Flexural Gravity Waves: The Mathematical Theory and Applications

This monograph describes mathematical techniques for various aspects of flexural gravity wave propagation, pertinent to ocean engineering. It focuses on frontier problems in hydroelasticity including blocking dynamics of flexural gravity waves in both homogeneous and stratified fluids. Various wave-structure interaction problems with similar dispersion relations are revisited and solutions are demonstrated through real-life physical problems. It covers developments in the frequency and time domain analysis of wave-structure interactions. Features: Provides comprehensive theoretical analysis and mathematical techniques crucial for advancing research in hydroelasticity, wave-structure interactions, and related fields Offers practical design solutions and methodologies applicable for development of VLFSs, offshore platforms, and coastal structures Focuses on both frequency- and time-domain problems, and both linear and nonlinear problems Methods used for wave scattering by harmonic propagating waves are generalized to deal with multiple propagating waves in the context of blocking dynamics. Various problems are discussed in two dimensions and in three dimensions in the case of oblique waves This book is aimed at graduate students and researchers in marine hydrodynamics, ocean engineering, wave-structure interaction and applied mathematics.

Table of Contents:
0. Front Matter. Section I. 1. Introduction. Section II. 2. Flexural Gravity Waves: An Introduction. 3. Wave ice interaction problems in shallow water. 4. Flexural gravity wave scattering in homogeneous fluid. 5. Flexural gravity waves in a stratified fluid. 6. Wave interaction with flexible submerged plate. 7. Ocean floor and water compressibility. 8. Waves due to a moving source. 9. Modulation effects in flexural-gravity waves. 10. Frequency downshifting. 11. Rossby waves in the ocean covered by compressed ice. 12. Closure. Appendix A: Gravity wavemaker theory. Appendix B: Glossary. Appendix C: Acknowledgements. Appendix D: References.

About the Author :
T Sahoo has expertise in both the analytic and numerical methods for dealing with a wide variety of problems in Hydroelasticity and Coastal hydrodynamics arising in Ocean Engineering. After his doctoral research based on Fourier analysis and allied methods for scattering and radiation of water waves, he has made a seminal contribution by pursuing interdisciplinary research on wave-structure interaction problems arising in ocean engineering during the last 28 years. His research contributions to mathematical and physical science are reflected in his 260 publications in journals and conference proceedings and a single-authored monograph published by CRC press. Moreover, he has contributed significantly to various outreach programmes to promote marine hydrodynamics in India, in addition to having more than 24 years of teaching and research experience at IIT Kharagpur. MH Meylan is an expert in wave scattering in both the time and frequency domains. Much of his research has been connected with wave water scattering, especially with hydroelasticity, but he has also worked on photonics and more general wave scattering theory. He is especially interested in the connection between frequency- and time-domain problems and the phenomenon of near-trapping. However, the primary focus of his research has been understanding the process of wave scattering in the Marginal Ice Zone. This scattering is an extremely complicated wave scattering which is very poorly understood. He has been responsible for some of the most important models developed in the last twenty-five years. Y Stepanyants is an expert in nonlinear wave theory. Most of his research was devoted to wave propagation in linear and nonlinear dispersive media. He studied wave-current interactions, shear flow instabilities, wave generation by moving sources, etc. He developed a concept of negative energy waves in application to hydrodynamic problems. He is also an expert in physical oceanography. He has studied solitary wave dynamics in the open oceans and in the coastal zones, taking into account Earth’s rotation, medium inhomogeneity, dissipation, cylindrical divergence, and other natural factors. Prof. Stepanyants is the author of the most cited reviews on oceanic solitary waves. He was the first to gather data on the manifestation of internal solitary waves in the World Ocean and create a map of observational results. He presented the statistics of internal solitary waves and suggested a method of calculation of soliton spectra and the distribution function of solitary waves. He also studied wave transformation on underwater obstacles, the dynamics of Rossby waves and vortices, as well as the influence of ice cover on Rossby and gravity waves. S Boral is an applied mathematician with six years of experience in wave structure interaction problems. His research focusses on the interaction of surface gravity waves with floating and submerged flexible structures in various fluid environments, including homogeneous and stratified fluids. He investigates the effects of lateral compressive forces on floating and submerged flexible structures and the scattering of flexural-gravity waves caused by structural heterogeneity and undulated seabeds. Recently, he has focused on the resonant response of floating flexible structures under external loads. Dr. Boral has published fourteen peer-reviewed international journal papers and completed his PhD a year ago. He is dedicated to advancing the field of wave-structure interactions. S Das is an applied mathematician working on wave structure interaction problems for the last 15 years. He has worked on various structures, such as porous, poroelastic, and viscoelastic in nature. His primary research objective lies in studying wave propagation, scattering, and trapping problems. Dr. Das has published more than 27 international peer-reviewed journal articles. Recently, he has made significant progress in the field of hydroelasticity by including the effect of wave blocking, which eventually contributes to the field of analogue gravity. Recently, he started working on acoustic-gravity waves (AGW) in the ocean, which could be a possible means for early tsunami wave detection.