We examine the rotation and propagation of the supercell-like convection produced by our three-dimensional cloud model. The rotation in the supercell is studied in terms of the conservation of equivalent potential vorticity and V. Bjerknes' first circulation theorem; neither of these have been used previously in this connection, and we find that they significantly contribute to the current level of understanding in this area. Using these we amplify the findings of our previous work in which we found that the source of midlevel rotation is the horizontally oriented vorticity associated with the environmental shear, while the low-level rotation derives from the baroclinic generation of horizontally oriented vorticity along the low-level cold-air boundary. We further demonstrate that these same processes that amplify the low-level rotation also produce the distinctive cloud feature known as the `wall cloud.'We find that the thunderstorm propagates rightward primarily because of the favorable dynamic vertical pressure gradient that, owing to storm rotation, is always present on the right flank of the updraft. Simulations without precipitation physics demonstrate that this rightward propagation occurs even in the absence of a cold outflow and gust front near the surface.