Delayed separation in eastward, rotating flow on a β-plane

Abstract

We consider the small-Rossby-number flow of a fluid past an obstacle in a coordinate frame in which the rotation rate varies linearly in the direction normal to the flow in a manner that models the variation of the Coriolis force for midlatitude planetary motions. The eastward flow is characterized by strong upstream divergence of the streamlines like that noted by Davies & Boyer (1982), and a similarly severe streamline convergence in the lee of the obstacle. Such a structure occurs for small values of the β-parameter that measures the importance of the lateral angular-velocity variation. In this parameter range, Rossby waves occur, but are confined to a narrow region in the lee of the object. The presence of these waves modifies the edge velocity ‘seen’ by the Stewartson quarter layer in such a way as to delay the onset of separation beyond what one might expect based on the analysis of Walker & Stewartson (1974) for a flow without beta-effect.