Semigeostrophic Flow over Orography in a Stratified Rotating Atmosphere. Part III. Evaluation of a Lee Cyclogenesis Mechanism

Abstract

Three-dimensional, adiabatic, inviscid flow over orography is examined by means of a semigeostrophic model expressed in isentropic coordinates. A nondimensional mountain height ε/D ≲ 0.5, based on the deformation depth D ∼ 3 × 103 m, and a Rossby number Ro ≲ 0.3, based on the mountain breadth L ≲ 3.5 × 105 m and a constant Coriolis parameter, f, provide constraints on the flow field. Vortex tube stretching is evaluated as a mechanism for lee cyclogenesis. It is shown that the convergence of both planetary and geostrophic relative vorticity filaments enhances geostrophic cyclonic vorticity in a semi-geostrophic model. In contrast, ageostrophic cyclonic vorticity is weakened by convergence. These features are illustrated in a numerical simulation of flow over an isentropic isolated mountain. The initial state is characterized by an isolated region of ageostrophic cyclonic vorticity in the lee of the obstacle, accompanied by convergence. A potential vorticity disturbance, associated with an internal cold front and a two-dimensional upper-level jet, is advected over the isolated obstacle. In principle, the coupling of ascending motion ahead of the disturbance with descending motion in the lee provides vortex tube stretching. It is shown that this mechanism does not initiate lee cyclogenesis in either a quasi-geostrophic or semigeostrophic model with isentropic boundaries. In particular, horizontal convergence and vertical stretching are significantly diminished by the intrusion of weakly stratified air into the lee. Additionally, the ageostrophic cyclonic vorticity present in the initial state is not effectively enhanced by vortex tube stretching, according to the ageostrophic vorticity theorem for semigeostrophic flow. The absence of both blocking by the obstacle and potential temperature gradients along the lower boundary is suggested as a possible reason for the failure of vortex tube stretching to initiate lee cyclogenesis in the model presented here.