On the stability of the swirling jet shear layer

Abstract

The linear stability analysis of a simple model of a swirling jet illuminates the competition and interaction of centrifugal and Kelvin–Helmholtz instabilities. By employing potential theory, analytical expressions are derived for the growth rate and propagation velocity of both axisymmetric and helical waves. The results show that centrifugally stable flows become destabilized by sufficiently short Kelvin–Helmholtz waves. The asymptotic limits demonstrate that for long axisymmetric waves the centrifugal instability dominates, while long helical waves approach the situation of a Kelvin–Helmholtz instability in the azimuthal direction, modulated by a stable or unstable centrifugal stratification. Both short axisymmetric and short helical waves converge to the limit of a plane Kelvin–Helmholtz instability feeding on the azimuthal vorticity.