This paper considers the "time-mean" circulation of wind-driven ocean gyres in the limit referred to as "inertial" or "almost-free." In this limit, potential vorticity is conserved following the flow with sources and sinks of potential vorticity balancing in an integral sense around the gyre. Approximate analytic solutions are obtained for a continuously stratified quasi-geostrophic ocean by neglecting the relative vorticity in the gyre interiors. The solutions have features similar to those found in the western part of ocean basins both in eddy-resolving numerical models and in observations. In particular, a deep westward recirculation, such as proposed by Worthington (1976) for the Gulf Stream system, arises naturally from the analysis as an enhanced barotropic flow inside the region where the "bowl" containing the circulation has intersected the ocean floor. This flow, which is driven by eddies and dissipated by bottom friction, leads to a sudden increase in westward velocity similar to that found between 35N and 36N in the long-term current records along 55W discussed by Schmitz (1977, 1978, 1980).
Greatbatch, Richard J.. 1987. "A model for the inertial recirculation of a gyre." Journal of Marine Research 45, (3). https://elischolar.library.yale.edu/journal_of_marine_research/1863