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

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.