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.
Salmon, Rick, and Rupert Ford. 1995. "A simple model of the ‘joint effect of baroclinicity and relief’ on ocean circulation." Journal of Marine Research 53, (2). https://elischolar.library.yale.edu/journal_of_marine_research/2138