Baroclinic instability in a two-layer, vertically semi-infinite domain

A quasi-geostrophic two-layer system with uniform, but different, shears and stratifications in two layers is examined for the occurrence of baroclinic instability. A derived necessary condition for instability requires that the shear in the upper, semi-infinite layer does not exceed a certain value (related to the stratification). For each configuration of the basic flow, there appear two short and two long neutral modes as well as a decaying and a growing mode at intermediate wavelengths. The short neutral modes are bound to either the surface or the interface, the long neutral modes to one or other of the layers. Instability appears if the foregoing modes propagate at a similar velocity. The depth of the waves is shown to be of less importance in the framework of potential vorticity dynamics. For some configurations, the growth rates surpass those of the classical Eady problem. Finally some consideration is given to the linkage between these results and the formation of polar lows.