The stratorotational instability of Taylor-Couette flows with moderate Reynolds numbers. Issue 6 (2nd November 2017) - Rüdiger, G.; Seelig, T.; Schultz, M.; Gellert, M.; Egbers, Ch.; Harlander, U.
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 (R e ) of rotation and the Brunt-Väisälä 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 (R n / R e ) map. The maximal possible rotation ratioμ max only slightly exceeds the shear value of the quasi-uniform flow withU ϕ ≃  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 numberF r which is defined by the ratio betweenR e and Rn . The cells are highly prolate forF r > 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.