On the structure of inertial western boundary currents with two moving layers

The structure of inertial western boundary currents with two moving layers is studied using a streamfunction coordinate transformation. This transformation converts the equation system, a stiff system over a semi-infinite domain in physical coordinates, into a non-stiff system over a finite domain in streamfunction coordinates. For simplicity, the interfacial slopes of the interior solution are assumed constant. The structure of the solutions can be classified into three categories in a phase plane which consists of two regions joining along a critical line. Within each region, solutions of the system appear in the form of two unconnected branches. As parameters approach values corresponding to those at the critical line, the two branches of the solutions join at a movable critical point to form a continuous solution. Although changes in the vorticity profile of the incoming flow or other parameters can alter the position and shape of the critical line, the general features of the system remain unchanged. Thus, requiring continuity of an inertial western boundary current through a critical point, implies certain constraints on the structure of the mid-ocean thermocline.