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 Ω as dimensionless parameters, the transition from TCF to RPCF can be studied continuously without singularities. Already for radius ratios η 0.9 we find that the simulation results for various radius ratios and for RPCF collapse as a function of R Ω , 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 Ω > 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 η → 1. The corresponding torque maximum disappears as well. Instead two new maxima of different origin appear for η 0.9 and RPCF, a broad and a narrow one, in contrast to the results for smaller η. The broad maximum at R Ω = 0.2 is connected with a strong vortical flow and can be reproduced by streamwise invariant simulations. The narrow maximum at R Ω = 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 × 10 4 , our simulations suggest that it will dominate at even higher Re S .

Shearing and rotational forces in fluids can significantly alter the transport of momentum. A numerical investigation was undertaken to study the role of these forces using plane Couette flow subject to rotation about an axis perpendicular to both wall-normal and streamwise directions. Using a set of progressively higher Reynolds numbers up to Re = 5200, we find that the momentum flux, measured by the wall shear stress, for a given Re is a non-monotonic function of rotation number, Ro. For low-to-moderate Reynolds numbers, we find a maximum that is associated with flow fields that are dominated by downstream vortices and calculations of 2D vortices capture the maximum also quantitatively. For higher Reynolds numbers, a second stronger maximum emerges at smaller rotation numbers, closer to non-rotating plane Couette flow. It is carried by flows with a markedly 3D structure and cannot be captured by 2D vortex studies. As the Reynolds number increases, this maximum becomes stronger and eventually overtakes the one associated with the 2D flow state. C 2015 AIP Publishing LLC. [http://dx

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