Structure of the Circulation Induced by a Shoaling Topographic Wave

Abstract

The structure of the potential vorticity flux and a mean flow induced by a topographic wave incident over a bottom slope are investigated analytically and numerically, with focus on the case that bottom friction is the dominant dissipation process. In this case it is shown that the topographic wave cannot be a steady source of the potential vorticity outside the bottom Ekman layer. Instead, the distribution of potential vorticity is determined from the initial transient of the topographic wave. This potential vorticity and the heat flux by the topographic wave at the bottom determine the mean flow and give a relation between the horizontal and vertical scales of the mean flow. When the horizontal scale of the mean flow is larger than the internal deformation radius and the potential vorticity is not so large, the mean flow is almost constant with depth independent of whether the topographic wave is bottom intensified. Then the mean flow is proportional to the divergence of the vertically integrated Reynolds stress. This divergence, which is caused by bottom friction, is large when the group velocity cg and the vertical scale ??1 of the wave motion are small. Thus, the mean flow tends to be large where cg and ??1 become small and decreases as the topographic wave is dissipated by bottom friction. Because bottom friction also dissipates the mean flow, the mean flow asymptotically approaches a constant value as the friction becomes zero. These features of the potential vorticity flux and the mean flow are reproduced in numerical experiments in which it is also shown that the distribution of the mean flow depends on the amplitude of the wave because of the Doppler shift of the wave by the mean flow. These features of the mean flow are preserved when stratification and bottom topography resembling those over the continental slope near the Gulf Stream are used. The transport of the mean flow is about 20 Sv (Sv ≡ 106 m3 s?1) when the wave amplitude is about 2 cm s?1. This transport is similar to that of the recirculation gyre in the Gulf Stream region.