Orlanski, I., 1986: Localized baroclinicity: a source for meso-a cyclones. Journal of the Atmospheric Sciences, 43 (23), 2857-2885.

Abstract: An investigation has been made using a two-dimensional model to solve the initial value problem describing the evolution of disturbances on a mean baroclinic state. Three main problems are considered:

1. the effect of static stability on meso-baroclinic waves in a periodic domain;
2. downstream instability in an open domain and the effect of surface sensible heat; and
3. the effect of moisture on these unstable waves.

It was found that a flow can be unstable to mesoscale baroclinic waves. The requirement for instability of wavelengths less than 1000 km is similar to that for the planetary quasi-geostrophic baroclinic waves.
The Rossby penetration height can be derived from the solution of the unstable waves as these unstable waves will only be sensitive to the baroclinicity of the atmosphere in a layer with a depth delta.
The characteristics of the finite-amplitude unstable waves suggest that the limiting amplitude for the baroclinic waves is achieved by an energy cascade to frontal scales.
Perhaps the most signicant finding of this study has been to demonstrate the importance of localized surface heating in producing the more intense development of short baroclinic waves. It was found that waves in the presence of surface heating grew twice as fast as those without. These waves, having a depth on the order of the boundary layer and horizontal scales of a few hundred kilometers, can organize convergence of surface moisture on these scales. With the addition of moisture, the shallow meso-baroclinic wave will explosively develop into a deep intense system.