Abstract
A major difficulty with two-layer ocean models, except in the linear approximation, is encountered in situations where the interface intersects the seabed. For the single mode, reduced-gravity version it is assumed that a passive deep lower layer exists everywhere, which in fact precludes any influence by bathymetry. These restrictions can be removed by employing a realistic continuous density stratification. Discussed here is a generalized, equivalent barotropic model in isopycnic coordinates that is based on the gravest vertical structure function E(σ) for current determined by the global, levelled-state density distribution. The eigenvalue problem employs a rigid-lid condition at the sea surface and requires E = 0 (a vanishing current) at the seabed for each local depth h. The gravest mode has monotonie E(σ) and an associated eigencelerity that is typical of a first baroclinic mode. Both the structure function and the celerity (hence the Rossby deformation radius) depend on the local depth h. The E(σ) based on realistic levelled-state density stratification closely resembles the dominant first empirical mode commonly found from observed current structure at mid-latitudes. The non-linear governing equations (admitting both gravity and Rossby waves) are developed using an energy-conserving, Galerkin projection of the primitive equations of motion onto the adopted vertical structure, taking into account the dependence on h. The resulting governing equations involve two important depth-dependent parameters: the celerity (C
e
) and a Flierl-type advection parameter (μ.). The role of bottom topography in this generalized, reduced-gravity model is illustrated via an application to the Loop Current evolution and to the interaction of mesoscale circulation features with bathymetry in the western Gulf of Mexico. This illustration employs a non-linear, quasi-geostrophic voracity version of the model in boundary-fitted, orthogonal curvilinear coordinates, implemented numerically.