Abstract
Theoretical models of frontogenesis using the semi‐geostrophic approximation have imagined the process to occur between air‐masses whose only difference is their respective surface potential temperature. This is equivalent to assuming the Ertel potential vorticity (PV) to be constant in the troposphere and that there is a horizontal temperature gradient at the surface. For many cases this is a good approximation and furthermore the constraint on the dynamics of such uniform PV is a fundamental one. In some locations and synoptic situations, however, the air‐masses not only have a different surface potential temperature but also have significantly different static stability. In this case the PV, as well as the boundary potential temperature, has a horizontal variation. Here we take the variation in PV to be entirely due to the static stability, holding f constant, although in reality there is a contribution due to the variation of f with latitude. Examples of this type of frontogenesis are coastal fronts, where the air over the ocean has a different stability to that over the land, some mesoscale polar vortices which form at the ice margin, and cold fronts with polar air moving southwards over a warmer ocean giving enhanced convection and hence lower stability.
Results are presented from a two‐dimensional semi‐geostrophic model of frontogenesis between two rigid horizontal surfaces to illustrate the effects of variations in PV. In many cases the conclusions can be deduced from the geometrical aspects of the problem. If the cold air‐mass has the larger stability the frontogenesis at the lower boundary proceeds at an increased rate compared to that at the upper boundary. Indeed it is possible for a particular stability difference between the air‐masses to eliminate the upper frontogenesis completely, producing a purely lower tropospheric phenomenon. the geometrically converse conclusions apply if the cold air‐mass has the smaller stability. the results also allow the role of the mean value of the PV or stability of the two air‐masses to be described.