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Momentum transport in Taylor–Couette flow with vanishing curvature

Published online by Cambridge University Press:  04 February 2016

Hannes J. Brauckmann ,
Matthew Salewski  and
Bruno Eckhardt
Hannes J. Brauckmann
Affiliation:
Fachbereich Physik, Philipps-Universität Marburg, Renthof 6, D-35032 Marburg, Germany
Matthew Salewski
Affiliation:
Fachbereich Physik, Philipps-Universität Marburg, Renthof 6, D-35032 Marburg, Germany Department of Aerodynamics and Fluid Mechanics, Brandenburg University of Technology Cottbus-Senftenberg, Siemens-Halske-Ring 14, D-03046 Cottbus, Germany
Bruno Eckhardt*
Affiliation:
Fachbereich Physik, Philipps-Universität Marburg, Renthof 6, D-35032 Marburg, Germany J. M. Burgerscentrum, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands
*
†Email address for correspondence: bruno.eckhardt@physik.uni-marburg.de
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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 $Re_{S}$.

JFM classification

Turbulent Flows: Rotating turbulence Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 790 , 10 March 2016 , pp. 419 - 452
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© 2016 Cambridge University Press 

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