## Water waves: relating modern theory to advanced engineering applicationsSelf-contained and accessible, Water Waves provides an up-to-date introduction to the mathematical and physical aspects of water wave theory. Written particularly for undergraduates engineering, physics, and mathematics students, the book contains a wealth of examples and exercises. It begins with the derivations of the fundamental mathematical equations, outlining differential equations appropriate for the description of physical phenomena. It goes on to detail the development of wave equations (including the essential boundary conditions), and to describe small amplitude wave theory, finite amplitude wave theory, tidal dynamics in shallow water, wave statistics and the wave energy spectrum, and nonlinear long waves in shallow water. The book concludes with a description of the inverse scattering technique used to solve solitary wave problems. Rigorous and coherent, Water Waves is ideal for students and professionals approaching the subject for the first time. |

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### Contents

Introduction | 3 |

Solution techniques of partial differential equations | 60 |

Theory of surface waves | 101 |

Copyright | |

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### Common terms and phrases

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

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