Consideration is given to the influence of an un- derwater 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 dis- sipative effects due to bottom friction, internal energy dissi- pation, 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 com- pared. A particular bathymetry is chosen to illustrate the gen- eral method, and it is found that the Boussinesq system pre- dicts 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.
['Denys Dutykh', 'Henrik Kalisch']
Boussinesq modeling of surface waves due to underwater landslides