Turbulent Taylor-Couette flow with stationary inner cylinder

Abstract: A series of direct numerical simulations of Taylor-Couette (TC) flow, the flow between two coaxial cylinders, with the outer cylinder rotating and the inner one fixed, were performed. Three cases, with outer cylinder Reynolds numbers $Re_o$ of $Re_o=5.5\cdot10^4$, $Re_o=1.1\cdot10^5$ and $Re_o=2.2\cdot10^5$ were considered. The radius ratio $\eta=r_i/r_o$ was fixed to $\eta=0.909$ to mitigate the effects of curvature. The vertical aspect ratio $\Gamma$ was fixed to $\Gamma=2.09$. Being linearly stable, outer cylinder rotation TC flow is known to have very different behavior than pure inner cylinder rotation TC flow. Here, we find that the flow nonetheless becomes turbulent, but the torque required to drive the cylinders and level of velocity fluctuations was found to be smaller than those for pure inner cylinder rotation at comparable Reynolds numbers. The mean angular momentum profiles showed a large gradient in the bulk, instead of the constant angular momentum profiles of pure inner cylinder rotation. The near-wall mean and fluctuation velocity profiles were found to coincide only very close to the wall, showing large deviations from both pure inner cylinder rotation profiles and the classic von Karman law of the wall elsewhere. Finally, transport of angular velocity was found to occur mainly through intermittent bursts, and not through wall-attached large-scale structures as is the case for pure inner cylinder rotation.