Momentum transport in Taylor-Couette flow with vanishing curvature

Abstract

We numerically study turbulent Taylor-Couette flow (TCF) between two independently rotating cylinders and the transition to rotating plane Couette flow (RPCF) in the limit of infinite radii. By using the shear Reynolds number $Re_S$ and rotation number $R_\Omega$ as dimensionless parameters, the transition from TCF to RPCF can be studied continuously without singularities. Already for radius ratios $\eta\geq0.9$ we find that the simulation results for various radius ratios and for RPCF collapse as a function of $R_\Omega$, indicating a turbulent behaviour common to both systems. We observe this agreement in the torque, mean momentum transport, mean profiles, and turbulent fluctuations. Moreover, the central profiles in TCF and RPCF for $R_\Omega>0$ are found to conform with inviscid neutral stability. Intermittent bursts that have been observed in the outer boundary layer and have been linked to the formation of a torque maximum for counter-rotation are shown to disappear as $\eta \rightarrow 1$. The corresponding torque maximum disappears as well. Instead, two new maxima of different origin appear for $\eta\geq0.9$ and RPCF, a broad and a narrow one, in contrast to the results for smaller $\eta$. The broad maximum at $R_\Omega=0.2$ is connected with a strong vortical flow and can be reproduced by streamwise invariant simulations. The narrow maximum at $R_\Omega=0.02$ only emerges with increasing $Re_S$ and is accompanied by an efficient and correlated momentum transport by the mean flow. Since the narrow maximum is of larger amplitude for $Re_S=2\cdot10^4$, our simulations suggest that it will dominate at even higher $Re_S$.