## Water Waves: Relating Modern Theory to Advanced Engineering ApplicationsThe purpose of this book is to present a self contained introduction to the mathematical and physical aspects of the theory of water waves. The book is aimed at undergraduate and graduate levels for engineers, physical scientists and mathematicians. Each chapter is concluded with practical problems expressed as exercises and accompanied by ample references for further studies. The book consists of ten chapters arranged into three parts: Part I: Basic Fluid Mechanics and Solutions Techniques which cover chapters 1-3. Part II: Water Waves covering chapters 4-7. Part III Advanced Water Waves which covers chapters 8-10. Parts I and II are elementary in nature; whereas Part III is more advanced. The first three chapters give the derivations of the fundamental mathematical equations. Chapter 2 outlines appropriate differential equations to describe the physical phenomena, and Chapter 3 reviews solution techniques of some simplified partial differential equations. Chapter 4 gives the developmental of wave equations, including the essential boundary conditons and describes small amplitude wave theory. Chapter 5 deals with finite amplitude wave theory and Chapter 6 outlines the study of tidal dynamics in shallow water. For random wave case, the deterministic methods described in previous chapters do not hold good. Therefore, chapter 7 is clearly devoted to wave statistics and wave energy spectrum. The application of wave theory is demonstrated in Chapter 8. Chapter 9 examines the nonlinear long waves in shallow water from a mathematical view point. The book concludes with Chapter 10 which illustrates the inverse scattering technique to solve solitary wave problem. |

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### Contents

Introduction | 3 |

Solution techniques of partial differential equations | 60 |

Theory of surface waves | 101 |

Copyright | |

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amplitude assumed axes Bernoulli's equation boundary condition Chapter coefficients complex potential consider constant corresponding cos(fcc cos2 cosh k(z cosh kh cylinder deep water defined determined diffraction dispersion relation dt dx dy dx dx dynamic eigenvalues elevation energy equation of motion estuary flow fluid particle Fourier free surface given Hence horizontal incident wave incompressible inertia integral irrotational KdV equation Laplace's equation linear long waves mathematical method nonlinear obtain ocean parameter partial differential equations physical plane polar coordinates pressure problem progressive wave propagation Rayleigh distribution respect scattering Schrodinger equation second-order separation of variables shallow water waves shown in Fig sin(fcc sin2 sinh solitary wave soliton spectrum standing wave Stokes stream function streamlines Substituting tidal tion transformation velocity components velocity potential velocity vector vertical wave equation wave forces wave height wave solution wave theory wavelength written yields zero