TOPOGRAPHIC OCEAN GYRES - A WESTERN BOUNDARY SLOPE

The appropriate lateral boundary condition for an oceanic general circ ulation model is not yet well determined. A large-scale current is inh ibited 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 formula tion of general circulation models. In the true situation the western boundary current associated with a midlatitude, wind-driven gyre may b e located on the continental slope. Since the streamfunction tends to follow the ambient potential vorticity contours, there will be an equa torward tail to the gyre that also occurs on the slope. Here a linear barotropic theory is developed for the following three cases: 1) a qua sigeostrophic model with Rayleigh friction, 2) a quasigeostrophic mode l with lateral viscosity, and 3) an equatorial beta-plane model with R ayleigh friction. These can be viewed as generalizations of Stommel an d Munk solutions for an oceanic basin with a vertical side boundary. T he general characteristics of the solutions and the dependence on the parameter representing the slope and/or the friction are studied. It i s found that in the steep-slope limit the solutions in the hat region for 1) and 2) approach the Stommel solution and the Munk solution, res pectively. In the former case, the streamfunction at the outer edge of the slope decreases as (slope)(-1/2) and the current velocity suddenl y vanishes in the slope region in this limit; in the latter case, the streamfunction there also decreases as (slope)(-1/2), while the veloci ty varies as (slope)(-1/4). From the solution for 3), it, is found tha t the tail decays rapidly in low latitudes and cannot cross the equato r. II is also found that if the frictional torque is stronger than the effect of the vortex stretching over the slope, the tail length is si gnificantly reduced, even if the friction coefficient is not large.