Exact internal waves in the presence of mean currents and rotation

Abstract

We construct a new exact solution that represents a Pollard-like, three-dimensional, nonlinear internal wave propagating on a uniform zonal current in the presence of the Earth’s rotation. The solution is presented in Lagrangian coordinates, and in the process, we derive a dispersion relation for the internal waves in a stably stratified ocean. We show that the presence of a mean zonal current produces an intrinsically nonlinear mode of wave motion, representing a slow, inertial, internal wave.