Boussinesq modeling of surface waves due to underwater landslides

Denys Dutykh (1, 2, 3, 4) , Henrik Kalisch (5)

1 LAMA - Laboratoire de Mathématiques
2 School of Mathematical Sciences [Dublin]
3 USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc
4 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
5 Department of Mathematics

Consideration is given to the influence of an underwater landslide on waves at the surface of a shallow body of fluid. The equations of motion which govern the evolution of the barycenter of the landslide mass include various dissipative effects due to bottom friction, internal energy dissipation, and viscous drag. The surface waves are studied in the Boussinesq scaling, with time-dependent bathymetry. A numerical model for the Boussinesq equations is introduced which is able to handle time-dependent bottom topography, and the equations of motion for the landslide and surface waves are solved simultaneously. The numerical solver for the Boussinesq equations can also be restricted to implement a shallow-water solver, and the shallow-water and Boussinesq configurations are compared. A particular bathymetry is chosen to illustrate the general method, and it is found that the Boussinesq system predicts larger wave run-up than the shallow-water theory in the example treated in this paper. It is also found that the finite fluid domain has a significant impact on the behavior of the wave run-up.

Mots clés: Surface waves; Boussinesq model; submarine landslides; wave run-up; tsunami

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Milieux et Changements globaux; Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Dynamique des Fluides [physics.flu-dyn]; Physique Numérique [physics.comp-ph]; Hydrologie; Analyse numérique [cs.NA]; Modélisation et simulation; Formation de Structures et Solitons [nlin.PS]; Systèmes Solubles et Intégrables [nlin.SI]; Physique Atmosphérique et Océanique [physics.ao-ph]; Géophysique [physics.geo-ph]; Géophysique [physics.geo-ph]

Denys Dutykh, Henrik Kalisch. Boussinesq modeling of surface waves due to underwater landslides. Nonlinear Processes in Geophysics, 2013, 20, pp.267-285. ⟨10.5194/npg-20-267-2013⟩. ⟨hal-00654386v4⟩