The equations of motion for a square ocean basin of dimension L on the β-plane are solved approximately for the case where a wind-strew curl of the form sin (x/L) sin (y/L)[0≤x,y≤πL] is applied to the surface. The stream function is expanded in a double Fourier sine series and this representation is truncated after only four terms. The resulting set of equations contains the effects of non-linearity, time dependence, linear variation of the Coriolis parameter, friction, and wind-stress. Multiple solutions to the steady-state equations exist when the wind-stress is sufficiently strong. One of the solutions can be related to Sverdrup's (1947) solution for an ocean basin with one longitudinal boundary. A second solution is dominated by the non-linear interactions of the system. Integration of the non-linear transient equations are carried out for the case where the wind-stress starts at some initial time. In some cases the system goes through a series of oscillations of decreasing amplitude before i... Abstract The equations of motion for a square ocean basin of dimension L on the β-plane are solved approximately for the case where a wind-strew curl of the form sin (x/L) sin (y/L)[0≤x,y≤πL] is applied to the surface. The stream function is expanded in a double Fourier sine series and this representation is truncated after only four terms. The resulting set of equations contains the effects of non-linearity, time dependence, linear variation of the Coriolis parameter, friction, and wind-stress. Multiple solutions to the steady-state equations exist when the wind-stress is sufficiently strong. One of the solutions can be related to Sverdrup's (1947) solution for an ocean basin with one longitudinal boundary. A second solution is dominated by the non-linear interactions of the system. Integration of the non-linear transient equations are carried out for the case where the wind-stress starts at some initial time. In some cases the system goes through a series of oscillations of decreasing amplitude before i...