A LINEAR HOMOGENEOUS MODEL OF WIND-DRIVEN CIRCULATION IN A BETA-PLANECHANNEL

An analytical solution is sought for a wind-driven circulation in the inviscid limit in a linear barotropic channel model of the Antarctic C ircumpolar Ocean in the presence of a bottom ridge. There is a critica l height of the ridge, above which all geostrophic contours in the cha nnel are blocked. In the subcritical case, the Sverdrup balance does n ot apply and there is no solution in the inviscid limit. In the superc ritical case, however, the Sverdrup balance applies and an explicit fo rm for the zonal transport in the channel is obtained. In the case wit h a uniform wind stress, the transport in the beta-plane channel is in dependent of the width of the ridge, linearly proportional to the wind stress and the length of the channel, while inversely linearly propor tional to the ridge height. In the f plane with beta = 0, the transpor t is even independent of the width of the channel. In the case with a nonuniform wind stress tau(x) = tau(0)(1 - cos pi gamma/D), the Sverdr up flow driven by the vorticity input always induces a form drag again st the mean wind stress. Now, the transport depends on the width of th e ridge but not on the length of the channel. The model clearly demons trates how the topographic form drag is generated in a linear barotrop ic model, which is fundamentally different from the nonlinear Rossby w ave drag generation. Here, in this linear model, the presence of a sup ercritical high ridge is essential in the inviscid limit. The form dra g is generated regardless of the flow direction. Besides, the model de monstrates that most of the potential vorticity dissipation occurs at the northern boundary where the ridge is located.