Non-axisymmetric instability of density-stratified Taylor-Couette flow

Abstract

The stability of density-stratified viscous Taylor-Couette flows is considered. We find that the nonaxisymmetric modes can be the most unstable ones. The nonaxisymmetric modes are unstable also beyond the Rayleigh line. For such modes the instability condition seems simply to be such that angular velocity should decrease with radius as stressed by Yavneh, McWilliams and Molemaker (2001). However, we never found unstable modes for too flat rotation laws fulfilling the condition that linear azimuthal velocity increase with radius. The Reynolds numbers rapidly grow to very high values if this limit is approached. The marginal stability lines for the higher azimuthal numbers do less and less enter the region beyond the Rayleigh line so that we might have to consider the stratorotational instability as a ‘low-m instability’. The results application to the accretion disk stability with their strong density stratification and fast rotation is shortly discussed.