Analytic Solution of Barotropic Wind Forced Ocean Gyre Circulation

Abstract

In this study, we provide analytic solution of barotropic wind forced ocean gyre circu lation. The governing equations are solved analytically using vorticity-stream function together with boundary conditions. To obtain the analytic solution, we rst establish the governing equations of our model by making shallow water assumption on Navier-Stokes equations. Then, the momentum equations of the governing equations are combined to produce vorticity equation by a cross partial derivatives of the momentum equations. A stream function is de ned so as to write the vorticity equation as a fourth-order equation in terms of only the stream function. The solution of the stream function is obtained by the assumptions that streamlines at the boundary are chosen to be zero and that, there are no slippages against the boundary. Finally, the solution of free surface height is established to vary directly with the stream function. The analytic solution, just like the numerical solution obtained by running the Mas sachusetts Institute of Technology General Circulation Model(MITgcm), shows west ern intensi cation of streamlines, a result that is due to the e ect of Coriolis force. Moreover, di erent values of the Coriolis force in both the analytic and numerical so lution show that the intensi cation of streamlines at the western boarder is relatively intense with higher Coriolis force