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$R_{{\it\Omega}}$as dimensionless parameters, the transition from TCF to RPCF can be studied continuously without singularities. Already for radius ratios${\it\eta}\geqslant 0.9$we find that the simulation results for various radius ratios and for RPCF collapse as a function of$R_{{\it\Omega}}$, indicating a turbulent behaviour common to both systems. We observe this agreement in the torque, mean momentum transport, mean profiles and turbulent fluctuations. Moreover, in TCF and RPCF for$R_{{\it\Omega}}>0$, the profiles in the central region 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${\it\eta}\rightarrow 1$. The corresponding torque maximum disappears as well. Instead, two new maxima of different origin appear for${\it\eta}\geqslant 0.9$and RPCF, a broad and a narrow one, in contrast to the results for smaller${\it\eta}$. The broad maximum at$R_{{\it\Omega}}=0.2$is connected with a strong vortical flow and can be reproduced by streamwise-invariant simulations. The narrow maximum at$R_{{\it\Omega}}=0.02$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$Re_{S}=2\times 10^{4}$, our simulations suggest that it will dominate at even higher$Re_{S}$.