Some Aspects of the Quasi-Geostrophic Flow over Mountains

Previous models of quasi-geostrophic airflow over mountains have used one or more of the following assumptions: 1) the Boussinesq approximation, 2) a rigid lid upper boundary condition, and 3) the idealization of an infinitely long ridge and two-dimensional flow. To investigate the physical nature of these assumptions, the flow of an unbounded, slightly compressible fluid over an isolated mountain is considered. In this case, the mountain feels a strong “lift” force acting to the left of the stream (in the Northern Hemisphere) due to the cross-stream pressure gradient, while the airstream receives an equally strong impulse to the right. Using the Kutta-Joukowski formula, the rightward impulse given to the airstream can be represented in terms of a far-field barotropic circulation which in turn is associated with the production of vorticity by volume expansion as the air parcels rise over the mountain.