Structure of the Circulation Induced by a Shoaling Topographic Wave*

Abstract

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 integrat...