Orlanski, I., and B. B. Ross, 1984: The evolution of an observed cold front. Part II: mesoscale dynamics. Journal of the Atmospheric Sciences, 41 (10), 1669-1703.

Abstract: A detailed analysis is made of a three-dimensional numerical simulation of the evolution of an observed moist frontal system over a 48 h period. The simulated front undergoes an initial period of frontogenetic growth, characterized by an alignment of vertical vorticity and horizontal convergence near the surface. The front then evolves to a mature, quasi-steady state as the line of maximum convergence moves ahead of the maximum vorticity. This phase shift is shown to be the result of a negative feedback mechanism which inhibits further vorticity growth while reducing the amount of viscous damping required to achieve a steady state. The influence of viscosity and surface drag upon this mechanism is also assessed.
When moisture is included in the numerical solution, the squall line which develops along the front exhibits a dual updraft structure with low-level convergence near the nose of the front and midlevel convergence located 100 km to the rear at a height of 3 km. This configuration is very similar to that found by Ogura and Liou in their analysis of an Oklahoma squall line not associated with a cold front.
Analysis of the equations of motion within the convective zone of the mature squall line shows the diabatic heating to be closely balanced by adiabatic cooling due to vertical temperature advection. As a result, the only net warming within this region occurs as adiabatic warming in the clear air outside of the cloud zone.
A linear, two-layer, dry model containing stable lower and unstable upper layers is shown to reproduce the dual updraft structure for certain low-level wind intensities without requiring microphysics. Also, for all wind conditions, this simple model produces strong convergence at the interface between the two layers. This suggests that the occurrence of a convergence maximum at the level of free convection should be a common feature of convectively unstable cloud systems.