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Energy of tsunami waves generated by bottom motion

Denys Dutykh (LAMA CMLA), Frédéric Dias (CMLA, LRC Meso)
Arxiv ID: 0808.2861Last updated: 2/20/2020
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.

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