ON THE STABILITY OF THE SWIRLING JET SHEAR-LAYER

The linear stability analysis of a simple model of a swirling jet illu minates the competition and interaction of centrifugal and Kelvin-Helm holtz instabilities. By employing potential theory, analytical express ions are derived for the growth rate and propagation velocity of both axisymmetric and helical waves. The results show that centrifugally st able flows become destabilized by sufficiently short Kelvin-Helmholtz waves. The asymptotic limits demonstrate that for long axisymmetric wa ves the centrifugal instability dominates, while long helical waves ap proach the situation of a Kelvin-Helmholtz instability in the azimutha l direction, modulated by a stable or unstable centrifugal stratificat ion. Both short axisymmetric and short helical waves converge to the l imit of a plane Kelvin-Helmholtz instability feeding on the azimuthal vorticity.