A simple model of the ‘joint effect of baroclinicity and relief’ on ocean circulation

We offer a simple model for studying the joint effect of baroclinicity and relief (jebar) on large-scale ocean circulation, based upon the planetary geostrophic equations. Applying a Galerkin approximation to the buoyancy equation, and asssuming that the temperature diffusion and vertical stratification are weak, we obtain a simple relation between the ocean temperature and the streamfunction ψ for the vertically-averaged horizontal transport. Substituting this relation back into the vertically-averaged vorticity equation yields a single, generally nonlinear equation for ψ, in which jebar corresponds to a clockwise ‘advection’ of ψ along the continental slope (for the realistic case of temperature increasing with ψ). Numerical solutions resemble those obtained by Salmon (1994) using a more accurate model, and provide a physically transparent explanation for the northward excursion of the Gulf Stream along the western continental slope observed in the previous study