Instability mechanisms in swirling flows

We investigate the stability of the screened Rankine vortex with added plug flow where the azimuthal velocity decreases abruptly outside the core of the vortex. The jump in circulation is known to induce centrifugal and azimuthal Kelvin–Helmholtz instabilities. Their effect on the stability of the different azimuthal wave number m is discussed using physical considerations associated with asymptotic expansions and numerical computations of the dispersion relation. It is shown that the axial shear and centrifugal instability are active for all m, and that modes with |m|⩾2 are also destabilized by azimuthal shear. In contrast, the bending modes m=±1 are stabilized by a coupling with Kelvin waves in the core. Effects of rotation on the absolute/convective transition are also discussed. The absolute instability of positive helical modes is seen to be promoted by centrifugal instability and azimuthal shear.