Two models are employed to study the effect of topographically induced planetary islands (i.e. closed contours of potential vorticity) on the abyssal circulation of an ocean basin. The first is a steady state calculation using a 1½ layer model of the abyssal ocean forced by a uniform upwelling. Planetary geostrophic dynamics yield a characteristic equation in which the inverse potential vorticity serves as a streamfunction for the characteristic velocity field. Aside from warping the classic Stommel-Arons flow in the immediate vicinity of the planetary island, the topography introduces two new elements to the zonal flow west of the topography. The first of these is a system of two zonal jets, flowing in opposite directions and centered on the separatrix contour. The second is an acceleration (or retardation) of the zonal flow (with respect to the classic flat-bottom result) in a broader region of the basin. The strengths of both the double jets and the broader regions of enhanced/retarded zonal flow are found to be determined by forcing in relatively small areas of the basin. The former are excited in the vicinity of saddle points of potential vorticity whereas the latter are excited primarily where the curvature of potential vorticity contours is large. The second model, a time dependent 2½ layer planetary geostrophic model is then used to investigate the spin-up problem. The model is forced by a uniform upwelling through each of the two interfaces. The density jump at the upper interface (e.g. the thermocline) is chosen to be ten times that at the lower interface, a disparity which leads to a separation in time scale between the fast and the slow waves of the system. Topography, however, induces a strong coupling between these two modes and results in a quick baroclinization of the flow over the topography. This baroclinization occurs well before the arrival of the nondispersive wave front from the eastern boundary and thus differs from the traditional view of spin-up.
Straub, David N., and Peter B. Rhines. 1990. "Effects of large-scale topography on abyssal circulation." Journal of Marine Research 48, (2). https://elischolar.library.yale.edu/journal_of_marine_research/1968