At-sea experiment of a hybrid spar type offshore wind turbine. In: Proceedings of the 32nd international conference on offshore mechanics and arctic engineering (OMAE2013), ASME, 9–14 June 2013, Nantes, France, OMAE2013-10655 11. Shin H (2011) Model test of the OC3-Hywind floating offshore wind turbine. In: Proceedings of the 21st international offshore and polar engineering conference (ISOPE2011), 19–24 June 2011, Maui, HI, USA, pp 361–367 12. Sethuraman L, Venugopal V (2013) Hydrodynamic response of a stepped-spar floating wind turbine: numerical modelling and tank testing. Renew Energy 52:160–174 13. Duan F, Hu Z, Niedzwecki JM (2016) Model test investigation of a spar floating wind turbine. Marine Struct 49:76–96 14. Martin HR, Kimball RW, Viselli AM, Goupee AJ (2014) Methodology for wind/wave basin testing of floating offshore wind turbines. ASME J Offshore Mech Arctic Eng 136:020905 15. Ruzzo C, Fiamma V, Nava V, Collu M, Failla G, Arena F (2016) Progress on the experimental set-up for the testing of a floating offshore wind turbine scaled model in a field site. Wind Eng 40(5):455–467 16. Ruzzo C, Fiamma V, Failla G, Arena F, Collu M, Nava V (2016) Open-sea 1:30 scale tests on a spar-type offshore wind turbine in parked conditions: progress and future work. In: Progress in renewable energies offshore—Proceedings of the 2nd international conference on renewable energies offshore (RENEW 2016), Lisbon, Portugal, pp 609–616 17. Ruzzo C, Fiamma V, Collu M, Failla G, Nava V, Arena F (2018) On intermediate-scale opensea experiments on floating offshore structures: feasibility and application on a spar support for offshore wind turbines. Mar Struct 61:220–237 18. Ruzzo C (2017) A new approach for intermediate-scale open-sea experimental activities on offshore structures. Application to spar buoys for wind energy exploitation via a 1:30 scale activity. Ph.D. thesis, Mediterranea University, DICEAM, Reggio Calabria, Italy 19. Jonkman J (2010) Definition of the floating system for phase IV of OC3. Technical Report NREL/TP-500-47535. National Renewable Energy Laboratory (NREL) 20. Haslum HA, Faltinsen OM (1999) Alternative shape of spar platforms for use in hostile areas. In: Proceedings of offshore technology conference, 3–6 May, Houston, Texas, USA. OTC10953-MS 21. Koo BJ, Kim MH, Randall RE (2004) Mathieu instability of a spar platform with mooring and risers. Ocean Eng 31(17–18):2175–2208 22. Gao Z, Saha N, Moan T, Amdahl J (2010) Dynamic analysis of offshore fixed wind turbines under wind and wave loads using alternative computer codes. In: Proceedings of the TORQUE 2010 conference, FORTH, Heraklion, Crete, Greece 23. Natural Ocean Engineering Laboratory, Mediterranea University, DICEAM, Reggio Calabria, Italy Website Information: http://noel.unirc.it/

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Performance Simulation of Wave-Powered Navigational Buoy Using CFD and Experimental Study Ashwani Vishwanath, Nitinesh Awasthi, Purnima Jalihal and Prasad Dudhgaonkar

Abstract The article discusses the pneumatic performance of wave-powered navigational buoy through numerical prediction and experimental study. In the proposed NIOT configuration, navigational buoy utilizes wave energy for powering a beacon lamp on top of the buoy beside other oceanographic instruments. The functional requirement of navigational buoy, operational power requirement and the wave climate in the location of deployment decides the dimensions of a navigational buoy. The design of the navigational buoy was carried out to suit an existing Impulse turbine which was tested successfully in previous sea trials on another floating wave energy device of similar capacity. The Oscillating Water Column (OWC) diameter decides the discharge and pressure across the turbine and hence plays a critical role in the overall sizing of navigational buoy. The numerical study was carried out in RANS-based CFD commercial code STAR-CCM+. The article discuses the predicted performance parameters like motion response of the buoy in moored condition, pressure drop across orifice, volumetric flow rate and consequently pneumatic power generated for two OWC sizes of 0.9 and 1.1 m in the proposed buoy configuration in a sea environment. The article also discusses about, experiments that were conducted on scaled down (1:8) physical model of the navigational buoy in the wave flume for the various wave conditions. The article discusses various findings useful in finalizing the design of wave powered navigational buoy as a result of this study. Keywords Wave powered navigational buoy · Pneumatic power · OWC · CFD Moorings · Physical model

1 Introduction Among the various technologies available for harnessing wave energy, one of the most popular is Oscillating Water Column (OWC) principle based wave energy converter. OWC principle utilizes pressurization and depressurization of entrapped A. Vishwanath (B) · N. Awasthi · P. Jalihal · P. Dudhgaonkar National Institute of Ocean Technology, Pallikaranai, Chennai 600100, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_64

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air column inside a wave energy device which causes the turbine coupled to an electrical generator to rotate thereby generating the electrical power. Work on OWC based small scale wave energy device has been undertaken around the world for quite some time. Sheng et al. analyzed the feasibilities of physical modeling with some important scaling issues on physical modeling of wave energy devices [1]. Pathak et al. [2] carried out testing on a scaled down model of a Backward Bent Ducted Buoy (BBDB) in wave basin for different wave heights and periods. Effect of various geometrical parameters of BBDB and wave conditions was studied in this exercise at IIT Madras. Ram et al. [3] experimentally studied the air flow characteristics in a fixed OWC device. Air flow through the OWC was analyzed using particle image velocimetry (PIV) technique. NIOT successfully carried out open sea trials on BBDB during 2011–2015. The results and understandings from this experience is paving up the way for the development of higher capacity wave energy prototype. Yoshio Masuda developed wave energy converter based navigational buoy which was the earliest device in Japan. A navigational buoy is commonly used in port/harbor to indicate ship movement channels, dangerous rocks and for a variety of other navigational purposes. In the proposed NIOT configuration, wave powered Navigational Buoy utilizes wave energy using OWC principle for its working. Primary conversion of wave energy is attained by an oscillating system, a floating body, and oscillating water column within a structure. The primary objective of the current effort is to develop a methodology for assessment of flow rates, pressure drops, and power generation by wave powered navigational buoy through Computational Fluid Dynamics (CFD) and experimental study. For experimental study, a physical model (scale 1:8) was fabricated and tested in wave flume at Anna University, Chennai.

2 CFD Studies This study was aimed at numerical prediction of performance of the given navigational buoy, which works on the principle of Oscillating Water Column (OWC) for its wave energy conversion. For solving three-dimensional nonlinear wave problems, the flow field and the unknown free surface locations are calculated by coupling the Reynolds-averaged Navier–Stokes equation with a volume of field (VOF) method for tracking the free surface [4]. The method is based on finite volume technique. The fraction of fluid in each cell is represented by a function F, where the zero value contains cell with no fluid and unity indicated the cell full of fluid. The evolution of F field is governed by following transport Eq. (1) written in conservative form. ∂F ∂uF ∂vF ∂wF + + +  0, ∂t ∂x ∂y ∂z

(1)

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where (x, y, z) are the Cartesian system, (u, v, w) Cartesian components of the velocity and t is a physical time. Through all the faces of a cell, the selection of the function F in each cell is made from flux calculation of F. Equations 2 and 3 show the integral form of Navier–Stokes equations.     d (2) ρdv + ρ v − vg · da  0 dt v s       d ρdv + ρv v − vg · da  (T − pI) · da + ρbdV, (3) dt v

s

s

v

where ρ is the fluid density, V is the control volume bounded by a closed surface S, v is the fluid velocity vector, vg is the velocity of the control volume surface, t is time, p is pressure, b is body force vector, a is face area vector normal to S directed outwards and T is viscous stress tensor. The motion of buoy was analyzed using Dynamic Fluid Body Interaction (DFBI) morphing mesh technique. This section discusses CFD results on pressure drop across the orifice (used to simulate turbine at the top of buoy), volumetric flow rate and consequently power generated from the given buoy configuration in a sea environment.

2.1 Design Parameters and Methodology The functional requirement of navigational buoy, operational power requirement and the wave climate in the location of deployment decides the dimensions. The OWC diameter decides the discharge and pressure across the turbine so it plays a critical role in the overall sizing of navigational buoy. Initial sizing of buoy was arrived from earlier performance of power module and sea trials. 0.9 m of OWC diameter was arrived at from these sea trial studies. The section below describes the final OWC sizing arrived at using extensive CFD studies. STAR-CCM+ CFD-based solver was used for the present investigation. CFD studies have been performed for 100 mm orifice for two different OWC diameters, 0.9 and 1.1 m to find the size which will produce more pneumatic power for the same input wave condition. Table 1 shows the parameters used for modeling the buoy. Figure 1 shows buoy modeled in STAR-CCM+. Since buoy in open sea would require mooring system for station-keeping, effect of mooring lines was also incorporated in the study. Mooring system with sufficient pretension was adopted for the present study. Table 2 shows the mooring line properties used in the simulation.

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Table 1 Parameters of navigational buoy with OWC of 0.9 and 1.1 m diameter Oscillating column diameter (m)

0.9

1.1

Floater diameter (m)

3

3

Total height of the buoy (m)

5.1

5.1

Orifice diameter (mm)

100

100

Total weight of buoy (kg)

3686.2

4301.16

Draft (m)

3.6

3.6

Fig. 1 Buoy model in STAR CAD Table 2 Mooring line properties

Mode

Catenary

Mass per unit length

3.91 kg/m

Stiffness Pretension force Relaxation length

2930 N/m 3000 N 37.8 m

2.2 Modeling and Domain Description The orifice shown in Fig. 1 simulates the turbine of equivalent diameter. Wave condition used for the study was chosen based on the normal condition prevalent at Ennore coast (Time period of 4.4 s and wave height 0.8 m). Regular wave conditions were used in the study. The parameters estimated in the simulation through the orifice are pressure drop dp (Pa), volume flow rate Q (m3 /s) and Pneumatic power (dp*Q) P (W). The power estimated is pneumatic output power of the oscillating air chamber. Overset meshing technique is used for the DFBI problem involving 2 degrees of freedom (heave and pitch). Mesh generation Overset mesh technique was used effectively in this simulation to predict motion of the buoy. Overset mesh are block-structured grids (i.e., grids with overlapping sub domains) employed in regions likely to show steeper gradients of problem variables.

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Fig. 2 Domain description

Fig. 3 Mesh description

Figures 2 and 3 shows the domain and mesh description respectively. Table 3 list the domain parameters. Table 4 list the recommended mesh size for the problem. One half of the domain was modeled using symmetry conditions and results were extrapolated for the full model. Catenary mooring with properties given above was modeled to give real-time situation in predicting the hydrodynamic performance of the buoy. Overset mesh method for high precision in estimating flow parameters around buoy was used in the specific area of interest. Volume of Fluid model was used for multiphase flow.

2.3 Results Flow parameters in OWC for assessing its hydrodynamic performance were effectively captured in the buoy motion simulation. Probes across the orifice and in OWC were created to capture pressure drop across the orifice and water surface elevation and buoy with mooring during simulation. Figure 4 shows the buoy model with mooring lines. Velocity vectors in VoF model is shown in Fig. 5 during inhaling of OWC in the buoy. Simulations were run for 0.9 and 1.1 diameter of OWC with mooring and comparisons are plotted as below.

874 Table 3 Domain parameters

A. Vishwanath et al. Domain

Dimension (m)

Background Length

100

Breadth Height

12 30

Water surface Length

100

Breadth Height

12 5.5

Overlap

Table 4 Mesh size description

Length

24

Breadth Height

6 15

Overset Length

6

Breadth Height

3 9

Region

Mesh size in x Mesh size in z Mesh size in y direction (m) direction (m) direction (m)

Buoy

λ/1305

H/117

λ/326

Water surface Background

λ/391 λ/98

H/35 H/9

λ/82 λ/41

Fig. 4 Buoy motion with mooring

Comparison between 0.9 and 1.1 m OWC diameter Simulation with 0.9 m OWC diameter was carried out initially and subsequently with 1.1 m OWC diameter to assess the buoy performance with higher OWC diameter, since the estimated power in 0.9 m OWC turned out to be less than 100 W on an

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Fig. 5 Velocity vectors in VoF model

Pressure drop (pa)

3000 2000 1000 0 -1000

0

5

10

15

-2000

20

25

OWC dia 0.9m

-3000

OWC dia 1.1

Time (s)

-4000

Mass flow rate ( kg/s )

Fig. 6 Comparison of pressure drop 1 0.8 0.6 0.4 0.2 0 -0.2 0 -0.4 -0.6 -0.8 -1

0.9 OWC dia

5

10

15

1.1 m OWC dia

20

25

Time (s)

Fig. 7 Comparison of mass flow rate

average. Figures 6, 7 and 8 show the comparison of flow parameters between 0.9 and 1.1 m diameter of OWC. Average power (with 1.1 m dia OWC)  192 W Average power (with 0.9 m dia OWC)  74 W It can be observed that 1.1 m OWC diameter gives higher pneumatic power.

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0.9 OWC Dia

Power (W)

1500 1000 500 0

0

5

-500

10

15

20

25

Time (s)

Fig. 8 Comparison of pneumatic power

3 Experimental Study 3.1 Model Description Experiments were carried out in the wave flume in the PG Hydraulics Laboratory of Centre for Water Resources, Anna University, Chennai. The dimension of the flume is 30 m × 1 m × 1 m. One end of the tank has a wave generator. At the other end, 40 mm aggregate is spread in a slope of 1:8 so that the waves do not reflect but break due to the beach effect. This holds good only for water depth up to 0.7 m. In hydraulic structures and for wave motions studies the gravity effect is usually predominant in the prototype. So Froude number similarity is used. The prototype of 1.1 m OWC diameter was scaled down to 1:8 ratio (due to limit in the wave flume) and the model was fabricated using acrylic sheets material which had a thickness of 3 mm. The buoy consisted of a floater pierced by a hollow tail tube opened at the bottom to the waves and at the top to the pneumatic chamber. For the fabrication of buoyancy chamber, acrylic sheets were rolled to form cylindrical shape. For matching the center of mass and mass moment of inertia of the prototype with model, 12 weights (225 g each) were placed in radial direction equidistant from the center. Total weight of the buoy was 8.4 kg. Figure 9 shows dimensions of scaled down model. All dimensions are in cm. The model was tested in regular wave conditions available in the flume. In addition to the Froude similitude, the Cauchy similitude was used to decide the mooring lines of the buoy. The Cauchy similitude requires that stiffness of a model must be related to that of the prototype by the relation, (EA) Prototype  λ3 (EA) Model. Badminton string (Nylon, E  5 * 104 MPa) with diameter 0.3 mm was chosen as the mooring line. The mooring line was connected to the navigational buoy using small door lock pads which were screwed at four equal distant corners in the bottom of the buoyancy chamber of the navigational buoy. Four turning buckles were used to adjust small change in length of the mooring line to arrive to its pretension value. The mooring line passes through the pulley and its bottom end is connected to the load cell which is fixed. Figure 10 shows the end connection set-up for mooring line.

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Fig. 9 Dimensions of 1:8 scaled down model

Fig. 10 End connection set-up for mooring line

Instruments used were pressure transmitter for pressure drop across orifice, wave probe for wave conditions, under water load cell for mooring loads and tri-axial accelerometer for motion measurements. Accelerometer was put on the top of the buoy. An equivalent orifice (mimicking turbine) was placed at the top end of the buoy. The orifice was calibrated to estimate the air flow discharge rate from measured pressure drop. Static stability check, free vibration test and orifice calibration tests were also carried out in addition to motion and pneumatic performance tests.

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Displaceent (m)

0.3 0.2 0.1 0 0.00 -0.1 -0.2

2.00

4.00

6.00

8.00

10.00

Time (s)

-0.3

Fig. 11 Free vibration test

3.2 Results 3.2.1

Free Vibration Test

The free vibration test was carried out to determine the natural period and damping of the buoy. Figure 11 shows the free vibration test carried out in flume. Damping period of the model was found to be 0.8 s (Prototype natural period  2.26 s). The Damping ratio ζ is a dimensionless measure measures how oscillations in a structure decay after a disturbance. loge

xk  2πζ xk+1

xk , xk + 1 are the amplitude of two successive peaks in the free vibration test graph. Thus, the Damping ratio is found to be ζ  7.3%. The high damping may be attributed to the presence of OWC in the buoy.

3.2.2

Pneumatic Performance

The navigational buoy model was connected to the mooring line with the required pretension. The differential pressure was obtained from the pressure transducer. It had two ports, one was connected to OWC chamber at the top below the orifice and another port connected to tube which was open to atmosphere. The pressure transducer was then connected to the NI Instrumentation module which was then connected to the laptop. The laptop logged the readings of the wave height in the wave flume, differential pressure (dp) and mooring load from the load cell. The experiments were carried out for different regular wave conditions possible in the flume. Pneumatic performance can be gauged by its efficiency. Output power is the product of pressure and flow rate. Input power depends on wave height and wave period. The sampling time interval was 0.1 s. Differential pressure (dp) was measured

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and air discharge was estimated from the measured dp. Coefficient of discharge (Cd) value was obtained from orifice calibration test. Pneumatic Efficiency, Pe 

Output Power Input Power

Output power  Q* dp, where, Q—Discharge from the model (m3 /s), dp—Differential pressure (Pa)  2 ∗ dp A Q  Cd*   ρ A 2 −1 a where, A a ρ dp

Area of OWC (m2 ) Area of orifice (m2 ) Mass density of air Differential pressure (Pascal) Input power 

ρg2 H2 TD 32π

where, g ρ H T– D

Acceleration due to gravity Mass density of water Wave height in flume (m) Wave period (s) Diameter of buoy (0.375 m)

For a typical wave conditions of 6.28 cm wave height and 2 s wave period (prototype condition 50.2 cm, 5.6 s), Output Power Pneumatic Efficiency, Pe  Input Power  Pneumatic Efficiency, Pe  11.92%

0.337 2.83

∗ 100

Avg. Output power (Prototype)  0.337 ∗ 83.5  488 W Following observations are made from Figs. 12 and 13 regarding pneumatic performance: • The maximum dp recorded was 4 mbar (400 Pa) corresponding to 3200 Pa in prototype. • Negative pressure observed in the pressure transducer during the inflow of air into the OWC chamber causing the drop of pressure in the graph.

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Fig. 12 dp graph (H  6.28 cm, T  2 s)

6.00 4.00

dp (mbar)

2.00 0.00

1.20

6.20

11.20

16.20

-2.00 -4.00

Time (s)

-6.00 0.8

Fig. 13 Pneumatic power (H  6.28 cm, T  2 s) Output power (W)

0.6 0.4 0.2 0 1.20

- 0.2

6.20

11.20

16.20

- 0.4 - 0.6 - 0.8

Time (s)

• Positive pressure observed in the pressure transducer during the outflow of air from the OWC chamber causing the rise in pressure in the graph. • More recorded values below the draft level of the OWC chamber than above the draft level. So the water level drops down slowly and rises quickly in the OWC chamber. • The output power is a function of the differential pressure. The maximum output power is 0.62 W in the model. • The maximum output power is 317.44 W in the prototype for this wave condition. Average pneumatic power was estimated to be 172.78 W. The experiments were carried out for two wave conditions and results are shown in Table 5.

Table 5 Pneumatic efficiency in different wave conditions Wave condition (model) Wave condition (Prototype)

Efficiency (%)

6.28 cm, 2 s

50.24 cm, 5.65 s

11.9

8.53 cm, 1.5 s

68.2 cm, 4.2 s

11.6

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Mooring Load

0.3 kg pretension load in each mooring line was initially given with the help of turning buckles. Two loads cells, one at forward end and one at aft end were fixed for measuring tension in mooring lines. Figure 14 shows the loads measured by forward and aft load cell during the test for one such wave condition. Figure 15 shows the comparison of measured tension for various wave conditions. Following observations are made from Figs. 14 and 15: • As expected, the forward end of the buoy shows a greater mooring load than the aft end of the cylindrical navigational buoy. • Mooring load acting on to the structure increases due to increase in wave height and decrease in wave period.

0.6

Fig. 14 Mooring loads for H  6.28 cm, T  2 s

Forward end

AFT end

Mooring load (kg)

0.5 0.4 0.3 0.2 0.1 6E - 16 40.00

50.00

2

70.00

Time (s)

- 0.1

Fig. 15 Comparison of forward mooring loads

60.00

H=6.28 cm T=2s

H=7.8 cm T=1.7S

Mooring load (kg)

H=8.53 cm T=1.5s 1.5

1

0.5

0 35

40

45

Time (s)

50

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• The maximum mooring load of 1.9 kg is recorded for the wave condition of 8.53 cm and 1.5 s wave period. The corresponding prototype is expected to experience load of 973 kg.

4 Conclusions Motion behavior and power estimation were carried out in CFD-based solver for a given configuration of navigational buoy for a given wave condition. Selection of crucial OWC diameter was done based on study of two different OWC diameters of 0.9 and 1.1 m. Comparison was done for mass flow rate, pressure drop across orifice and the pneumatic power. 1.1 m diameter predicted higher power conversion. Experiments were carried out in wave flume on the scaled down model of 1.1 m diameter OWC navigational buoy. 1:8 scale ratio was selected and model was fabricated of acrylic material. Although exact wave conditions for numerical and experimental study could not be matched, however pneumatic power in numerical study and experimental study was estimated to be 192 W and 172 W respectively for the closest possible wave conditions prevalent at Ennore port. 1.1 m OWC size was further used to size the buoy external buoyancy tank and other parts of the navigational buoy for its prototype development. Acknowledgements The authors acknowledge Mr. R. Venkateshwaran and Prof. B. V. Mudgal’s guidance and support for the experimental studies at Anna University, Chennai.

References 1. Sheng W, Raymond A, Tony L (2014) Physical modelling of wave energy converters. Ocean Eng 84:29–36 2. Pathak AG, Subramanian VA, Masuda Y (1999) Performance studies on a scaled model of backward bent ducted buoy (BBDB) type wave energy converter in regular and random waves. In: International offshore and polar engineering conference, Brest, France, 30 May–4 June 1999. ISBN 1-880653-39-7 3. Ram K, Faizal M, Ahmed MR, Lee YH (2010) Experimental studies on the flow characteristics of oscillating water column device. J Mech Sci Technol 24(10):2043–2050 4. Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys 39:201–225

Performance Evaluation of Floating Two-Body Wave Energy Converter with Hydraulic Power Take-Off System Sudharsan Kalidoss

and Arindam Banerjee

Abstract In the present work, the dynamic coupling between a self-reacting floating two-body wave-energy converter (WEC) and hydraulic power take-off (PTO) system is evaluated. The WEC is surface meshed; the hydrodynamic properties are calculated using WAMIT, a boundary element method code. The multi-body dynamics of the WEC was analyzed using the open-source code WEC-Sim. The hydraulic PTO system considered for the present analysis is a constant pressure system with valves which rectify the flow to high-pressure and low-pressure accumulators. The heave response amplitude operator of the WEC for varying wave period shows that the float and torus have different peak heave response which makes them oscillate with a phase difference. In the combined mode, the WEC exhibits a peak heave frequency which is less than the natural frequency of the float. Various parameters that include the shaft power, absorbed power, and usable electric power for varying hydraulic motor rpm and the area of the hydraulic piston is calculated. The most probable sea state condition that exists on the US East Coast (wave height  5.5 m and wave period  7 s) is used for analyzing the WEC. The absorbed power of WEC initially increases with an increase in the size of the hydraulic piston. Once the WEC reached maximum absorbed power, increasing the hydraulic piston diameter decreases the absorbed power. The increase in hydraulic piston area increases the pressure energy stored in accumulators. Since the volume flow rate to the hydraulic motor is constant, increase in the area reduces the limiting velocity of the PTO system. Therefore, hydraulic motor and hydraulic piston should be chosen such a way that the PTO system will work at maximum efficiency. The maximum RPM of a hydraulic motor is determined by the size of the hydraulic piston, smaller the size of hydraulic piston lower the limit of hydraulic motor RPM and vice versa. Keywords Wave energy converter · Hydraulic PTO system Constant pressure hydraulic system · Hydraulic motor RPM · PTO efficiency S. Kalidoss (B) · A. Banerjee Lehigh University, Bethlehem, PA, USA e-mail: [email protected] A. Banerjee e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_65

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1 Introduction Ocean waves are one of the world’s most abundant, predictable, and consistent sources of renewable energy. Efficient and economical harvesting of the energy in ocean waves offers an electricity future in which we can diversify our supply portfolio, reduce greenhouse gas emissions, and enable a more sustainable energy future. Numerous designs of wave energy converters (henceforth referred to as WECs) have been proposed in the scientific literature to extract energy from ocean waves. According to the Electric Power Research Institute, one-third of the annual electricity consumption of U.S. can be satisfied with wave energy resource available along the U.S. coasts. WECs can be broadly classified into point absorbers, wave activated bodies, oscillating water column and overtopping devices [1–6]. Amongst the available WEC technologies, a floating two-body point absorber has demonstrated promising performance with ease in operation and maintenance [7]. The floating two-body WEC is a self-reacting, axisymmetric point absorber that operates in heave mode to convert wave energy into electricity. It consists of two concentric bodies having different resonant frequencies in heave mode; the deeper body is called the float, while the shallower body is called the torus. Muliawan et al. [8] analyzed the performance of floating two-body wave energy converter with a linear power take-off (PTO) and mooring lines in regular and irregular waves. In their time domain analysis, the linear PTO parameters such as spring stiffness and damping coefficient are varied. It is concluded that increasing the damping coefficient and spring stiffness increases the peak absorbed power and shifts the peak to higher wave periods. For optimized performance of the WEC, both the damping coefficient and spring stiffness need to be chosen within the bandwidth of the wave period. Babarit et al. [9] numerically compared the performance of eight WECs, a linear PTO system was used to analyze the power capture performance of the devices. It was concluded that the annual absorbed energy per unit characteristic mass was 1 MW-hr/ton, while the value of absorbed energy per unit (RMS of) PTO force was 2 MW-hr/kN for all the devices. Most researchers use a linear PTO system when modeling WEC; the optimization of which can be done based on a priori knowledge of the sea state. However, in a real ocean environment, predicting the future sea state is difficult which results in reduction in performance. This drop in performance can be avoided by decoupling the PTO system from the WEC. Falco [10] modeled a hydraulic PTO system with a single heaving bouy, the volume flow rate to the hydraulic motor and difference in pressure between the accumulators are considered as the control parameters. The optimized hydraulic PTO shows negligible impact due to a change in significant wave height; the PTO performance was also weakly related to the wave period. Henderson [11] developed a hydraulic PTO system for the Pelamis. Similar to the system proposed by Falcao [10], the PTO decoupled the dynamic action of WEC from the power generating system the power absorbed by the WEC is stored in accumulators and gives the WEC provides a constant energy output that is independent of the wave height. The efficiency of hydraulic PTO system was reported to be high for both the cases [10, 11]. Payne et al.

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[12] introduced a digital displacement (DD) hydraulic motor for the hydraulic PTO system in Pelamis and obtained an increase in performance over the conventional hydraulic motors. DD hydraulic motors have the ability to perform well in part load conditions. Plummer and Schlotter [13] analyzed the performance of a hydraulic PTO with losses in heaving vertical cylinder; it was reported that the performance reduces by 30% in real sea condition. Ricci et al. [14] extended the study of hydraulic PTO system to a single oscillating WEC. The power output of the PTO system was improved by modulating the resistive torque of the electric generator; as a control strategy a gas accumulator was introduced into the system that controls the resistive torque of the generator and improves the maximum power output. In another control strategy, an additional accumulator was introduced to store the extra energy from the PTO system together with a properly controlled valve to release the energy and improve the performance. Both control strategies resulted in improvements in the power output of the PTO system. Fan et al. [15] introduced a fuzzy logic controller into the open loop hydraulic PTO system in a WEC operating under irregular wave condition. Accumulators were introduced to store and release the energy by controlling the generator torque. Costello et al. [16] compared the performance of a constant pressure PTO system with a variable pressure PTO system. Both systems showed improved performance when operated with a digital displacement motor. Cargo et al. [17] optimized a hydraulic PTO system with heaving single body WEC under regular wave condition. Optimizing the displacement of the hydraulic motor increases the power output of the hydraulic PTO system. It was also found that the wave period has a significant effect on the PTO system. Various losses were introduced to check the performance of the optimized hydraulic PTO system which showed a trend similar to the case without losses; however, a reduction in power was reported. Liu et al. [18] introduced a control strategy using hydraulic cylinders; the strategy was to the effective area of the hydraulic cylinder which in turn controls the moment acting on the buoy. The PTO system with this hydraulic cylinder control strategy extracted 27% more power than the PTO system without a hydraulic cylinder control. Liu et al. [19] optimized a two raft-type WEC with hydraulic PTO system operating under regular and irregular wave conditions. The peak power capture factor (ratio of output power to the PTO force) demonstrates negligible effect with significant wave height but depends on the wave period. In irregular waves, both parameters shows a similar trend with a reduction in magnitude. In the present paper, the performance of a hydraulic PTO system in a floating selfreacting two-body WEC is investigated. A constant pressure hydraulic PTO system is chosen to decouple the dynamic behavior of the WEC from the power production. The performance evaluation is carried out in regular sea state condition with control parameters that include the hydraulic motor RPM and hydraulic piston area.

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2 Theoretical Background 2.1 Point Absorber Wave Energy Converter The schematic of the WEC used for the present analysis is shown in Fig. 1. The WEC consists of two concentric axisymmetric bodies. It is a self-reacting point absorber operating in heave mode. The deep (longer) body is called float while the shallower body is called torus; both bodies operate in heave mode at different oscillating frequency. The difference in frequency leads to a relative motion between the bodies which is stored as hydraulic energy and converted into electricity. The time domain equation of motion for a point absorber WEC which is moving in heave on the water surface is formulated similar to the mass-spring-damper system with the addition of few forcing terms. These forcing terms account for the wave-structure interaction of the WEC. Cummins [20] created an integro-differential equation of motion with impulse response for ship motions that can be written as: (M + μ∞ )X¨  Fex −

t

K(t − τ )X˙ (τ )dt + FH + FPTO + FV + Fes ,

(1)

0

where M is the mass matrix of the device, Fex is the wave excitation force, μ∞ is the added mass matrix, K(t) is the memory function of the radiation forces. FPTO , FV , FH, and Fes are the PTO force, damping force, hydrostatic force and end stop force respectively. Using linear potential theory, the pressure force acting on the WEC from wavestructure interaction is written as the sum of the wave excitation force and the radiation force. The wave excitation force in Eq. (1) is given as

Fig. 1 Schematic of floating two-body wave energy converter [8]

Performance Evaluation of Floating Two-Body Wave Energy …

     i(2πfi t+φi ) Fex (t)  R 2S(fi )f F ex (fi )e ,

887

(2)

i

where S(f) is the incident wave spectrum, f is an adequate frequency step, ϕi is a set of random phases and Fex are complex vectors of wave excitation force per meter of wave amplitude in the frequency domain. The radiation force is given by the Eq. (3),  t Frad  −μ∞ X¨ − K(t − τ )X˙ (τ )d τ (3) 0

The hydrodynamic coefficients Fex and μ∞ and radiation memory function K(t) is calculated using Boundary Element Code (WAMIT). The hydrostatic force is the restoring force of the water on the WEC body and it is given by Eq. (3). FH  ρSW gAx,

(4)

where ρSW is the density of salt water, g is acceleration due to gravity and A is the cross-sectional area of the body. For the safe operation of the WEC, the relative motion between the float and the torus should be in the safe range (assumed to be 3 m for the current WEC design [8]). The amplitude of oscillation of the WEC is controlled by the end stops; whenever the torus exceeds the limiting stroke length, the end stops dampens the motion. Numerically the end stops are modeled as spring with high stiffness coefficient. The end stop force acting on the WEC is given as: Fes  −Kes diag(X + Xes )u(X − Xes ) − Kes diag(X − Xes )u(X − Xes ),

(5)

where Kes is the stiffness constant of end stop, u(·) is the element-wise Heaviside step function and Xes is the amplitude of constraint vector.

2.2 Hydraulic PTO System The power output from the WEC is constant. The absorbed power of the WEC varies with the irregular ocean state. The constant pressure hydraulic system decouples the WEC and the PTO system for smooth power production. The schematic for hydraulic PTO system is shown in Fig. 2. The closed-loop hydraulic PTO system consists of a piston moving inside a hydraulic cylinder, a rectifying valve, a high-pressure accumulator (HP), a hydraulic motor connected to an electric generator and a low-pressure accumulator (LP). The relative motion between the two bodies of the WEC is transferred to the piston that

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Fig. 2 Schematic of a constant pressure hydraulic PTO system [16] used for present analysis

moves up and down in the hydraulic cylinder, to pressurize the hydraulic oil in the cylinder. The upward movement of the piston creates high pressure in region A and low pressure in region B (see Fig. 2). The rectifying valve passes the pressurized oil to the high-pressure accumulator where it is stored. The pressurized oil from the high-pressure accumulator passes through the hydraulic motor, which runs at constant RPM, followed by the low-pressure accumulator. The low-pressure accumulator acts as a reservoir for the system. The hydraulic oil from the low-pressure accumulator is transferred to the low-pressure region in the hydraulic cylinder, thus closing the circuit. Irrespective of the wave condition, the hydraulic motor runs at constant rpm so that the output power will be relatively smooth. For the present analysis, the hydraulic fluid is assumed to be incompressible and the total mass in the system remains constant. From conservation of mass principles, the volume of fluid entering the high-pressure accumulator is equal to the volume of fluid flow out of the hydraulic cylinder. The rate of change of volume of hydraulic oil in the high-pressure accumulator is the difference in hydraulic fluid flow from the cylinder and the flow towards the motor as shown in Eq. (6). Similarly, the rate of change of volume of hydraulic fluid in the low-pressure accumulator is the difference in fluid flow from the motor and flow towards the cylinder shown in Eq. (7). d Vf ,HP  V˙HP,in − V˙m dt d Vf ,LP  V˙m − V˙LP,out dt  q  Kv Pc − Pa

(6) (7) (8)

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Fig. 3 Heave RAO of float and torus (inset) for different wave periods

The flow (q) through the rectifying valve is given by Eq. (8). The rectifying valve ensures that the high-pressure hydraulic oil is passed on to the high-pressure accumulator. In Eq. (8), Kv is the valve flow-coefficient that accounts for frictional losses in the valve, a value of Kv = 1 is chosen for simplicity any pressure loss in the valve. Pc and Pa are the cylinder pressure and the accumulator pressure; the rectifying valve switches the flow based on the pressure in the cylinder and the accumulator. The PTO force and power output (Pout) is given by FPTO  −pApist sign(˙x)

(9)

Pout  τ ωm ,

(10)

where p is the difference in pressure between the high-pressure and low-pressure accumulators, Apist is the area of the piston in the hydraulic cylinder, τ is the generator torque, and, ωm is the hydraulic motor rpm.

3 Numerical Modeling 3.1 Hydrodynamic Modeling The hydrodynamic coefficients such as added mass (matrix) and damping coefficients of the WEC are calculated using a Boundary Element Method (BEM) code WAMIT [21]. WAMIT is a potential flow solver, which assumes linear wave theory. The heave response amplitude operator (RAO) of the WEC is calculated separately for the float and torus as shown in Fig. 3. In the combined mode, the float and the torus oscillate as a single body. The heave RAO in the combined mode is shown in Fig. 4 and is in good agreement with values reported in literature [8]. Figure 3 shows different heave frequencies for the float and torus. The float exhibits a peak response at a wave period of 21 s, whereas the torus shows peak response at wave period of 10 s. This difference in peak response periods results in a relative

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Fig. 4 Heave RAO in combined mode for different wave periods

motion between the two bodies which is required for harnessing the available energy in the ocean waves. In combined mode, the WEC attains a peak response at a wave period of 10s.

3.2 Multibody Dynamic Modeling The WEC is modeled in SIMULINK, the multibody interaction of WEC is modeled and solved in WEC-Sim [22], a MATLAB-SIMULINK based open-source code. The simulation is run with regular wave spectrum of significant wave height 5.5 m and wave period 7 s. The simulation was run for approximately 72 wave periods to obtain a steady-state solution. The performance parameters such as absorbed power, mechanical power, PTO efficiency are time averaged and are discussed next.

4 Results and Discussion The area of the piston is varied from 0.01 to 0.25 m2 while the hydraulic motor size was kept constant. Figures 5 show the high-pressure and low-pressure accumulator pressures during operation. The pressure difference between the accumulators remains constant irrespective of the direction of motion of the hydraulic piston. The difference in pressure is directly proportional to the energy stored in the PTO system. The absorbed power absorbed by the PTO system is sinusoidal as shown in Fig. 6. This sinusoidal power generation produces stress in electrical components which reduces the life and performance of the components. Due to the decoupled action of hydraulic PTO system, the mechanical and electrical power output of the WEC remains constant. The absorbed power of the PTO system increases with increase in hydraulic piston area until it reaches a peak absorbing power as shown in Fig. 7. Once the PTO

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Fig. 5 Pressure in high-pressure and low-pressure accumulators during operation of two-body WEC

Fig. 6 Absorbed power, mechanical power and electrical power extracted by the PTO

Fig. 7 Power absorbed by the PTO system

system reaches the peak, any subsequent increase of the hydraulic piston area leads to a decrease in the absorbed power. The absorbing power capacity of the hydraulic PTO is limited by the volume flow rate of the hydraulic motor which is kept constant for the analysis present in this paper. Increasing the hydraulic piston area reduces the limiting velocity of the hydraulic piston as shown in Eq. (11). vlim  qflow /A

(11)

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Fig. 8 Pressure differential stored in accumulators

Fig. 9 Capture width ratio (CWR) of the WEC operating in constant speed (rpm)

Figure 8, shows the difference in accumulator pressures when the hydraulic piston area is varied. It is noted that the peak absorbed power and peak difference in pressure occurs at different values of hydraulic piston area. Increasing the hydraulic piston area increases the pressure differential and the energy stored in the accumulator, however, it is not utilized or converted into usable energy as the limiting velocity (defined in Eq. 11) reduces with an increase in area when the hydraulic motor rpm is held constant. The capture width ratio (CWR) is defined as the ratio between capture width and diameter of the buoy follow the same trend as absorbed power shown in Fig. 9. Since the capture width ratio is proportional to the absorbed power of the WEC, the capture width ratio, hydrodynamic efficiency and overall efficiency of the WEC shows peak performance at hydraulic piston area of 0.03 m2 . The maximum hydrodynamic and overall efficiency of the WEC reaches 10 and 8% (Figs. 10 and 11). The PTO system reaches maximum efficiency at hydraulic piston diameter of 0.03 m2 ; increasing the hydraulic piston area did not show any notable change in the efficiency of the PTO system. The hydraulic motor reaches its maximum performance when the optimum hydraulic piston area is chosen. The efficiency of the PTO system is shown in Figs. 12 and 13, is thus limited by the hydraulic motor. To further explore the performance of the hydraulic PTO system, the hydraulic motor rpm is varied from 500 to 2000 rpm while the hydraulic piston diameter is

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Fig. 10 Hydrodynamic efficiency at constant rpm for varying hydraulic piston area

Fig. 11 Overall efficiency of the WEC for varying hydraulic piston area at constant motor rpm

Fig. 12 Mechanical efficiency of the PTO system for varying hydraulic piston area at constant motor rpm

held constant. Figures 14 and 15, shows the absorbed power and CWR of the WEC. The absorbed power of the WEC is linearly proportional to the hydraulic motor rpm. From Eq. (10) it is noted that increasing the rpm of the hydraulic motor increases the power output. The efficiency of the PTO system shows increasing trend for an increase in hydraulic motor rpm, shown in Fig. 16. Upon reaching the maximum efficiency, the power output of the PTO system reduces with increase in hydraulic motor rpm.

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Fig. 13 Overall efficiency of the PTO system for varying hydraulic piston area at constant motor rpm

Fig. 14 Absorbed power of the WEC for varying motor rpm (size of hydraulic piston is kept constant)

Fig. 15 Capture width ratio of the WEC for varying motor rpm (size of hydraulic piston is kept constant)

The PTO system showed maximum efficiency near to 100% with an increase in hydraulic piston area. In increasing the hydraulic motor rpm, the efficiency of PTO system reaches near to 95%. Figure 17, shows the overall efficiency of the PTO system. Figures 18 and 19, show the hydrodynamic and overall efficiency of the WEC. Increasing the rpm of the PTO system increases the efficiency of the WEC by 2%. For the WEC to extract maximum power from the ocean, it requires proper selection of the size of the hydraulic motor with optimum hydraulic piston area.

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Fig. 16 Mechanical efficiency of the PTO for varying motor rpm (size of hydraulic piston is kept constant)

Fig. 17 Overall efficiency of the PTO system for varying motor rpm (size of hydraulic piston is kept constant)

Fig. 18 Hydrodynamic efficiency of the WEC for varying motor rpm (size of hydraulic piston is kept constant)

5 Conclusion The performance of a hydraulic PTO system on floating two-body WEC is evaluated. The observed heave response of the float and the torus are different due to relative motion between the bodies. From the present analysis, the following conclusions are drawn. • The hydraulic PTO system decouples the power production from the WEC motion by storing the energy in the accumulators.

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Fig. 19 Overall efficiency of the WEC for varying motor rpm (size of hydraulic piston is kept constant)

• The PTO system reaches its maximum performance when hydraulic piston area is 0.03 m2 . Increasing the hydraulic piston area above this threshold value leads to a decrease in WEC efficiency as the excess pressure stored in the accumulator is not converted into usable energy. • The power produced is also limited by the volume flow rate of the hydraulic motor. This indicates that for maximum wave energy extraction requires proper selection of hydraulic motor with an optimum hydraulic piston area. • Increasing the hydraulic motor rpm increases the capture width ratio of the WEC followed by an increase in overall efficiency by 2%. However, the PTO efficiency drops after reaching maximum efficiency. In the present analysis, the losses due to compressibility effect on hydraulic oil, rectifying valve losses are ignored. For better accuracy, these losses need to be considered while modeling the hydraulic PTO system. Acknowledgement The authors would like to acknowledge the U.S. National Science Foundation for financial support for this work through the CYBERSEES program (Award # 1442858 ) and the GOALI program (Award # 1400164).

References 1. Drew B, Plummer A, Sahinkaya MN (2009) A review of wave energy converter technology. Proc Inst Mech Eng Part A J Power Energy 223(8):887–902 2. Falnes J (2007) A review of wave-energy extraction. Mar Struct 20(4):185–201 3. Guedes Soares C, Bhattacharjee J, Karmakar D (2014) Overview and prospects for development of wave and offshore wind energy. Brodogradnja 65(2):87–109 4. Knight C et al (2014) A review of ocean energy converters, with an Australian focus. AIMS Energy 2(3):295–320 5. Mehrangiz S et al (2013) Various technologies for producing energy from wave: a review. Int J Smart Grid Clean Energy 2(2) 6. Morim J et al (2014) A review of wave energy estimates for nearshore shelf waters off Australia. Int J Mar Energy 7:57–70

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7. French M (2006) On the difficulty of inventing an economical sea wave energy converter: a personal view. Proc Inst Mech Eng Part M J Eng Marit Environ 220(3):149–155 8. Muliawan M et al (2011) Analysis of a two-body floating wave energy converter with particular focus on the effect of mooring system on energy capture. In: 30th international conference on ocean, Offshore and Artic engineering 9. Babarit A et al (2012) Numerical benchmarking study of a selection of wave energy converters. Renew Energy 41:44–63 10. Falcao A (2007) Modelling and control of oscillating-body wave energy converters with hydraulic power take-off and gas accumulator. Ocean Eng 34(14):2021–2032 11. Henderson R (2006) Design, simulation, and testing of a novel hydraulic power take-off system for the Pelamis wave energy converter. Renew Energy 31(2):271–283 12. Payne GS et al (2005) Potential of digital displacement hydraulics for wave energy conversion. In: Proceedings of the sixth European wave and tidal energy conference, Glasgow 13. Plummer A, Schlotter M (2009) Investigating the performance of a hydraulic power take-off. In: Proceedings of the eight European wave and tidal energy conference, Uppsala 14. Ricci P et al (2011) Control strategies for a wave energy converter connected to a hydraulic power take-off. IET Renew Power Gener 5(3):234–244 15. Fan Y, Mu A, Ma T (2016) Design and control of a point absorber wave energy converter with an open loop hydraulic transmission. Energy Convers Manag 121:13–21 16. Costello R, Ringwood J, Weber J (2011) Comparison of two alternative hydraulic PTO concepts for wave energy conversion. In: Proceedings of the 9th European wave and tidal energy conference (EWTEC). School of civil engineering and the environment, University of Southampton 17. Cargo CJ et al (2012) Determination of optimal parameters for a hydraulic power take-off unit of a wave energy converter in regular waves. Proc Inst Mech Eng Part A J Power Energy 226(1):98–111 18. Liu C et al (2015) Maximum wave power absorption by a control strategy through combining hydraulic cylinders. In: 2015 international conference on fluid power and mechatronics (FPM). IEEE 19. Liu C, Yang Q, Bao G (2017) Performance investigation of a two-raft-type wave energy converter with hydraulic power take-off unit. Appl Ocean Res 62:139–155 20. McCormick ME (2013) Ocean wave energy conversion. Courier Corporation 21. V7.1, WAMIT Users Manual 22. WEC-Sim User Manual http://www.wec-sim.github.io/WEC-Sim

Pitch Motion Studies of Barge Supporting 5-MW-NREL Offshore Floating Wind Turbine with Gyrostabilizer P. Manmathakrishnan and R. Panneer Selvam

Abstract The cyclic motion of a floating structure induces fatigue load on the floating wind turbine cause damage and trim the performance of the wind turbine. One has to minimize the pitch and roll angular motions to eradicate fatigue load and thereby mitigating the structural damage and increase the life time of the wind turbine. The ITI barge type floating wind turbine have highest fatigue load due to cyclic pitch motion in contrast with other basic types of floaters. For ITI barge the pitch motion is dominated over the roll for following and head sea, were roll is dominated for beam sea condition. A novel damping technique called gyroscopic motion counterpoise is used to reduce the pitch motion. Gyrostabilizer is used in various industries for motion stabilization, in ocean engineering it is used in ships and yachts for roll stabilization and in ocean energy converters for harvesting energy. For the first time the gyro-stabilizer is used in the floating wind turbine to damp the rotational motion. The numerical analysis is carried for ITI energy barge with gyrostabilizer supported 5-MW (National Renewable Energy Laboratory) NREL floating wind turbine. The results imply that the cyclic pitch rate is abated substantially by the gyrostabilizer. Keywords Offshore wind · Pitch · Fatigue · Energy barge · Beam sea · Head sea Following sea · Gyrostabilizer

1 Introduction In the past decades, the world was dependent on highly polluting electrical energy producing methods like nuclear reactor, thermal power plants and from petroleum products through large-scale turbines. By knowing more about the insight of pollution P. Manmathakrishnan (B) · R. Panneer Selvam Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai 600036, TN, India e-mail: [email protected] R. Panneer Selvam e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_66

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to environment and thereby hazardous to the human life researchers and scientists in early 80s come across with the concept of wind turbine and solar energy, which alter the place of other methods in the electrical energy production. The wind turbine is subdivided into onshore and offshore. The offshore wind turbine has more recognition than onshore in terms of wind availability, not affecting environmental views, decreased death of birds. Hence research teams and industry were egger towards the offshore wind energy, In spite of having disadvantage of less cost effect compared to the onshore one. The offshore wind energy involves two types of wind turbines, i.e., fixed and floating wind turbines. Fixed one is limited to shallow water due to increase in the cost of substructure if water is more deeper and in shallow water there is a less perpetual wind availability lead researchers to move towards the floating platform based wind turbines. The reason behind the less cost effectiveness is due to the design of floater, installation, storage of power and maintenance of offshore wind turbines. The cost effectiveness is elevated by choosing the floater which takes care of all mentioned factors is ITI Energy barge that achieves the stability by buoyancy. Jonkman and Matha [1] studied the motion response of three types of floaters namely MIT/NREL TLP, Spar buoy, ITI Energy barge that supports the NREL offshore 5-MW baseline wind turbine and the study shows that, among the three types of floaters, the barge type floating platform induce ultimate fatigue load in all turbine components and have highest fatigue load due to cyclic pitch and roll motion of whole system in comparison with other basic types of floaters. The consequences of using the quasi-static mooring line models was discussed with the comparison tests performed on ITI barge by incorporating both steady and stochastic wind and wave conditions [2]. The set of optimum tuned mass dampers are established by creating a limited degree-of-freedom model for four various offshore wind platforms. Tower fatigue damage reductions of between 5 and 20% are achieved for the various Tuned mass damper (TMD) configurations [3]. The floating wind turbine with a hybrid actuation system having combination of (TMD) and active vertical vane to reduce platform pitch and roll motions was discussed. The potency of this hybrid actuation system was exhibited through the simulations which are explained out in accordance with the IEC 61400-3 standard design load case 1.2 fatigue load testing. The hybrid actuation system stabilized the platform in the two significant (fore-aft and side-to-side) degrees of freedom of the wind turbine [4]. An actively controlled vertical vanes discussed to increase damping in the roll direction of floating wind turbine. FAST an aero-elastic computer aide- engineering tool for horizontal axis wind turbine is modified to simulate floating turbine including vane according to Kane’s method. The controller is designed by use of Proportional Integral-based individual pitch controller and variable torque control. Simulation results shows that damping in the roll direction was increased and side-to-side bending moments at tower was reduced considerably by use of vertical vane control [5]. The establishing controller for the roll motion damping on a ship-shaped small vessel with sliding mode technique for dealing the uncertainties in the dynamic model was discussed. The controller is designed based on a simple on-off logic while the version that is a sliding mode controller with boundary layer to avoid chattering. The roll angle of the vessel is compared among the no-control, on-off control and sliding mode control

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[6]. The variable blade pitch control of (Offshore Floating Wind turbine) OFWT for power tracking and fatigue load devaluation on a barge platform with robust adaptive control scheme with memory-based compensation for blade pitch control was discussed [7]. The theory of gyroscope and its various applications on gyrocompass, attitude instrument, platform stabilization with different degrees of freedom specifications are discussed [8]. The precept and various function of gyroscopes, like in torpedo instrument for war, stabilizing ships at sea, gyrocompass, aircraft precession control, camera platform stabilization, etc., were explained [9]. A new gyroscopic scheme of active transportation control on marine vehicles was conferred, in which Gyroscopic stabilization is used to minimize control moments [10]. An approach to control the direction of a robot using a control moment gyroscope (CMG) is projected with a semi absolute system that clone a bipedal robot on which an off-the-shelf battery powered gyroscope is seated to a gimbal with Two different actuation assembly, is used solely to prove the potential of a control moment gyroscope in generating large angle turns that are not viable in alternate methods using reaction wheels [11]. Crafting gyrostabilizer with scrutinized control form that does not require roll motion history was considered and used the controller that urge the gyrostabilizer as supplementary roll damper to the vessel using precession gesture data. Reviewed the roll damping limitation over the scope of frequencies with the control strategy endorsed [12]. The conduct of wave energy converter is appraised over the gyro effects in string with the power take off- device. By utilizing the state feedback controller, precession couple is provoked with precession angle and precession rate, which edge the control scheme for maximum inferred power [13]. Nonlinear sliding mode control is used to revamp the clout of twin wheel gyroscope for roll stabilization utilization [6]. It is visualized that pitch motion stabilization of ITI Energy barge supporting 5-MW-NREL is a research gap and stabilization of pitch motion with Vertical axis gyrostabilizer is focused here. There is less discussion on stabilization device for motion reduction of ITI barge is available. Using gyrostabilizer as a damping device is a novel technique for ITI barge which is not reported earlier.

2 NREL 5-MW Turbine on ITI Energy Barge 2.1 NREL 5-MW Wind Turbine A baseline wind turbine of 5-MW was identified by the NREL for regularizing the reference wind turbine to furnish practical input values for offshore wind energy study and developed the, “NREL offshore 5-MW baseline wind turbine” [2], which is identified in this study as the NREL 5-MW turbine. The NREL 5-MW turbine is based on the REpower 5M machine is a traditional three-bladed upwind turbine is taken for this analysis and the specifications are given in the Table 1.

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Table 1 NREL 5-MW baseline wind turbine scheme Description Rating Rotor orientation, configuration

Upwind, 3 blades

Control

Variable speed, collective pitch

Drivetrain

High speed, multiple-stage gearbox

Rotor, hub diameter, hub height

126 m, 3 m, 90 m

Cut-in, rated, cut-out wind speed

3 m/s, 11.4 m/s, 25 m/s

Cut-in, rated rotor speed

6.9 rpm, 12.1 rpm

Rated tip speed, overhang, shaft tilt, precone

80 m/s, 5 m, 5°, 2.5°

Rotor mass, nacelle mass, tower mass

110,000 kg, 240,000 kg, 347,460 kg

Coordinate location of overall CM

(−0.2 m, 0.0 m, 64.0 m)

Fig. 1 Schematic diagram of 5-MW-NREL wind turbine supported by ITI barge

2.2 ITI Energy Barge ITI Energy barge is a simple square type floater established by the Department of Naval Architecture and Marine Engineering at the Universities of Glasgow and Strathclyde through a contract with ITI Energy [1]. It is a Platform that achieves stability through the use of distributed buoyancy and taking advantage of wetted water plane area for righting moment. The draft is achieved by ballasting the sea water and the station keeping of barge is done by the 8 slack catenary mooring lines of which two in each corner separated by 450. The barge particulars are given in Table 2 and Fig. 1 shows the schematic diagram of ITI Energy barge supporting reference wind turbine.

Pitch Motion Studies of Barge Supporting 5-MW-NREL Offshore … Table 2 ITI energy barge specifications Description

903

Rating

length × width × height

40 × 40 × 10 (m)

Draft, freeboard

4 (m), 6 (m)

Water displacement

6,000 (m3 )

Mass, including ballast

5,452,000 (kg)

CM location of the platform below SWL

0.2818 (m)

Roll moment of inertia about CM

726,900,000 (kg m2 )

Pitch moment of inertia about CM

726,900,000 (kg m2 )

Yaw moment of inertia about CM

1,454,000,000 (kg m2 )

Number of mooring lines

8

Depth to fairleads, anchors

4, 150 (m)

Radius to fairleads, anchors

28.28, 423.4 (m)

Un-stretched line length

473.3 (m)

Line diameter

0.0809 (m)

Line mass density

130.4 (kg m−1 )

Fig. 2 Motion representation of ITI energy barge

2.3 Pitching Equation of Motion ITI Barge is symmetric in lateral and longitudinal directions. The motion of platform for unidirectional wave circumstances in lateral and longitudinal directions is same and it is taken as single degree-of-freedom Pitch motion in this analysis. Figure 2 shows the motion coordinates of ITI barge and the uncoupled pitch equation of motion is given by

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I55 θ¨ + B55 θ˙ + C55 θ  Mθ

(1)

I55 Is the Pitch moment of inertia of ITI barge including added mass, B55 is the Pitch potential damping coefficient, C55 is the Pitch restoring coefficient, θ is the Pitch angle, Mθ is the Wave induced pitch moment.

3 Single Axis Gyrostabilizer A gyrostabilizer is a device with a spinning flywheel and gimbal, with the determined tendency of a gyrated flywheel to maintain its plane of rotation. Gyrostabilizer works based on the principle of conservation of angular moment and obeys gyroscopic laws. The uncoupled equation of motion of a gyrostabilizer is given by Igs ψ¨ + Bgs ψ˙ + Cgs ψ  Hgs θ˙ cos ψ

(2)

Igs is the moment of inertia of the orbiting flywheel along the precession axis, Bgs is the damping coefficient due to friction in shaking bearings, Cgs is the restoring coefficient related to the mass distribution  of the orbitingflywheel, θ -Precession angle, Hgs -orbiting angular momentum Hgs  ωspin × Ispin Equations (1) and (2) describes the pitch dynamics of floating barge and gyrostabilizer dynamics about the precession axis for a torque acts on an rotating flywheel with an axis perpendicular to that of spin axis in an uncoupled way.

4 Mathematical Modeling of System 4.1 Coupled Equation of Motion The unidirectional wave activated torque will induce the pitch motion in a floating barge and as the pitch motion progress; the pitch rate will induces a torque along the lead axis of the orbiting flywheel. As a flywheel promotes precession, there is reaction torque act on the floater that resists the wave activated torque. The reaction torque is the Pitch stabilizing torque and is given by Mgs  −nHgs ψ˙ cos ψ I55 θ¨ + B55 θ˙ + C55 θ  Mθ − nHgs ψ˙ cos ψ

(3) (4)

The precession rate is approximately proportional to the pitch rate with some proportionality constant [12] in the selected frequencies of wish. ψ ≈ qθ˙

(5)

Pitch Motion Studies of Barge Supporting 5-MW-NREL Offshore …

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while q is a constant and the system will create damping to the floater.   I55 θ¨ + B55 + nHgs q θ˙ + C55 θ  Mθ

(6)

And the equation is a restraint established on operational mode of gyrostabilizer, in (3) n denotes the number of flywheel. Equations (2) and (4) gives the coupled equations of motion of ITI energy barge carrying 5 MW-NREL floating wind turbine with gyrostabilizer.

4.2 Coupled Equation of Motion The mathematical model of ITI barge with wind turbine system with gyrostabilizer is modeled in Simulink through transfer function method. The transfer function of wave stimulating moment to pitch moment while gyrostabilizer is switched on is given by [14] H (S) 

θ (S) Mθ (S)

  Igs S 2 + Bgs S + Cgs   H (S)   2 S2 Igs S 2 + Bgs S + Cgs I55 S 2 + B55 S + C55 + nHgs

(7)

The precession rate to pitch rate transfer function is given by G(S) 

θ˙ (S) ˙ Mθ (S)

Hgs S  H (S)   Igs S 2 + Bgs S + Cgs

(8)

The transfer function of pitch couple by cause of wave to the precession angle is Hgs S   H (S)   2 2 S2 Igs S + Bgs S + Cgs I55 S 2 + B55 S + C55 + nHgs The selected parameters of gyrostabilizer are in Table 3.

(9)

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Table 3 Scheme of gyrostabilizer and barge S. no Parameters

Specification

1

Flywheel diameter

0.64 m

2

Flywheel mass

783 kg

3

Mass moment of inertia (I YY )

54.8 kg m2

4

Mass moment of inertia (I XX = I ZZ = I G )

47.2 kg m2

5

Flywheel material

Steel

6

Angular velocity of flywheel

1047.2 rad/s

7

Gyro damping coefficient (BG ) 1200 N m−s

8

Gyro restoring coefficient (C G )

7000 N m

9

Pitch moment of inertia (I 55 )

1.81 × 109 kg m2

10

Pitch damping coefficient (B55 )

3.12 × 107 N m−s

11

Pitch restoring coefficient (C 55 )

1.342 × 107 N m

4.3 Wave Motion The fatigue response of floating platforms due to irregular wave environment in the deep offshore is predominant. The random sea state is non-imitating and time differing, it is common mythology to describe sea contingency as a statically stationary, which is neither growing nor crumbling. Design load Case (DLC 1.2) specify the requirements for loads resulting from stochastic sea states that occur during normal operation of an offshore wind turbine throughout its lifetime. Here DLC 1.2 sea state is considered with a single value of significant wave height for each relevant mean wind speed is given in Fig. 3. The Jonswap (Joint North Sea Wave Project) spectrum is used to imitate not-fully established sea. The proposed spectrum estimates the random sea contingency. The classical wave potential perception of Jonswap spectrum in a frequency domain has the form [fossen]   −944 H2 (10) SJ (ω)  1.55 s4 exp (γ )Y T1 T14 ω4      0.07 for ω ≤ 5.24/T1 0.191ωT1 − 1 2 Where Y  exp − σ  √ 2σ 0.09 for ω > 5.24/T1 H s is the significant wave height, ω is the frequency of the wave, T 1 is the average wave period and T z is the average zero-crossing period and γ is the peak enhancing

Pitch Motion Studies of Barge Supporting 5-MW-NREL Offshore …

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Fig. 3 Second-order wave spectrum

factor and γ  3.3. The Jonswap spectrum is revealed as the linear second-order wave transfer function to represent wave forces on floater and it is given by [15] h(s) 

S2

Kw S , + 2λωp S + ωp2

(11)

where Kw is a gain constant and it is given by Kw  2λωp σw . λ is the damping coefficient, ωp is a crest frequency and σw is a constant terming wave severity. The wave model is produced by passing band limited white noise through the second  order wave transfer function and the parameters ωp , σ, λ  0.1 of the transfer functions are identified based on the IEC 61400-3 Standard design load case and it is given in the Table 4.

5 Pitch Response The vertical axis gyrostabilizer is placed on ITI barge for motion studies and the Fig. 4 shows the pitch rate time series comparison between gyrostabilizer on and off scenario. The time series is estimated by solving the coupled equation of motion (2) and (6) of floater and gyro by transfer function method Eqs. (7)–(9) and the gyro parameters for single flywheel arrangement was taken from the literature [15], were they used the twin flywheel rotating in opposite direction for ship shaped structure. The wave elevation is given by second-order wave transfer function indicated by the Eq. (11), through the band limited white noise as an input and the input parameters like peak frequency, gain constant are calculated for JONSWAP spectrum with damping coefficient 0.1. The time series of pitch rate in the plot shown in the Fig. 5 shows that the motion rate is reduced more than 90%, this indicates that if the change in angular rate is reduced then the pitch angle get minimized and thereby barge

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Table 4 IEC 61400-3 standard design load case DLC

V w (m/s)

H s (m)

T p (s)

ωp (rad/s)

Smax (ω) (m2 s)

σ (ms1/2 )

6.4a 1.2a 1.2b 1.2c 1.2d 1.2e 1.2f 1.2g

2 4 6 8 10 12 14 16

1.07 1.1 1.18 1.31 1.48 1.7 1.91 2.19

6.03 5.88 5.76 5.67 5.74 5.88 6.07 6.37

1.042 1.069 1.091 1.108 1.095 1.069 1.035 0.986

0.1066 0.135 0.1297 0.1831 0.1243 0.2409 0.5169 0.4608

0.3265 0.3674 0.601 0.4279 0.3526 0.4908 0.719 0.6788

1.2h 1.2i 1.2j

18 20 22

2.47 2.76 3.09

6.71 6.99 7.4

0.936 0.899 0.849

0.9186 1.245 0.3218

0.9584 1.1158 0.5673

1.2k 6.4b

24 30

3.42 4.46

7.8 8.86

0.806 0.709

0.9554 1.18

0.9775 1.086

Fig. 4 Pitch rate time series plot for DLC 6.4b

Fig. 5 Pitch rate time series plot for DLC 1.2k

supporting OFWT will have less impact of recurring motion due wave excitation, thereby increase in the performance and life time of wind turbine will increase.

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Fig. 6 Root mean square (RMS) comparison of pitch rate

5.1 Results The Root Mean Square (RMS) is a statistical analysis of the intensity of a varying quantity either wave form or random numbers. The pitch rate comparison of floater supporting wind turbine with gyro off and on situation is analyzed and given by pitch rate (RMS) value plot, Fig. 6 shows the rms plot; over 94.8% of pitch rate reduction is achieved by the un-axis gyrostabilizer for unidirectional random wave environment. Figures 7 and 8 shows the pitch rate spectral density comparison of barge with and without gyrostabilizer for IEC 61400-3 Standard Design Load Case (DLC) mentioned in Table 4. Comparing the spectral density indicates that the pitch rate is reduced when the gyro is on and initial peak in the gyro-on plot is due the initial flywheel take off of rpm, i.e. before reaching to the constant angular velocity. Once the constant angular velocity is achieved and it is maintained for further damping of the motion.

6 Conclusion The NREL 5-MW offshore floating wind turbine was selected for the pitch motion studies with single axis vertical gyrostabilizer parameters taken from the literature and the wave excitation is given by the second order wave transfer function for Jonswap spectrum and the numerical results implies that pitch motion is reduced considerably more than 90% for IEC 61400-3 Standard Design Load Case uni-

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Fig. 7 Spectral density plot for pitch rate

Fig. 8 Spectral density plot for pitch rate

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directional random wave environment. This shows the feasibility of gyrostabilizer for pitch damping and using gyrostabilizer for the motion stabilization of offshore floating wind turbine with barge is not reported earlier.

References 1. Matha D, Jonkman J (2009) Model development and loads analysis of an offshore wind turbine on a tension leg platform, with a comparison to other floating turbine concepts. NREL/SR500-45891 February 2010 2. Sebastian T, Lackner M (2012) Analysis of the induction and wake evolution of an offshore floating wind turbine. Energies 5(4):968–1000 3. Hall MTJ (2010) Mooring line modelling and design optimization of floating offshore wind turbines. MS Thesis, University of Victoria. https://dspace.library.uvic.ca/handle/1828/4636 4. Stewart GM (2012) Load reduction of floating wind turbines using tuned mass dampers. Master thesis, University of Massachusetts Amherst. http://scholarworks.umass.edu/theses/781/ 5. Yang Z, Li Y (2013) Active vertical-vane control for roll motion of floating offshore wind turbine. In: 51st AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, aerospace sciences meetings, American Institute of Aeronautics and Astronautics, Grapevine (Dallas/Ft. Worth Region), Texas 6. Haghighi H, Jahed-Motlagh MR (2012) Ships roll stabilization via sliding mode control and gyrostabilizer. In: Proceedings of national maritime and shipping conference, vol 8, no 12, Fasc1 7. Zuo S, Song YD, Wang L, Song Q (2013) Computationally inexpensive approach for pitch control of offshore wind turbine on barge floating platform. Sci World J (Hindawi Publishing Corporation) 2013, Article ID 357849 8. Wrigley W, Hollister WM (1965) The gyroscope: theory and application. J Sci 149(3685) 9. Sperry EA (1913) Engineering application of the gyroscopes. J Frankl Inst CLXXV 10. Townsend NC, Murphy AJ, Shenoi RA (2017) A new active gyrostabiliser system for ride control of marine vehicles. J Ocean Eng 34(11–12):1607–1617 11. Boddiford A, Manion C, Kim KS, Radhakrishnan P, Sentis L (2013) Experiments to validate the use of a control moment gyroscope (CMG) to turn robots. In: Proceedings of the ASME 2013 international design engineering technical conferences and computers and information in engineering conference IDETC/CIE 2013, DETC2013-12285, pp V06BT07A051 12. Perez T, Steinmann PD (2009) Analysis of ship rolls gyrostabilizer control. In: IFAC proceedings volumes-8th IFAC conference on manoeuvring and control of marine craft, vol 42, no 18, pp 310–315 13. Perez T, Santos-Mujica M, Ruiz-Minguela JP (2009) Performance analysis and control design of a gyro-based wave energy converter. In: Proceedings of the European control conference 2009. IEE Proceedings, pp 3743–3748 14. Townsend NC, Shenoi RA (2014) Control strategies for marine gyrostabilizers. IEEE J Ocean Eng 39(2):243–255 15. Fossen TI (2011) Handbook of marine craft hydrodynamics and motion control, 1st ed (Chap. 8). Wiley, 4435-36/7, Ansari road, Daryaganj, New delhi-110 002 India, pp 199–224

Wave Energy Conversion by Multiple Bottom-Hinged Surging WEC A. K. Kumawat, D. Karmakar and C. Guedes Soares

Abstract The power capture and performance of arbitrary array of submerged bottom-hinged deflectors of finite width is analysed for two different configurations. The bottom-hinged deflectors are modelled as non-zero thickness and rotated at small angle in the vertical plane about an axis located in the seabed orthogonal to the direction of the wave propagation. The numerical study is performed on the hydrodynamic performance of the flapping deflector type oscillating wave surge converter (OWSC). Three-dimensional boundary element method is used to calculate hydrodynamic coefficients in frequency domain. A parametric study was made by comparing two geometrically different deflectors, i.e., rectangular and wedge crosssection for power capture assessment. Further, the analysis is performed for arbitrary array configurations of OWSC with oblique incident wave heading angles and the power take off (PTO) system is modelled as a linear damper and spring. The study for multiple arrays of the flap-type wave energy converters is essential for economical design of project in order to exploit more renewable energy from the ocean waves. Keywords Wave energy · Bottom-hinged deflector · Wave surge converter Power take-off · Arrays of WEC

1 Introduction The oscillating wave surge energy converter (OWSC) is a bottom-hinged flapping plate type of wave energy converter (WEC) which is forced to move back and forth at small angle about an axis perpendicular to the direction of propagating waves. A. K. Kumawat · D. Karmakar (B) Department of Applied Mechanics and Hydraulics, National Institute of Technology Karnataka, Surathkal, Mangalore 575025, Karnataka, India e-mail: [email protected] C. Guedes Soares Centre for Marine Technology and Ocean Engineering (CENTEC), Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049001 Lisbon, Portugal © Springer Nature Singapore Pte Ltd. 2019 K. Murali et al. (eds.), Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Lecture Notes in Civil Engineering 23, https://doi.org/10.1007/978-981-13-3134-3_67

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The OWSC captures the energy by relative motion of the flapping plate against the waves interacting with the WEC device. OWSC is a single degree of freedom system which is generally installed in the near shore or shoreline region in a water depth of 10–20 m [22]. In the recent decade, various analytical, numerical and experimental studies have been carried out on OWSC and many bottom-hinged wave energy converters like Oyster, WaveRoller, bioWave, Langlee, etc., are analysed and deployed for commercial purposes in the ocean. Most of the study performed by researchers discussed power capturing performance of the OWSC numerically and experimentally but few studies were performed on the comparative performance of different shapes and arbitrary array configurations of the oscillating wave energy converter device. The concept of WECs in arrays was first introduced by Falnes and Budal [5] considering the absorption of power by an infinite linear array of evenly spaced equal group of oscillating body using linear wave theory. Mavrakos [12] investigated the linearized hydrodynamic forces applied on multiple vertical axis symmetrical bodies in finite water depth. A semi-analytical method was developed to solve radiation problem of arrays consisting arbitrary number of bodies. The rolling motion of a bottom-pierced vertical thin plate in finite water depth is examined by Evans and Porter [4]. The linear wave theory was considered for the analysis while Galerkin method was used for formulation of solution. Folley et al. [6] presented the experimental and numerical study of a bottom pivoted oscillating wave surge energy converter. The study suggests that the hydrodynamic and power capture performance of the flap-type wave surge converter is affected by the “water column” between the paddle and back wall. They also found that oscillating wave surge energy converter has high power capturing ability than a shoreline oscillating water column and pendular (inverted flap). Considering different sea-state conditions, Folley et al. [7] analysed the performance of oscillating wave surge converters for different water depths. The result shows that incident wave power is significantly reduced by water depth mainly due to dissipation of wave energy. It is also stated that captured power is closely related to incident wave force than incident wave power. Folley et al. [8] developed a numerical model and calibrated using wave-tank experimental data, and it was found that the device capture factor increases as the wave force increases. A significant study is performed based on the experimental, numerical and analytical approach to examine the performance of oscillating wave energy converters. Gomes et al. [9] considered linearized water wave theory for conversion of wave energy of fully submerged bottom-hinged plates of finite width and used three dimensional boundary element methods to calculate hydrodynamic coefficients. Whittaker and Folley [22] described the characteristics of the nearshore wave surge energy converter along with the useful design parameters on the hydrodynamics of OWSC and explained the development of Oyster. Renzi and Dias [15] derived a potential flow model for a large flap-type wave surge converter and hypersingular integral equation was obtained for the jump in potential across the flap. The solution is found in terms of the Chebyshev polynomials of second kind and even order through series expansion. Renzi et al. [16] developed the mathematical theories for wave conversion of wave

Wave Energy Conversion by Multiple Bottom-Hinged Surging WEC

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surge energy converters and explained the concepts of governing mechanism of wave power absorption by the Oyster concept. Further, a semi-analytical and fully numerical model was presented by Renzi et al. [17] in order to investigate the dynamics of a wave farm consisting flap-type wave energy converters in the nearshore. Bozo et al. [2] studied the conversion of wave energy of fully submerged surging plates of finite width. The extraction of power was assessed by varying the flap-plate width, height and thickness. Gomes et al. [10] presented a numerical study on the hydrodynamics of bottom-hinged and surface piercing plate wave energy converter in regular and non-regular wave conditions. Sarkar et al. [19] analytically formulated the behaviour of the flap-type oscillating wave energy converter near a straight coast based on linear potential flow model. Dev and Karmakar [3] recently described a comparative study on the design and analysis of the two different geometrical, bottom-hinged surging plates namely, rectangular and wedge OWSCs to exploit the beneficial effect of incident wave force on the flapping plate to capture more power. The influence of varying water depth and incident wave angle for both the geometries was computed and captured power was assessed. Tom et al. [21] analysed a novel wave energy converter concept which combines an oscillating wave surge energy converter with control surfaces. A linear frequency domain analysis is used to calculate the performance of the device. Recently, Wilkinson et al. [23] presented modular concept of oscillating wave surge converter. The physical modelling was used to assess the hydrodynamic power capture performance of OWSC. In the recent decade several attempts were made to investigate the interaction impact among the WECs present in the array. In this context, Babarit [1] investigated a numerical model to study the wave interaction using linear wave theory and measured the impact on the absorbed wave power of the separating distance between the two systems with oblique wave direction. Renzi and Dias [14] explained the interaction of the plane incident waves with a wave farm in the open ocean. The farm consists of a periodic array of large type wave energy converters. The expressions of reflection, transmission, and radiation coefficients of the system are obtained by asymptotic analysis. Sarkar et al. [18] presented a mathematical model based on Greens integral equation formulation, yielding hypersingular integrals which were solved by using Chebyshev polynomial of the second kind to analyse the hydrodynamic behaviour of oscillating wave energy converter based on the linear potential theory in the random seas. Yu et al. [24] described a study on the design and analysis of an oscillating wave surge energy converter. In this study, cost-driven design strategy is introduced to determine cost-efficiency of OWSC. The power generation performance for three different design configurations of wave surge energy converter is carried out using time-domain numerical simulation model. Noad and Porter [13] modelled a finite array of hinged flap-type wave energy converters using a mathematical approach. Sarkar et al. [20] recently presented a study on hydrodynamic analysis and performance of arrays of wave energy converters by using semi-analytical and numerical models using boundary element method. The performance of the WECs arrays was predicted by using a statistical emulator and a generic algorithm is used to obtain optimal layout of WECs.

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In the present study, the absorbed power is calculated based on linear water wave theory for two geometrically different configurations namely rectangular and wedge bottom-hinged flapping plate OWSCs. In the past literature, numerical model analysis is presented only for two OWSCs in a cluster. On the other hand, a parametric study is made for an isolated OWSC and multiple OWSCs in five different array configurations is presented in detail. In first part, a comparison is made between two different shape bottom-hinged flapping OWSC while in second part, system performance parameter for rectangular shaped bottom-hinged multiple flap OWSCs is computed and analysed.

2 Numerical Modelling of OWSC The bottom-hinged flapping plate with height L, width W and thickness T is considered pierced at the bottom of sea bed in water depth h is only allowed to rotate in roll motion about an horizontal axis orthogonal to the incident wave propagation, x -axis. The coordinate system and geometry adopted in the study is represented in Fig. 1. The vertical axis of the plate is considered as reference axis to measure the variable angle  (|| 0◦ , when plate is in the vertical position perpendicular to bottom surface of sea bed).

Fig. 1 Representation of a bottom hinged plate dimension

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2.1 Hydrodynamic Parameters The velocity potential  satisfies Laplace equation in the fluid domain is given by ∇ 2   0.

(1)

The linearized kinematic-dynamic boundary condition on the free surface is of the form tt + gzz  0 at z  0,

(2)

where g is the acceleration due to gravity, whereas no flux boundary condition at the sea bed yields z  0 at z  −h.

(3)

An isolated device equipped with single flap hinged to a rigid foundation at the sea bed (Fig. 1). The WEC is modelled using a non-zero rigid plate, and the kinematic boundary condition on the surface is expressed as x  −(z + h)H (z + h), for y  yc ± ε, ε → 0, xA < x < xB ,

(4)

where yc is the y-coordinate of centre of the isolated flap, xA and xB are the xcoordinates corresponding to the two edges of the device and H is the Heaviside step function. The interaction between rolling plate and waves is given by ¨  me (t) + mr (t) + mh (t) + md (t) + mm (t), I θ(t)

(5)

where, I is the moment of inertia about x -axis, θ¨ is the instantaneous plate angular acceleration, me is the excitation moment caused by the incident waves, mr is the radiation moment associated with the plate motions, mh is the hydrostatic restoring moment, md is the drag moment caused by viscous effects and mm is the mechanical moment applied by the PTO unit. The time-dependent plate position, velocity, acceleration, and moment [9] are calculated as     θ, θ˙ , θ¨ , me , mr , mh , mm } (t)  Re , iω, −ω2 , Me , Mr , Mh , Mm (ω)eiωt , (6) where , ||, Mr , Mh , Mm are frequency dependent complex amplitudes. The frequency-dependent radiation moment can be expressed as   Mr (ω)  −ω2 A(ω) + iωB(ω) (ω),

(7)

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where A and B are the frequency-dependent added mass and radiation damping coefficients respectively. The frequency dependent wave excitation moment is expressed by Me (ω)  Aw (ω),

(8)

where Aw is the amplitude and (ω) is the complex excitation moment coefficient, whose amplitude and phase are given by |(ω)| and  (ω) respectively. The hydrostatic restoring moment, which is dependent of sin θ therefore, the model can be linearized for only small oscillation (sin θ  θ) of the plate,   Mh (ω)  H (ω)  ρw gνzb − mgzg (ω),

(9)

where, H is the linear hydrostatic restoring coefficient, m is plate mass, v is the plate volume, g is acceleration due to gravity, zg is the z-coordinates of the centre of gravity, zb is the z-coordinates of the centre of buoyancy, ρw is the density of water. The PTO system is modelled as a linear damper plus a linear spring. The produced moment on the plate by energy extraction unit in frequency domain model is given as Mm (ω)  (iωC(ω) + K(ω))(ω),

(10)

where C and K are the frequency dependent damping and spring coefficients that models the PTO. For energy extraction the value of C has to be positive while K can take positive or negative values. The complex amplitude of the flapping plate rotation is given by || 

Aw (ω) , −ω2 (I + A) + iω(B + C) + (K + H )

(11)

The values of || higher than 30° are not considered in this study to justify the small oscillation assumptions within linear water wave theory. The equation of timeaveraged power extraction from the regular waves through the linear PTO unit is given by P(ω) 

1 2 2 ω C |(ω)|2 , 2

(12)

The moment of inertia about x -axis, which is calculated as Bozo et al. [2] given by I

α ρT W L3 , 3

(13)

where, α  ρ/ρw and ρ is the plate density [24], the hydrostatic coefficient is simplified by assuming zg  zb and considering both centre of gravity and centre

Wave Energy Conversion by Multiple Bottom-Hinged Surging WEC

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of buoyancy coincident with the centre of the plate which satisfies the condition zg  zb  L/2. Thus, simplified value of the hydrostatic coefficient is given by H

(1 − α) ρw gT W L2 . 3

(14)

In the PTO mechanism, for each frequency the damping coefficient C and the spring coefficient K are set to be optimal by applying the condition of maximum energy absorption of form C(ω)  B(ω) and K(ω)  ω2 {I + A(ω)} − H .

(15)

Based on the conditions given in the above equation both phase and amplitude of motion of the surging plate are optimized for each frequency. It is assumed that a wave frequency dependent dumper and a fixed spring coefficient tuned for sea conditions of 12 s wave period [2] in PTO mechanism.

2.2 System Performance The performance of the system is measured with the interaction factor q described in Sarkar et al. [18]. The interaction factor is defined as the ratio of the total power of an array of N flaps to the power captured by an isolated WEC of the same type multiplied by number of flaps. q

Parray . NPisolated

(16)

The value of q > 1 and q < 1 indicates gain and loss in the net captured power from wave array farm respectively. Since factor q does not quantify the individual WEC captured power performance hence a new factor was found by Babarit [1] given as, n  qmodified

Pn − Pisolated , max(Pisolated )

(17)

where, n  1, 2, 3 . . . , N , Pn is the power captured by nth flap while max(Pisolated ) n represents the perforis the maximum value of Pisolated . The modified factor qmodified n mance of each individual WEC, if qmodified > 0 shows a beneficial influence while n < 0 shows negative wave interaction effect. qmodified

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3 Computation of Captured Power This section describes the numerical approach used for the calculation of captured power of the bottom-hinged flapping plate as in Eq. (12). The results obtained from the numerical calculations are presented and compared with available literature. WAMIT, a three dimensional panel method code with source or dipole distributions based on linear water wave theory is used to compute the hydrodynamic coefficients [11]. The integral equations of the radiation and diffraction velocity potential are derived by Green’s theorem. These potentials are integrated over the wetted surface of the body to calculate radiation and diffraction coefficients. In this method loworder surface discretization is employed to define the wetted surface of the flapping plate. A proper discretization is adopted to avoid the possibility of singularity of Green’s integral equations. A plane of symmetry at x  0 was defined since the only mode of motion in the system is roll which rotates over the x-axis. So, due to the symmetry of the diffraction and radiation potential, the systems of linear equations is solved and hydrodynamic coefficients are computed.

3.1 Geometry Description of Single OWSC Two different geometrical shapes of flapping plate namely, rectangular and wedge (Fig. 2a, b) are used to analyse the five arbitrary array configurations of OWSC for water depth of 16 m. These flapping plates are designed to rotate against the fixed supporting frame about hinged joint to convert wave energy into electrical power from the relative rotational motion, induced by incoming waves. The dimension of the individual flapping plate is listed in Table 1 [24].

Fig. 2 Modelling of a rectangular flap-plate, b wedge-shaped flap-plate

Wave Energy Conversion by Multiple Bottom-Hinged Surging WEC Table 1 Dimension for the WEC Design Design Series Parallel

921

S-I

S-II

S-III

Number of flapping plates 5

5

5

5

5

Flapping plate width (m)

25

25

25

25

25

Flapping plate height (m)

16

16

16

16

16

Flapping plate thickness at 1 top (both rectangular and wedge plate) (m)

1

1

1

1

Rectangular-shaped plate thickness at bottom (m)

1

1

1

1

1

Wedge-shaped plate thickness at bottom (m)

0.5

0.5

0.5

0.5

0.5

3.2 Array Layout of Multiple OWSC A parametric study is made considering five arbitrary array combinations (Fig. 3) for three different spacing’s such as 27.50, 40.0, and 52.50 m centre-to-centre distances of flapping plate (edge-to-edge distances 2.5, 15.0, and 27.50 m.) In the array layout, the magnitude of the spacing between neighbouring flaps in all the cases is fixed at “a” in x-direction and “b” in y-direction under wave amplitude Aw = 0.5 m.

Fig. 3 Five different layout of 5 OWSC

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4 Numerical Result and Discussion The numerical study of OWSC is performed considering both wedge shape and rectangular flap configurations.

4.1 Isolated OWSC Configuration In order to understand the performance of multiple OWSC in an array, an isolated (single flap) bottom-hinged rectangular flap- and wedge-shaped flap OWSC is considered first. In this section, captured power is computed and compared for isolated (single flap) bottom-hinged rectangular flap- and wedge-shaped flap OWSCs based linear potential flow theory. Two isolated geometrically different flap OWSCs are studied. Figure 4a represents the variation of captured power P at different incident wave angles against the wave periods, which shows that there is not much difference in captured power between wedge flap and rectangular flap OWSC in all the wave incidence cases. Further, Fig. 4b shows the variation of flap rotation || at different incident wave angles against the wave periods, which represents that for wave period 12 s there is slight difference in magnitude of rotation angle || while wave periods other than 12 s show similar value of || between the two flaps about x -axis. Recently, Bozo et al. [2] reported similar trends of variation of captured power (P) and flap rotation ||. Since there is no significant difference in the captured power between the two different flap OWSCs, only the wedge-shaped bottom-hinged flap OWSC is considered in the study of multiple OWSCs in the array.

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Fig. 4 Comparative analysis between rectangular and wedge-shaped flap OWSCs for a captured power and b angle of rotation of flap for L  14.4 m, W  16 m and T  5 m

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4.2 Multiple Array of OWSC Configuration In this study, five different possible arrays consisting of five wedge-shaped bottomhinged flap OWSCs are considered. These five arrays are named as, parallel, inline, staggered-I (S-I), staggered-II (S-II) and staggered-III (S-III), and three different centre-to-centre spacing (27.50, 40.0 and 52.50 m) of flaps are consider for analysis.

4.2.1

Parallel Layout

In Fig. 5, the performance parameter q is plotted against the incident wave period. The peak of performance parameter shifts with the reduced magnitude as the spacing among the flaps increases with the wave periods. However, after certain wave period all the curves tend to converge at each incident wave angle for all the three spacing conditions. Overall, the strongest constructive interaction is achieved for ϕ  90° while ϕ  30° shows maximum destructive influence on the array efficiency. A significant difference is noted for the q values as one increases the centre-to-centre spacing among the flaps in the wave farm under different sea-state condition. In Fig. 6, the beneficial influence decreases as the incident wave angle decreases for both the considered flap-type WECs. Figure 6a shows the most beneficial influence for ϕ  90° while least beneficial for ϕ  30°. The front flap-type WEC shows beneficial influence up to 10 s wave period but afterwards rear-end flap-type WEC presents disadvantageous influence for all the wave periods irrespective of incident angle due to presence of four front flaps that are justifying strong sheltering effect.

4.2.2

Inline Layout

In Fig. 7, the graphs show that as the incident wave angle (ϕ) increases, the performance parameter q decreases except 27.50 m spacing condition. In fact in this particular case as the incident wave angle (ϕ) increases q value also increases against the incident wave periods. For the 40.0 m and 52.50 m spacing condition, since the performance parameter q > 1 at ϕ  30° and 45° for all the wave periods therefore it indicates the beneficial interaction among all the flaps. This array configuration shows factor q > 1 and maximum in magnitude among all the considered array under the action of larger wave period for all the wave incidence cases.

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Fig. 5 Performance parameter q for the parallel layout considering centre-to-centre spacing of each flap (a) 27.5 m, (b) 40 m and (c) 52.5 m

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n Fig. 6 Individual captured power performance qmodified of a front flap, b rear-end flap WEC for the parallel layout considering centre-to-centre spacing of each flap 27.5 m

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Fig. 7 Performance parameter q for the inline layout considering centre-to-centre spacing of each flap a 27.5 m, b 40 m and c 52.5 m

4.2.3

Staggered-I (S-I) Layout

In Fig. 8, the staggered-I array configuration shows that as the wave period increases the performance factor q also increases in all the cases. In the first two spacings, the performance parameter q shows maximum and minimum constructive convergence for the incident wave angle ϕ  90° and ϕ  30° respectively while reverse for the 52.50 m spacing. The convergence in the value of performance parameter is observed with the increased spacing among the flaps.

4.2.4

Staggered-II (S-II) Layout

In Fig. 9, as centre-to-centre spacing increases the peak value of q decreases. For the initial wave periods (up to 11–12 s), the performance factor q decreases as the incident wave angle (ϕ) increases and shows maximum and minimum constructive convergence for the ϕ  30° and ϕ  90° respectively. Later on, after 11–12 s the situation gets reversed. As the spacing among the flaps increases the magnitude of the q become almost constant for higher wave periods.

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Fig. 8 Performance parameter q for the Staggered-I (S-I) considering centre-to-centre spacing of each flap a 27.5 m, b 40 m and c 52.5 m

4.2.5

Staggered-III (S-III) Layout

In Fig. 10, the graph shows that lower wave periods value of parameter q decreases as the incident wave angle increases while for larger wave period value of parameter q approaches to one. The peak of the q parameter shifts with the decreased magnitude towards higher wave period as one increases the spacing in the particular case of array. Here, ϕ  30° shows the most constructive interaction among the flaps present in the array. These patterns of performance factor q also confirm the patterns observed in Sarkar et al. [18].

5 Conclusion A numerical model based on linear water wave theory has been used to analyse the hydrodynamic interaction for single OWSC device and OWSCs in arbitrary array configurations. In the case of single OWSC device, the maximum captured power is approximately the same for both rectangular and wedge flap OWSC for different incidence cases, which indicates that wedge flap is more economical as compared

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Fig. 9 Performance parameter q for the Staggered-II (S-II) considering centre-to-centre spacing of each flap a 27.5 m, b 40 m and c 52.5 m

to rectangular flap because quantity of the material required is less if the density of material is same for both flaps. In the present study, power capture by an array of five OWSCs is also studied for five different layouts. It is shown that dynamics of the bottom-hinged flapping plate OWSCs array strongly depends on the wave period and incident wave angle. The interaction factor q varies with the centre-to-centre spacing between the flaps present in array. It is also observed that the performance factor q for almost all the array configurations shows constructive interaction up to 11–12 s but afterwards value of q tends to converge near q = 1 for all the incident wave angles. In all the arrays, an inline configuration with all angle of incidence shows the best beneficial constructive interactions among the flaps due to lack of sheltering effect. This study helps to understand the variability in the performance of array of OWSCs one can expect with a numerical model.

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Fig. 10 Performance parameter q for the Staggered-III (S-III) considering centre-to-centre spacing of each flap a 27.5 m, b 40 m and c 52.5 m

Acknowledgements The authors acknowledge Science and Engineering Research Board (SERB), Department of Science and Technology (DST), Government of India for supporting financially under the Young Scientist research grant no. YSS/2014/000812 and DST for India-Portugal Bilateral Scientific Technological Cooperation Project grant no. DST/INT/Portugal/P-13/2017.

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