Topographic Ocean Gyres: A Western Boundary Slope

Abstract

The appropriate lateral boundary condition for an oceanic general circulation model is not yet well determined. A large-scale current is inhibited from ascending the continental slope because of the restriction of the potential vorticity conservation. As a consequence the current may never be in contact with a side boundary that has vertical walls; nevertheless, side boundaries have always been assumed in the formulation of general circulation models. In the true situation the western boundary current associated with a midlatitude, wind-driven gyre may be located on the continental slope. Since the streamfunction tends to follow the ambient potential vorticity contours, there will be an equatorward tail to the gyre that also occurs on the slope. Here a linear barotropic theory is developed for the following three cases: 1) a quasigeostrophic model with Rayleigh friction, 2) a quasigeostrophic model with lateral viscosity, and 3) an equatorial ?-plane model with Rayleigh friction. These can be viewed as generalizations of Stommel and Munk solutions for an oceanic basin with a vertical side boundary. The general characteristics of the solutions and the dependence on the parameter representing the slope and/or the friction are studied. It is found that in the steep-slope limit the solutions in the flat region for 1) and 2) approach the Stommel solution and the Munk solution, respectively. In the former case, the streamfunction at the outer edge of the slope decreases as (slope)?1/2 and the current velocity suddenly vanishes in the slope region in this limit; in the latter case, the streamfunction there also decreases as (slope) ?1/2, while the velocity varies as (slope) ?1/4. From the solution for 3), it is found that the WI decays rapidly in low latitudes and cannot cross the equator. It is also found that if the frictional torque is stronger than the effect of the vortex stretching over the slope, the tail length is significantly reduced, even if the friction coefficient is not large.