The Inviscid Motion of a Vortex Pair in a Compressible and Stratified Atmosphere

Abstract

The movement of an inviscid vortex pair in a compressible atmosphere including bouyancy effects is described by analytic solutions. The effects of compressibility are dealt with in an isentropic atmosphere. The work of compression done by the atmosphere onthe vortex is entirely consumed by the isentropic change of the thermodynamic state of the vortex pair. The acceleration of the accompanying and apparent mass is given by the displacement of the two vortices towards each other. The effects of bouyancy are investigated by means of a two-dimensional, incompressible, inviscid vortex pair which is heavier than the ambient fluid. It turns out that the condition of pressure continuity across the separating streamline can be achieved only by assuming an increase in circulation of the two vortices. The mass accompanying the vortex pair under the effect of non-conservative forces converts a fraction of its gravity potential into an increase of stagnation pressure.