Energy of tsunami waves generated by bottom motion

Abstract

In the vast literature on tsunami research, few articles have been devoted to energy issues. A theoretical investigation on the energy of waves generated by bottom motion is performed here. We start with the full incompressible Euler equations in the presence of a free surface and derive both dispersive and non-dispersive shallow-water equations with an energy equation. It is shown that dispersive effects only appear at higher order in the energy budget. Then we solve the Cauchy-Poisson problem of tsunami generation for the linearized water wave equations. Exchanges between potential and kinetic energies are clearly revealed.

20 pages, 12 figures. Accepted to Proceedings of the Royal Society A. Other authors papers and supporting material can be downloaded at http://www.lama.univ-savoie.fr/~dutykh

References in corpus (2)

• Linear theory of wave generation by a moving bottom
• Comparison between three-dimensional linear and nonlinear tsunami generation models

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• Hamiltonian approach to modelling interfacial internal waves over variable bottom
• Dispersive shallow water wave modelling. Part II: Numerical simulation on a globally flat space