Stability of density-stratified viscous Taylor-Couette flows

Abstract

We consider the stability of density-stratified viscous Taylor-Couette flow using the Boussinesq approximation, but without any use of the short-wave approximation. Flows which are unstable according to the Rayleigh criterion (μ̂ < 1, as stressed by Yavneh, McWilliams & Molemaker (2001). However, if the rotation law is too flat, fulfilling the condition μ̂ > η̂, we never found unstable modes. The Reynolds numbers grow rapidly to very large values as this limit is approached (see Figs. 3 and 4). Also striking is that the marginal stability lines for the higher m penetrate less and less into the region beyond the Rayleigh line, so that we have to consider the stratorotational instability as a "low-m instability". Finally, we briefly discuss the applicability of these results to the stability problem of accretion disks, with their strong density stratification and rapid rotation. © ESO 2005.