Cyclogenesis in a conditionally unstable moist baroclinic atmosphere

This paper reports the analytic solution of the instability problem of a conditionally unstable moist baroclinic basic flow for a general heating profile and the quantitative results for the special case of a uniform heating profile. There are 4 discrete eigenmodes arising from the existence of potential vorticity (PV) anomalies at only 4 discrete vertical levels in this generic model setting. There is one unstable mode for a weak to moderate heating. The growth rate and wavelength of the most unstable moist Eady mode have a strongly nonlinear dependence on the heating intensity in this range. Significant enhancement in the growth rate and reduction in the wavelength of this mode are found when the heating intensity is increased to a moderate value. The trends of variation of these instability properties with the heating intensity are reversed for stronger heating due to a strong interference of the interactions among the PV anomalies at the four levels. The phase velocity of this mode is affected relatively little by the condensational heating. For a moderate to strong heating, there are two new branches of shorter unstable modes. The modes of one branch have a large phase velocity and are largely confined between the model tropopause and the top of the heating layer. They primarily arise from the interaction of the PV anomalies at those 2 levels. The modes of the other branch are largely confined between the model surface and the bottom of the heating layer with a small phase velocity arising from a similar dynamical origin. The self-induced heating and the basic baroclinic shear are jointly responsible for the existence of these modes. These 2 branches of mode may coexist. The energetic of the unstable modes is consistent with such a dynamical interpretation.