Energy of tsunami waves generated by bottom motion

Denys Dutykh (1, 2, 3, 4) , Frédéric Dias (2, 5)

1 LAMA - Laboratoire de Mathématiques
2 CMLA - Centre de Mathématiques et de Leurs Applications
3 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
4 USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc
5 LRC MESO - Laboratoire de recheche conventionné MESO

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.

Mots clés: water waves; shallow-water equations; tsunami energy

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Physique Atmosphérique et Océanique [physics.ao-ph]; Géophysique [physics.geo-ph]; Géophysique [physics.geo-ph]; Equations aux dérivées partielles [math.AP]; Océan, Atmosphère; Systèmes Solubles et Intégrables [nlin.SI]; Formation de Structures et Solitons [nlin.PS]; Physique Numérique [physics.comp-ph]

Denys Dutykh, Frédéric Dias. Energy of tsunami waves generated by bottom motion. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2009, 465 (2103), pp.725-744. ⟨10.1098/rspa.2008.0332⟩. ⟨hal-00311752v2⟩