Separate and Combined Effects of Static Stability and Shear Variation on the Baroclinic Instability of a Two-Layer Current

The instability characteristics of quasi-geostrophic disturbances are studied through the use of a linearized two-layer Eady model, in which both the static stability and the zonal current shear are uniform but different in each layer. It is shown that the qualitative character of the instability is determined by the sign of the basic-state potential vorticity gradient at the layer interface. There is a qualitative similarity between the effects of Richardson number variations due to changes in static stability and those due to changes in shear. When the Richardson number is different in each layer, the range of instability extends to shorter wavelengths. Furthermore, the instability characteristics, especially at short wavelengths, are affected not only by the variation of the Richardson number but also by the way in which the Richardson number is made up. The two-layer model is also used to construct an analog of Williams' (1974) continuous model of generalized Eady waves. The basic state in this case has zero potential vorticity gradient in the interior. The two-layer model results are in good agreement with Williams' results.