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.
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The Two Basic Approximate Theories
Waves Maintained by Simple Harmonic Surface Pressure
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addition amplitude angle applied appropriate approximation assumed assumption boundary conditions bounded breaking calculations carried Chapter characteristics consider constant continuous coordinate 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 once origin oscillations particles path period phase plane positive possible prescribed present pressure problem progressing waves propagation quantities reasonable region relation require respect result river satisfies seen shallow water ship shock side simple singularity slope solution solved speed steady taken theory tion treated uniqueness values variables velocity vertical wave wave length yield zero