Conditional Convective Heating in a Baroclinic Atmosphere: A Model of Convective Frontogenesis

It is shown here that there exists a regime of balanced frontogenesis that is forced almost entirely by the diabatic hating due to convection at a front. This theory is explored in the context of the two-dimensional semigeostrophic equations with an Eady basic state: convection is parameterized to be dependent on the low-level moisture convergence of the cross-frontal ageostrophic flow, in accordance with recent diagnostic studies. The significant result is that the growth rate of the convective frontal system becomes independent of the total wavelength of the domain once the diabatic heating exceeds a relatively large threshold magnitude. In this regime the frontal zone has a width and structure dependent on the heating magnitude but not on the wavelength. The system is described as “solitary” or “isolated” since the dynamics are self-contained and independent of the far field. The energetics of the system have a diabatic conversion that is an order of magnitude greater than that due to the large-scale alongfront temperature gradient. The large-scale forcing is, however, necessary as a catalyst in maintaining a weak ageostrophic convergence that allows the convective heating to be triggered. The constraint of alongfront geostrophic balance means that convective forcing alone cannot maintain frontogenesis. It is suggested that the dynamics exhibited by the convectively dominated front may also be important in the study of midlatitude squall lines. The propagation and dynamics of the front are interpreted in terms of the notion of a “diabatic Rossby wave.”