## Water Waves: The Mathematical Theory with ApplicationsOffers an integrated account of the mathematical hypothesis of wave motion in liquids with a free surface, subjected to gravitational and other forces. Uses both potential and linear wave equation theories, together with applications such as the Laplace and Fourier transform methods, conformal mapping and complex variable techniques in general or integral equations, methods employing a Green's function. Coverage includes fundamental hydrodynamics, waves on sloping beaches, problems involving waves in shallow water, the motion of ships and much more. |

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### Contents

Introduction | vii |

PART I | 1 |

Basic Hydrodynamics | 3 |

The Two Basic Approximate Theories | 19 |

PART II | 33 |

Simple Harmonic Oscillations in Water of Constant Depth | 37 |

Waves Maintained by Simple Harmonic Surface Pressure in Water of Uniform Depth Forced Oscillations | 55 |

Waves on Sloping Beaches and Past Obstacles | 69 |

Twodimensional Waves on a Running Stream in Water of Uniform Depth | 198 |

Waves Caused by a Moving Pressure Point Kelvins Theory of the Wave Pattern Created by a Moving Ship | 219 |

The Motion of a Ship as a Floating Rigid Body in a Seaway | 245 |

PART III | 289 |

Long Waves in Shallow Water | 291 |

Mathematical Hydraulics | 451 |

PART IV | 511 |

Problems in which Free Surface Conditions are Satisfied Exactly The Breaking of a Dam LeviCivitas Theory | 513 |

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addition amplitude angle applied appropriate approximation assumed assumption boundary conditions bounded breaking calculations carried Chapter characteristics Consequently consider constant continuous course curve defined depth derivatives determined differential equations discussion disturbance effect energy example existence fact Figure finite fixed flood flow follows formula free surface front function given harmonic hence important indicated initial integral interest introduce known leads linear mathematical means method motion moving numerical observe obtained occur Ohio once origin oscillations particles period phase plane positive possible prescribed present pressure problem progressing waves propagation quantities reasonable reflection region relation requires respect result river satisfies seen shallow water ship shock side simple singularity slope solution solved speed steady taken theory tion treated uniqueness values vanishes variables velocity vertical wave wave length yield zero