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.