A Numerical Investigation of a Nonlinear Model of a Wind-Driven Ocean

Abstract

Solutions are obtained for a time dependent, nonlinear model of a wind-driven ocean by a numerical integration of the corresponding initial value problem. Without time dependence the model and boundary conditions are equivalent to those of Munk, Groves and Carrier (1950). The vorticity equation of the model may be put in nondimensional form so that solutions are governed solely by the pattern of the wind stress, a Rossby number for the interior flow, and an effective Reynolds number for the western boundary current. For a Rossby number in the geophysical range, two regimes are found, depending on the Reynolds number. Below a critical value between 50 and 100 a steady-state solution is approached asymptotically. Above this transition a train of moving disturbances forms in the boundary current due to shear flow instability. There is no tendency for the boundary current to break away from the wall in the region of maximum wind curl for the range of Reynolds numbers (0 through 100) investigated. In examining other mechanisms which might give rise to separation, it is found that recirculations develop behind barriers placed along the western wall. Recirculation in one case increases the transport of the boundary current by 50 per cent compared to the corresponding linear solution. For wind-stress patterns which include areas of both positive and negative curl of the wind stress, southward moving as well as northward moving currents form along the western boundary. The linear response to this pattern includes a diffuse current moving out from the wall where these two currents collide. In the nonlinear model a tendency to conserve vorticity downstream allows this separation current to be as intense as the boundary currents.