Observations of Instabilities in Stratified Taylor-Couette Flow

Inviscid analyses by Molemaker et al. (Phys. Rev. Lett. 86, 5270, 2001) and by Dubrulle et al. (Astron. Astrophys. 29, 1, 2005) predicted that a fluid with a vertically varying density will be less stable than a uniform fluid when the fluid is contained inside a concentric rotating cylinder system and subject to anticyclonic shear. Dubrulle et al. named this instability the stratorotational instability and a subsequent viscous theory by Shalybkov and Rudiger (Astron. Astrophys. 438, 411, 2005) hypothesized that such stratified flow is stable when the ratio of outer and inner cylinder rotation rates $\mu$ is less than the ratio of the inner and outer cylinder radii $\eta$. Le Bars and Le Gal (Phys. Rev. Lett. 99, 064502, 2007) confirmed this hypothesis in experiments for $Re<1200$ with $Re\equiv (r_o-r_i)\Omega_i r_i/\nu$. However, we find the SRI exists for $\mu>\eta$ when the density gradient is large. We also find that the axial wavelength scales linearly with the internal Froude number and that the onset of the SRI is suppressed for $Re>4000$, a region previously unexplored in experiments. For $Re>8000$, we find that the fluid does not exhibit the SRI but transitions to a spatially nonperiodic state that mixes the fluid.