Large-Amplitude Geostrophic Dynamics: The Two-Layer Model

This paper is concerned with large-amplitude flows of a two-layer fluid on the β-plane. The Rossby number ε is small, while the displacement of the interface and the depth of the upper layer are both of the order of the total depth of the fluid. Two systems of equations are derived, corresponding to two asymptotic ranges of the parameter β/ε (where β is the ratio of the deformation radius to the earth's radius). With the help of the equations derived, the stability of parallel density-driven flows is examined. It is shown that all flows are unstable with respect to the perturbations with wave length being of the order of the deformation radius.