The Interaction of a Surface Wave with Waves on a Diffuse Interface

Abstract

A resonant interaction analysis is used to study the two-dimensional interaction of a surface wave with two waves on a diffuse interface in a stratified fluid. The fluid system is modeled as a combination of two homogenous finite-depth layers with a free surface, divided by a thin third layer. Two possibilities for the interaction are found: one between the surface wave and two first-mode interfacial waves and a second between the surface wave, a first-mode, and a second-mode interfacial wave. By taking the nondimensional density difference δ as a small perturbation parameter, the evolution equations of the interfacial waves are derived asymptotically. The analysis indicates that growth of the interfacial waves is possible only in the first case. The effects of viscosity on the interaction are discussed, and some preliminary experimental results are presented.