Boussinesq modeling of surface waves due to underwater landslides

TL;DR

This paper develops a numerical model based on Boussinesq equations to simulate surface waves caused by underwater landslides, accounting for time-dependent bathymetry and dissipative effects, and compares it with shallow-water theory.

Contribution

It introduces a novel numerical approach for Boussinesq equations with dynamic bottom topography and compares results with shallow-water models.

Findings

Boussinesq system predicts larger wave run-up than shallow-water theory.

Finite fluid domain significantly affects wave run-up behavior.

The model effectively handles time-dependent bathymetry and landslide dynamics.

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 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.