A Linear Homogeneous Model of Wind-Driven Circulation in a β-Plane Channel

Abstract

An analytical solution is sought for a wind-driven circulation in the inviscid limit in a linear barotropic channel model of the Antarctic Circumpolar Ocean in the presence of a bottom ridge. There is a critical height of the ridge, above which all geostrophic contours in the channel are blocked. In the subcritical case, the Sverdrup balance does not apply and there is no solution in the inviscid limit. In the supercritical case, however, the Sverdrup balance applies and an explicit form for the zonal transport in the channel is obtained. In the case with a uniform wind stress, the transport in the ?-plane channel is independent of the width of the ridge, linearly proportional to the wind stress and the length of the channel, while inversely linearly proportional to the ridge height. In the f plane with ? = 0, the transport is even independent of the width of the channel. In the case with a nonuniform wind stress τx = τ0(1-?cosπy/D), the Sverdrup flow driven by the vorticity input always induces a form drag against the mean wind stress. Now, the transport depends on the width of the ridge but not on the length of the channel. The model clearly demonstrates how the topographic form drag is generated in a linear barotropic model, which is fundamentally different from the nonlinear Rossby wave drag generation. Here, in this linear model, the presence of a supercritical high ridge is essential in the inviscid limit. The form drag is generated regardless of the flow direction. Besides, the model demonstrates that most of the potential vorticity dissipation occurs at the northern boundary where the ridge is located.