Unsteady convective atmospheric vortices

The convective atmospheric vortex models of Kuo (1966) and Kendall (1978) are extended to allow the formulation of similarity equations for the unsteady vortex arising from an ambient flow with unstable stratification and rotation. In particular, a new analytical solution is found which allows flow at large radius that is more physically realistic than in any earlier solutions. Additional unsteady solutions are obtained numerically but at large radius these are subject to the limitations of earlier solutions.