The Dynamics of Orographic Wake Formation in Flows with Upstream Blocking

Abstract

The development of orographic wakes and vortices is revisited from the dynamical perspective of a three-dimensional (3D) vorticity-vector potential formulation. Particular emphasis is given to the role of upstream blocking in the formation of the wake. Scaling arguments are first presented to explore the limiting form of the 3D vorticity inversion for the case of flow at small dynamical aspect ratio δ. It is shown that in the limit of small δ the inversion is determined completely by the two horizontal vorticity components?that is, the part of the velocity induced by the vertical component of vorticity vanishes in the small-δ limit. This result leads to an approximate formulation of small-δ fluid mechanics in which the three governing prognostic variables are the two horizontal vorticity components and the potential temperature. The remainder of the study then revisits the problem of orographic wake formation from the perspective of this small-δ vorticity dynamics framework. Previous studies have suggested that one of the potential routes to stratified wake formation is through the blocking of flow on the upstream side of the barrier. This apparent link between blocking and wake formation is shown to be relatively straightforward in the small-δ vorticity context. In particular, it is shown that blocking of the flow inevitably leads to a horizontal vorticity distribution that favors deceleration of the leeside flow at the ground. This process of leeside flow deceleration, as well as the subsequent time evolution of the wake, is illustrated through a series of numerical initial-value problems involving flows past 2D and 3D barriers. It is proposed that the initiation of the wake flow in these stratified problems resembles the flow produced by a retracting piston in shallow-water theory.