Dispersive barotropic equations for stratified mesoscalc ocean dynamics

Dispersive effects induced by weak hydrostatic imbalance in the presence of topography and stratification are incorporated into a new model of barotropic (vertically integrated) mesoscale ocean dynamics. This barotropic model is obtained by first expanding the solutions of three dimensional Euler-Boussinesq equations in a regular perturbation expansion in terms of the several small dimensionless parameters appropriate to mesoscale ocean dynamics. Vertically integrating from a fixed bottom topography to the free surface interface with the atmosphere and balancing orders in the expansion at fourth order in the small aspect ratio parameter then yields a system of reduced barotropic equations. These reduced barotropic equations are considerably more tractable than the starting equations and have appropriate limits to known dispersive wave equations such as the forced Kadomtsev-Petviashvili equation in one limit, and the rotating shallow water equations in another. This new model of barotropic ocean dynamics may be of use in developing numerical algorithms for global ocean circulation modeling.