Stability of Coaxial Rotating Jet and Vortex of Different Densities

Abstract

Stability of a rotating axisymmetric jet surrounded by a potential vortex to infinitesimal disturbances in the inviscid incompressible fluid approximation is considered. The jet and the vortex may have different densities. The dispersion relation for angular frequency covers a wide range of configurations. A rotating or nonrotating jet in a medium at rest is unstable for all density ratios. A vortex enclosing a stagnant core is stable for axisymmetric disturbances for all densities. A vortex with a rotating core without axial velocity is unstable if the jet fluid density is greater than the vortex fluid density. The jet vortex system is destabilized by the slightest amount of axial velocity; increasing jet fluid density has a destabilizing effect. A vortex around a rotating or nonrotating jet of any density suppresses some of the large scale instabilities. In general, axial velocity of the jet, its rotation, and increase in its density have a destabilizing effect. The surface tension between the two fluids has a stabilizing effect for small scale disturbances.