Gravity-capillary wave interactions generated by moving disturbances: Euler equations framework

TL;DR

This study uses the Euler equations framework to analyze gravity-capillary wave interactions caused by moving disturbances, revealing nonlinear effects, wave trapping, and regime-dependent behaviors in different flow conditions.

Contribution

It introduces a comprehensive Euler equations-based numerical approach to study wave interactions from multiple disturbances, highlighting new phenomena like wave trapping and mixed regime features.

Findings

Wave interactions can be strongly nonlinear leading to wave breaking.

Depression solitary waves are trapped between disturbances.

The critical regime exhibits features of both subcritical and supercritical flows.

Abstract

The aim of this work is to investigate the interaction of gravity-capillary waves resonantly excited by two moving disturbances along the free surface. The problem is formulated using the full Euler equations and numerical computations are performed in a simplified domain through the use of a conformal mapping which flattens the free surface. We focus on nearly-critical flows with intermediate capillary effects and characterise their main features. In the supercritical regime the wave interaction can be strongly nonlinear leading to the onset of wave breaking. In the subcritical regime depression solitary waves are generated remaining trapped between the disturbances bouncing back and forth. In addition, we notice a dependence of the number of trapped waves on the distance of the disturbances. Furthermore, differently from when only on disturbance is considered, we find that the critical regime captures features from the subcritical and supercritical regime simultaneously.