Stationary flow of a quasi-geostrophic, stratified atmosphere past finite amplitude obstacles

The stationary flow past finite amplitude bottom topography of a quasi-geostrophic atmosphere, uniform in wind and entropy stratification far from the obstacle, is studied on an f-plane. Analytic solutions for the two cases of finite slope (hemispheroid) and infinite slope (disc) mountains are discussed. The obstacles act on the flow in different ways in the two cases. In the case of finite slope the obstacle influences the model atmosphere through the lifting of isentropic surfaces near the lower boundary. The consequent shrinking of vortex tubes produces anti-cyclonic vorticity over the obstacle and, possibly, Taylor column formation, in agreement with previous results in the literature.

In the case of an infinite slope mountain a pronounced diffluence in the horizontal streamlines is produced near the obstacle. The total circulation, again associated with the lifting of isentropic surfaces, has to be prescribed in this case for the problem to be completely determined. However, the total disturbance does not vanish when the volume of the obstacle goes to zero, provided that its cross section remains finite. The implications for numerical modelling are discussed.