It is well known that the barotropic, wind-driven, single-gyre ocean model reaches an inertially-dominated equilibrium with unrealistic circulation strength when the explicit viscosity is reduced to realistically low values. It is shown here that the overall circulation strength can be controlled nonlocally by retaining thin regions of enhanced viscosity parameterizing the effects of increased mixing and topographic interaction near the boundaries. The control is possible even when the inertial boundary layer width is larger than the enhanced viscosity region, as eddy fluxes of vorticity from the interior transport vorticity across the mean streamlines of the inertial boundary current to the frictional region. In relatively inviscid calculations the eddies are the major means of flux across interior mean streamlines.