The Complete Classification of Large-Amplitude Geostrophic Flows in a Two-Layer Fluid

We examine two-layer geostrophic flows over a fiat bottom on the β-plane. If the displacement of the interface is of the order of the depth of the upper layer, the dynamics of the flow depends on the following non-dimensional parameters: (i) the Rossby number ε, (ii) the ratio δ of the depth of the upper layer to the total depth of the fluid, (iii) the "β-effect number" α=R0/R, cot 0, where R0 is the deformation radius, Re is the earth's radius and 0 is the latitude. In this paper, 1) we derive four sets of asymptotic equations which cover the parameter space (ε« 1,αβ). 2) In order to find out, which asymptotic regimes are relevant to the real ocean, we estimate aε, δ and « for a number of frontal flows in the Northern Pacific and Southern oceans. 3) We also discuss the stability properties of large-amplitude geostrophic flows and classify them in the (ε,α,δ)-space.