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.

Keywords

Bibliographic record

BibTeX Citation

@article{Dutykh2009energytsunami,
  author = {Dutykh, D. and Dias, F.},
  title = {Energy of tsunami waves generated by bottom motion},
  journal = {Proc. R. Soc. A},
  year = {2009},
  volume = {465},
  pages = {725--744},
  doi = {10.1098/rspa.2008.0332},
  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.},
  keywords = {water waves, dispersive effects, tsunami waves, bottom motion, water wave equations, shallow-water equations, potential energy, kinetic energy, Cauchy-Poisson problem, tsunami energy, energy budget}
}