1University College Dublin, School of Mathematical Sciences, Belfield, Dublin 4, Ireland
2LAMA, UMR5127, CNRS – Université de Savoie, Campus Scientifique, 73376 Le Bourget-du-Lac Cedex, France
3Department of Mathematics, University of Bergen, P.O. Box 7800, 5020 Bergen, Norway
Abstract. 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 that 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 that 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.