Resonant interactions between weakly nonlinear long surface and interfacial waves

Transient evolution of interacting long nonlinear surface and interfacial waves are analyzed. A set of Boussinesq-like equations are derived for two layer, density stratified, shallow, inviscid and immiscible fluid. The influence of different parameters on the interaction such as density ratio of the layers, relative thickness of the layers, surface wave frequency and surface wave amplitude on the evolution of the waves is discussed. Furthermore, weak viscosity is incorporated in the problem. It is shown that viscosity results in the attenuation of the surface waves as well as long term stabilization of interfacial waves.