Long Waves in Ocean and Coastal Waters

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Abstract
A brief survey and general discussion is presented on the generation, propagation and evolution of long waves in the ocean and coastal waters with special reference to tsunami phenomenon. A set of layer-mean transport equations is derived for water waves of arbitrary amplitude and wavelength. From these equations, which are exact for incompressible and inviscid fluids, a set of integral relations is secured regarding the conservation of the excess mass, the relationship between the impluse and excess momentum, and the rate of variation of the total energy. For treating various types of long water waves, a basic long-wave equation of the generalized Boussinesq class is derived for waves propagating in two horizontal dimensions in water of variable depth, both in space and time (for tsunami applications). From this basic equation the linear dispersive, linear nondispersive and nonlinear nondispersive long-wave models are deduced as subsystems.

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