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 $R{e}_S$ and rotation number $R_{\Omega }$ as dimensionless parameters, the transition from TCF to RPCF can be studied continuously without singularities. Already for radius ratios $\eta \ge 0.9$ 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 $\eta \to 1$. The corresponding torque maximum disappears as well. Instead, two new maxima of different origin appear for $\eta \ge 0.9$ 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 $R{e}_S$ and is accompanied by an efficient and correlated momentum transport by the mean flow. Since the narrow maximum is of larger amplitude for $R{e}_S=2\cdot 10^4$, our simulations suggest that it will dominate at even higher $R{e}_S$.

References in corpus (8)

• Multiple states in highly turbulent Taylor-Couette flow
• Exploring the phase diagram of fully turbulent Taylor-Couette flow
• Logarithmic temperature profiles in turbulent Rayleigh-Bénard convection
• Direct Numerical Simulation of turbulent Taylor-Couette flow
• Effects of the computational domain size on direct numerical simulations of Taylor-Couette turbulence with stationary outer cylinder
• Effect of the number of vortices on the torque scaling in Taylor-Couette flow
• On self-sustaining processes in Rayleigh-stable rotating plane Couette flows and subcritical transition to turbulence in accretion disks
• Turbulent states in plane Couette flow with rotation

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• Calculation of the mean velocity profile for strongly turbulent Taylor--Couette flow and arbitrary radius ratios
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