Internal Waves at an Interface between Two Layers of Differing Stability

Abstract

Internal waves in a two-layer fluid are considered. The layers have different values of the buoyancy frequency, assumed to be constant in each layer. The density profile is chosen to be continuous across the interface and the flow is Boussinesq. The solution is an expansion in the wave amplitude, similar to a Stokes expansion for free surface waves. The results show that the nonlinear terms in the interfacial boundary conditions require higher harmonics and result in nonlinear wave steepening at the interface. The first few harmonics are scattered by the interface, whereas the higher harmonics are evanescent in the vertical. The second-order correction to the wave speed is negative, similar to previous results with a rigid upper boundary.