The effect of side walls on homogeneous rotating flow over two-dimensional obstacles

Abstract

We consider the flow of a slightly viscous homogeneous fluid over a small two-dimensional obstacle perpendicular to the vertical side walls in a channel rotating about a vertical axis. The flow in the channel is obtained from the solution of the quasi-geostrophic potential vorticity equation in the limit ε = D/L→ 0, where D is the obstacle width and L the channel width. The lowest order, interior flow is shown to be a combination of three effects: a rotational flow caused by vortex stretching and Ekman boundary-layer pumping; a significant irrotational flow induced by the magnitude of the former flow at the vertical boundaries; and the interior Ekman drift due to the basic current. The maximum streamline displacement is calculated and compares very well with recent experiments in the identical parameter range by Boyer (1971a, b). This theory explains how the side walls are responsible for the dependence of the maximum streamline displacement on Rossby number.