The stratorotational instability of Taylor-Couette flows of moderate Reynolds numbers

TL;DR

This paper investigates the conditions under which Taylor-Couette flows with axial density stratification become unstable, revealing that instability occurs within specific Reynolds number ranges and depends on stratification and rotation profiles.

Contribution

It provides new insights into the stability boundaries of stratified Taylor-Couette flows at moderate Reynolds numbers, including the effects of stratification and rotation profiles.

Findings

Instability occurs between a lower and upper Reynolds number for fixed stratification.

Maximum instability occurs at the potential flow (Rayleigh limit) and diminishes for flatter rotation profiles.

Wave numbers are mainly determined by the Froude number, affecting the shape and migration of instability patterns.

Abstract

In view of new experimental data the instability against adiabatic nonaxisymmetric perturbations of a Taylor-Couette flow with an axial density stratification is considered in dependence of the Reynolds number Re of rotation and the Brunt-V\"ais\"al\"a number Rn of the stratification. The flows at and beyond the Rayleigh limit become unstable between a lower and an upper Reynolds number (for fixed Rn). The rotation can thus be too slow or too fast for the stratorotational instability. The upper Reynolds number above which the instability decays, has its maximum value for the potential flow (driven by cylinders rotating according to the Rayleigh limit) and decreases strongly for flatter rotation profiles finally leaving only isolated islands of instability in the (Rn/Re) map. The maximal possible rotation ratio $\mu_{\rm max}$ only slightly exceeds the shear value of the quasi-uniform flow with $U_\phi\simeq$const. Along and between the lines of neutral stability the wave numbers of the instability patterns for all rotation laws beyond the Rayleigh limit are mainly determined by the Froude number Fr which is defined by the ratio between Re and Rn. The cells are highly prolate for Fr>1 so that measurements for too high Reynolds numbers become difficult for axially bounded containers. The instability patterns migrate azimuthally slightly faster than the outer cylinder rotates.