Energy of tsunami waves generated by bottom motion

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 appear only 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.