Deep and shallow quasi-geostrophic flow over mountains

Abstract

The effect of a finite density scale height on steady quasi-geostrophic flow over an isolated mountain is examined using analytic solutions for an isothermal, uniformly stratified, vertically semi-infinite atmosphere on an f -plane. A nondimensional measure of the depth of flow and hence of the importance of the vertical density variations of the basic state is the ratio of the Rossby height of the flow, H R , to the density scale height H . Here H R = fa / N where a is the mountain halfwidth and N is the buoyancy frequency. The flow is deep for Λ = H R / H ≥ O(1) and shallow for Δ ⋍ 0. It is found that the mountain-induced surface anticyclone is stronger for a deep flow than for a shallow one. Unlike the shallow case, no region of cyclonic vorticity is generated. The enhanced response for deep flow decreases the critical mountain height necessary for the formation of a stagnation point (e.g., Taylor cone). This critical height decreases with decreasing scale height and with increasing stratification. In addition, the mountain's influence decays less rapidly with height for deep flow. The far-field response for the deep case exhibits a circulation consistent with the lift force acting on the mountain. Since it is shown that the volume of vertically displaced fluid at any level equals the mountain volume, the transmission of the lift to the fluid arises from the decreasing density field, while volume expansion generates the far-field anticyclonic vorticity. These results hold for both the standard and the modified quasi-geostrophic equations. In the modified theory, however, the mountain surface is not isentropic. DOI: 10.1111/j.1600-0870.1986.tb00462.x