A multiscale model for weakly nonlinear shallow water waves over periodic bathymetry
Abstract
We study the behavior of shallow water waves over periodically-varying bathymetry, based on the first-order hyperbolic Saint-Venant equations. Although solutions of this system are known to generally exhibit wave breaking, numerical experiments suggest a different behavior in the presence of periodic bathymetry. Starting from the first-order variable-coefficient hyperbolic system, we apply a multiple-scale perturbation approach in order to derive a system of constant-coefficient high-order partial differential equations whose solution approximates that of the original system. The high-order system turns out to be dispersive and exhibits solitary-wave formation, in close agreement with direct numerical simulations of the original system. We show that the constant-coefficient homogenized system can be used to study the properties of solitary waves and to conduct efficient numerical simulations.
Cite
@article{arxiv.2311.02603,
title = {A multiscale model for weakly nonlinear shallow water waves over periodic bathymetry},
author = {David I. Ketcheson and Lajos Lóczi and Giovanni Russo},
journal= {arXiv preprint arXiv:2311.02603},
year = {2025}
}