Baroclinic frontal dynamics in the presence of continuous stratification and topography

An investigation of subinertial dynamics involving oceanic fronts is presented in the context of layered models, which allow for vanishing thickness in the frontal layer and continuous stratification in the ambient fluid. The focus of the study is the baro-clinic destabilization and subsequent evolution of surface-trapped, bottom-trapped and intermediate-depth currents, as well as their interaction with topography. Two new theories are derived that include the effect of ambient stratification, and a previous theory is generalized. Reduction of all three models to simpler governing equations in the limit of no stratification is demonstrated and basic analytical results are established with respect to boundary conditions, flow invariants and linear stability criteria.; The linear stability problems for an abyssal current and a surface current in the presence of sloping topography are solved for physically-relevant configurations. It is shown that growth rates increase and dominant lengthscales decrease with the relative current thickness or ambient stratification. Predicted instability characteristics and results of fully nonlinear numerical simulations are compared with several oceanographic phenomena of interest, in particular the Denmark Strait Overflow. It is argued that the models presented provide a superior description of baroclinic dynamics than traditional quasigeostrophic theory, in that the assumed lengthscales are larger than the Rossby radius and variations in the frontal layer thickness scale with the layer thickness itself. The resulting balances still allow reasonably straightforward interpretation of the physical mechanisms involved but are appropriate in many situations where quasigeostrophic models are not.