Observations of the stratorotational instability in rotating concentric cylinders

We study the stability of density stratified flow between corotating vertical cylinders with rotation rates ohm(o) < ohm(i) and radius ratio r(i)/r(o) = 0.877, where subscripts o and i refer to the outer and inner cylinders. Just as in stellar and planetary accretion disks, the flow has rotation, anticyclonic shear, and a stabilizing density gradient parallel to the rotation axis. The primary instability of the laminar state leads not to axisymmetric Taylor vortex flow but to a nonaxisymmetric stratorotational instability (SRI). The present work extends the range of Reynolds numbers and buoyancy frequencies [N = root(-g/rho)(d rho/dz)] examined in previous experiments. We present the first experimental results for the axial wavelength. of the instability as a function of the internal Froude number, Fr = ohm(i)/ N; lambda increases by nearly an order of magnitude over the range of Fr examined. For small outer cylinder Reynolds number, the SRI occurs for inner inner Reynolds number larger than for the axisymmetric Taylor vortex flow (i.e., the SRI is more stable). For somewhat larger outer Reynolds numbers the SRI occurs for smaller inner Reynolds numbers than Taylor vortex flow and even below the Rayleigh stability line for an inviscid fluid. Shalybkov and Rudiger [Astron. Astrophys. 438, 411 (2005)] proposed that the laminar state of a stably stratified rotating shear flow should be stable for ohm(o)/ohm(i) > r(i)/r(o), but we find that this stability criterion is violated for N sufficiently large. At large Reynolds number the primary instability is not the SRI but a previously unreported nonperiodic state that mixes the fluid.