Effect of a western continental slope on the wind-driven circulation

Numerical solutions of a simple theoretical model of the wind-driven circulation with inertia for a constant density ocean depend strongly upon whether the western boundary is modeled with a vertical sidewall or a smooth continental shelf. In the basin with the continental shelf, unsteady single-gyre inertial solutions are obtained for anticyclonic winds while steady single-gyre inertial solutions typically are obtained for cyclonic winds. In the flat-bottom basin, however, the corresponding model solutions are steady for both anticyclonic and cyclonic winds. In addition, for cyclonic forcing, multiple equilibria are found in the basin with the western continental slope but not in the flat-bottom basin (although the uniqueness of the solutions in the flat-bottom basin has not been proven). The dependence of the model solutions on the topography and the sign of the wind forcing is attributed to the effects of friction, which are localized in the southwest corner of the basin for the continental slope topography, but which are important in boundary layers at vertical sidewalls for the flat-bottom topography.