Stratified, Rotating Flow Over Orography: The Rigid-Lid Boundary Condition and the Far-Field Circulation

Abstract

Steady, two-dimensional, rotating and stably stratified flow over a ridge in an atmosphere capped by a rigid lid is known to exhibit a permanent downstream streamline deflection. The three-dimensional counterpart of this model, flow over a finite ridge, is not characterized by a permanent deflection: the cross-stream velocity becomes vanishingly small at large distances from the obstacle. The discrepancy that exists between these solutions is isolated, and shown to be the result of extending the finite ridge to infinity; the solution over an infinite ridge becomes nonunique. More importantly, it is shown that this latter solution is not a sensible approximation to flow over a long, but finite, ridge. Further, the presence of an incorrect drag law, that may be derived from the two-dimensional model solution, is explained in terms of an upstream condition placed on the cross-stream geostrophic velocity.