Unsteady atmospheric vortices in a stratified atmosphere

Similarity equations relating to unsteady vortices in a stratified atmosphere are re-examined. A spectrum of solutions wider than hitherto reported in the literature has been found. The solutions relate to one- and two-cell vortices such that the radial and axial velocities are zero at large distances from the axis of the vortex. Far from the axis, the radial velocity is directed to the axis, whereas close to the axis, it can be directed towards the axis (for one-cell solutions) or away from it (for two-cell solutions). The axial velocity can be an up-draught or a system of up-draughts and down-draughts. It is also shown that small changes in the azimuthal velocity can result in large changes in the vertical and radial velocities of the system.