Gravity-capillary flows over obstacles for the fifth-order forced Korteweg-de Vries equation

TL;DR

This study numerically investigates gravity-capillary waves excited by obstacles in shallow water, using a fifth-order Korteweg-de Vries model to analyze wave interactions and resonance effects.

Contribution

It introduces a numerical analysis of the forced fifth-order KdV equation for gravity-capillary flows over obstacles, highlighting complex wave interactions in near-resonant conditions.

Findings

Flow is not solely governed by the larger obstacle.

Wave interactions depend on obstacle size and capillary effects.

Numerical results reveal complex resonance phenomena.

Abstract

The aim of this work is to investigate gravity-capillary waves resonantly excited by two topographic obstacles in a shallow water channel. By considering the weakly nonlinear regime the forced fifth-order Korteweg-de Vries equation arises as a model for the free surface displacement. The water surface is initially taken at rest and the initial value problem for this equation is computed numerically using a pseudospectral method. We study near-resonant flows with intermediate capillary effects. Details of the wave interactions are analysed for obstacles with different sizes. Our numerical results indicate that the flow is not necessarily governed by the larger obstacle.