Unsteady stratified swirling shear flows

Exact solutions of the Euler equations are used to describe the effect of density stratification on unsteady swirling shear flows of an incompressible fluid. Typically, in air, this stratification is produced by variations in the temperature and the concentration of moisture. In these flows, the horizontal pressure gradients vary with time and horizontal position, but not with height. The variations in the horizontal components of acceleration are produced solely by the fact that the fluid is stratified. The complex flow patterns model some of the main features of the flows that occur at the core of a tornado during both its spin-up and spin-down stages.