Energy of tsunami waves generated by bottom motion

TL;DR

This paper investigates the energy dynamics of tsunami waves generated by bottom motion using theoretical derivations of shallow-water equations and analyzes energy exchanges during wave generation.

Contribution

It derives energy equations from Euler equations and analyzes energy exchanges in tsunami generation, highlighting dispersive effects at higher orders.

Findings

Dispersive effects are higher order in energy budget.

Potential and kinetic energy exchanges are clearly identified.

Energy equations are derived for both dispersive and non-dispersive models.

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.