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.