Abstract
Abstract We examine two-layer geostrophic flows over a flat 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 ∊, (ii) the ratio δ of the depth of the upper layer to the total depth of the fluid, (iii) the “β-effect number” α = Ro/Re cot θ, where Ro is the deformation radius, Re, is the earth's radius and θ is the latitude. In this paper We derive four sets of asymptotic equations which cover the parameter space (∊ ≪ 1,α,δ). In order to find out, which asymptotic regimes are relevant to the real ocean, we estimate ∊, δ and α a number of frontal flows in the Northern Pacific and Southern oceans We also discuss the stability properties of large-amplitude geostrophic flows and classify them in the (∊, α, δ)
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