Where ζp is the potential vorticity; η the absolute vorticty; ƒc the Coriolis parameter; g is the gravitational force (negative cause it is directed towards the ground and dθ/dp is the difference in potential temperature divided by the difference in pressure. The above equation helps understand why at midlatitude cyclones form in the lee of mountain ranges. When air flows over a large barrier, such as the Alps, parameters like dθ/dp and the coriolis parameter, ƒc will undergo substantial change along the trajectory.
Fig. 1 Cyclogenesis at the lee of the Alps. (a) Vertical cross section and (b) a map of the airflow
As air approaches the Alps (Location A), some of the air near the surface will be blocked by the mountainous ridge, forcing higher air to rise over this blocked air (Location B). The column of air between point A and B will subsequently stretch, which leads to a decrease in dθ/dp. Hence from the above equation, ζ must thus become positive in order to conserve vorticity, meaning that if an air flow approaches a mountain ridge, the flow must/will turn cyclonically. Also, because of this poleward drift the coriolis parameter ƒc will increase, which will in turn reduce the change in ζ to conserve vorticity.As the air moves along, over the crest of the mountain, the column of air will compres. Vorticity is conserved and as a result of an increase in dθ/dp, anticyclonic flow will prevail (Location C). After the airflow has passed the crest of the mountain it will have a southerly component, resulting in a smaller ƒc . The relative vorticity will now slowly become positive. Alternatively, one can also say that the column of air is being stretched, leading to cyclonic flow and poleward deflection (Location D). When the airflow has reached its original latitude it will still have a poleward direction but slowly aquires more anticyclonic curvature. At location E the flow is being reversed to cyclonic direction. A Rossby wave has now been triggered. The conservation of potential vorticity explains how mountainous regions such as the Alps can induce Rossby waves. This process just described is called Lee cyclogenesis. It most favourably occurs when a low-level cold front approaches the Alps (McGinley, 1982)