Two-Layer Geostrophic Dynamics. Part I: Governing Equations

Abstract

Although the quasigeostrophic formalism has been a cornerstone in oceanographic modeling for over four decades, studies have shown time and time again that other geostrophic, but non-quasigeostrophic, regimes can also exist. These include a particular class of regimes representative of oceanic fronts and frontal eddies. The task undertaken here is the clarification and investigation of the possible geostrophic regimes, quasigeostrophic and otherwise, of a two-layer mean. To simplify the analysis, attention is restricted to a system on the midlatitude beta plane, above a flat bottom and below a rigid lid. Under the assumption of a small Rossby number, geostrophic regimes are sought, and the set of primitive equations is reduced to two prognostic equations, one for each of the barotropic and baroclinic pressure fields. These equations share with the quasigeostrophic equations the absence of inertia-gravity waves, but their greater range of validity allows order-one variations in the upper-layer depth. The various dynamical regimes are investigated, including a frontal geostrophic regime of particular importance. Finally, invariant properties are determined and discussed. As part of the analysis, the conditions under which the one-layer, reduced-gravity model is a valid approximation of the two-layer system are also considered.