A reduced model for nonlinear dispersive waves in a rotating environment

The simplest model for geophysical flows is one layer of a constant density fluid with a free surface, where the fluid motions occur on a scale in whi ch the Coriolis force is significant. In the linear shallow water limit, th ere are non-dispersive Kelvin waves, localized near a boundary or near the equator, and a large family of dispersive waves. We study weakly nonlinear and finite depth corrections to these waves, and derive a reduced system of equations governing the flow. For this system we find approximate solitary Kelvin waves, both for waves traveling along a boundary and along the equa tor. These waves induce jets perpendicular to their direction of propagatio n, which may have a role in mixing. We also derive an equivalent reduced sy stem for the evolution of perturbations to a mean geostrophic how.