Water Waves: The Mathematical Theory with Applications

Offers 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.

Spis treści:
Basic Hydrodynamics.
The Two Basic Approximate Theories.
WAVES SIMPLE HARMONIC IN THE TIME.
Simple Harmonic Oscillations in Water of Constant Depth.
Waves Maintained by Simple Harmonic Surface Pressure in Water of Uniform Depth: Forced Oscillations.
Waves on Sloping Beaches and Past Obstacles.
MOTIONS STARTING FROM REST: TRANSIENTS.
Unsteady Motions.
WAVES ON A RUNNING STREAM: SHIP WAVES.
Two–Dimensional Waves on a Running Stream in Water of Uniform Depth.
Waves Caused by a Moving Pressure Point: Kelvin′s Theory of the Wave Pattern Created by a Moving Ship.
The Motion of a Ship, as a Floating Rigid Body, in a Seaway.
Long Waves in Shallow Water.
Mathematical Hydraulics.
Problems in Which Free Surface Conditions Are Satisfied Exactly: The Breaking of a Dam;
Levi–Civita′s Theory.
Bibliography.
Indexes.