Steady, barotropic wind and boundary-driven circulation on a polar plane

Abstract

Steady, linear, barotropic wind and boundary forced circulation solutions in the presence of linear bottom friction are analytically derived in a circular basin of uniform depth on a polar tangent plane in which only first order effects of the Earth’s curvature are retained. Approximate solutions are constructed by using the well known method of aggregating the interior inviscid Sverdrup balance solution and the frictional wall boundary layer solution. In contrast to the width of mid-latitude frictional western boundary layers that scale as , the width of the polar frictional boundary layer adjacent to the basin wall is wider, scaling as , where is the bottom friction coefficient, is the coriolis parameter. Solutions are presented for a variety of wind stress curl distributions and for a prescribed inflow/outflow representative of the exchange of water masses between the Arctic and Atlantic basins. Boundary forced solutions are also derived in a basin with a uniform width step shelf. For this basin geometry the flow is mainly confined to the shelf, although a parameter regime is identified that supports significant flow in the deep basin.