Growth rate bounds and instability regions for azimuthal disturbances of inviscid swirling flows

General analytical results on the azimuthal unstable modes of variable density swirling flows between coaxial cylinders are obtained in the present paper. In particular estimates for the growth rate of unstable modes and instability regions within which the complex phase velocities should lie are obtained. All the results obtained indicate an important role for the basic flow vorticity and its variation on the instability of the swirling flows. The general analytical results obtained are illustrated in figures for various basic angular velocity profiles and a family of density profiles.