Nonlinear water waves at a submerged obstacle or bottom topography

A High-Order Spectral Method for Nonlinear Water Waves over Moving Bottom Topography

We present a numerical method for simulations of nonlinear surface water waves over variable bathymetry. It is applicable to either twoor three-dimensional flows, as well as to either static or moving bottom topography. The method is based on the reduction of the problem to a lower-dimensional Hamiltonian system involving boundary quantities alone. A key component of this formulation is the Dir...

Influence of Bottom Topography on Long Water Waves

Abstract. We focus here on the water waves problem for uneven bottoms in the long-wave regime, on an unbounded two or three-dimensional domain. In order to derive asymptotic models for this problem, we consider two different regimes of bottom topography, one for small variations in amplitude, and one for strong variations. Starting from the Zakharov formulation of this problem, we rigorously co...

On Nonlinear Water Waves in a Channel

Water waves generated by a moving bottom

Tsunamis are often generated by a moving sea bottom. This paper deals with the case where the tsunami source is an earthquake. The linearized water-wave equations are solved analytically for various sea bottom motions. Numerical results based on the analytical solutions are shown for the free-surface profiles, the horizontal and vertical velocities as well as the bottom pressure.

on nonlinear water waves in a channel