Part 1 Introduction ix Acknowledgments 1. Basic Hydrodynamics 1.1 The laws of conservation of momentum and mass 1.2 Helmholtz''s theorem 1.3 Potential flow and Bernoulli''s law 1.4 Boundary conditions 1.5 Singularities of the velocity potential 1.6 Notions concerning energy and energy flux 1.

7 Formulation of a surface wave problem 2. The Two Basic Approximate Theories 2.1 Theory of waves of small amplitude 2.2 Shallow water theory to lowest order. Tidal theory . 2.3 Gas dynamics analogy 2.4 Systematic derivation of the shallow water theory PART II Subdivision Waves Simple Harmonic in the Time 3.

Simple Harmonic Oscillations in Water of Constant Depth 3.1 Standing waves 3.2 Simple harmonic progressing waves 3.3 Energy transmission for simple harmonic waves of small amplitude 3.4 Group velocity. Dispersion 4. Waves Maintained by Simple Harmonic Surface Pressure in Water of Uniform Depth. Forced Oscillations 4.

1 Introduction 4.2 The surface pressure is periodic for all values of x 4.3 The variable surface pressure is confined to a segment of the surface 4.4 Periodic progressing waves against a vertical cliff 5. Waves on Sloping Beaches and Past Obstacles 5.1 Introduction and summary 5.2 Two-dimensional waves over beaches sloping at angles u> -- nßn 5.3 Three-dimensional waves against a vertical cliff 5.

4 Waves on sloping beaches. General case 5.5 Diffraction of waves around a vertical wedge. Sommerfeld''s diffraction problem 5.6 Brief discussions of additional applications and of other methods of solution Subdivision B Motions Starting from Rest. Transients 6. Unsteady Motions 6.1 General formulation of the problem of unsteady motions 6.

2 Uniqueness of the unsteady motions in bounded domains 6.3 Outline of the Fourier transform technique 6.4 Motions due to disturbances originating at the surface 6.5 Application of Kelvin''s method of stationary phase 6.6 Discussion of the motion of the free surface due to disturbances initiated when the water is at rest 6.7 Waves due to a periodic impulse applied to the water wheninitially at rest. Derivation of the radiation condition for purely periodic waves 6.8 Justification of the method of stationary phase 6.

9 A time-dependent Green''s function. Uniqueness of unsteady motions in unbounded domains when obstacles are present . Subdivision C Waves on a Running Stream. Ship Waves 7. Two-dimensional Waves on a Running Stream in Water of Uniform Depth 7.1 Steady motions in water of infinite depth with p = 0 on the free surface CHAPTER PAGE 7.2 Steady motions in water of infinite depth with a disturbing pressure on the free surface 7.3 Steady waves in water of constant finite depth 7.

4 Unsteady waves created by a disturbance on the surface of a running stream 8. Waves Caused by a Moving Pressure Point. Kelvin''s Theory of the Wave Pattern created by a Moving Ship 8.1 An idealized version of the ship wave problem. Treatment by the method of stationary phase 8.2 The classical ship wave problem. Details of the solution 9. The Motion of a Ship, as a Floating Rigid Body, in a Seaway 9.

1 Introduction and summary 9.2 General formulation of the problem 9.3 Linearization by a formal perturbation procedure 9.4 Method of solution of the problem of pitching and heaving of a ship in a seaway having normal incidence PART III 10. Long Waves in Shallow Water 10.1 Introductory remarks and recapitulation of the basic equations 10.2 Integration of the differential equations by the method of characteristics 10.3 The notion of a simple wave 10.

4 Propagation of disturbances into still water of constant depth 10.5 Propagation of depression waves into still water of constant depth 10.6 Discontinuity, or shock, conditions 10.7 Constant shocks: bore, hydraulic jump, reflection from a rigid wall 10.8 The breaking of a dam 10.9 The solitary wave 10.10 The breaking of waves in shallow water. Development of bores 10.

11 Gravity waves in the atmosphere. Simplified version of the problem of the motion of cold and warm fronts 10.12 Supercritical steady flows in two dimensions. Flow around bends. Aerodynamic applications 10.13 Linear shallow water theory. Tides. Seiches.

Oscillations in harbors. Floating breakwaters 11. Mathematical Hydraulics 11.1 Differential equations of flow in open channels 11.2 Steady flows. A junction problem 11.3 Progressing waves of fixed shape. Roll waves 11.

4 Unsteady flows in open channels. The method of characteristics 11.5 Numerical methods for calculating solutions of the differential equations for flow in open channels 11.6 Flood prediction in rivers. Floods in models of the Ohio River and its junction with the Mississippi River 11.7 Numerical prediction of an actual flood in the Ohio, and at its junction with the Mississippi. Comparison of the predicted with the observed floods Appendix to Chapter 11. Expansion in the neighborhood of the first characteristic PART IV 12.

Problems in which Free Surface Conditions are Satisfied Exactly. The Breaking of a Dam. Levi-Civita''s Theory 12.1 Motion of water due to breaking of a dam, and related problems 12.2 The existence of periodic waves of finite amplitude 12.2a Formulation of the problem 12.2b Outline of the procedure to be followed in proving the existence of the function 12.2c The solution of a class of linear problems 12.

2(1 The solution of the nonlinear boundary value problem Bibliography Author Index Subject Index.