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Statistics of turbulence in the energy-containing range of Taylor–Couette compared to canonical wall-bounded flows

Published online by Cambridge University Press:  06 October 2017

Dominik Krug Open the ORCID record for Dominik Krug [Opens in a new window] ,
Xiang I. A. Yang Open the ORCID record for Xiang I. A. Yang [Opens in a new window] ,
Charitha M. de Silva Open the ORCID record for Charitha M. de Silva [Opens in a new window] ,
Rodolfo Ostilla-Mónico ,
Roberto Verzicco Open the ORCID record for Roberto Verzicco [Opens in a new window] ,
Ivan Marusic  and
Detlef Lohse Open the ORCID record for Detlef Lohse [Opens in a new window]
Dominik Krug*
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Melbourne, Australia
Xiang I. A. Yang
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA
Charitha M. de Silva
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Melbourne, Australia
Rodolfo Ostilla-Mónico
Affiliation:
School of Engineering and Applied Sciences and Kavli Institute for Bionano Science and Technology, Harvard University, Cambridge, MA 02138, USA Kavli Institute for Theoretical Physics, Kohn Hall, University of California, Santa Barbara, CA 93106-4030, USA
Roberto Verzicco
Affiliation:
Dipartimento di Ingegneria Industriale, University of Rome ‘Tor Vergata’, Via del Politecnico 1, Roma 00133, Italy Physics of Fluids Group and Twente Max Planck Center, Department of Science and Technology, Mesa+ Institute, and J.M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
Ivan Marusic
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Melbourne, Australia
Detlef Lohse
Affiliation:
Physics of Fluids Group and Twente Max Planck Center, Department of Science and Technology, Mesa+ Institute, and J.M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
*
†Email address for correspondence: dominik.krug@unimelb.edu.au
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Abstract

Considering structure functions of the streamwise velocity component in a framework akin to the extended self-similarity hypothesis (ESS), de Silva et al. (J. Fluid Mech., vol. 823, 2017, pp. 498–510) observed that remarkably the large-scale (energy-containing range) statistics in canonical wall-bounded flows exhibit universal behaviour. In the present study, we extend this universality, which was seen to encompass also flows at moderate Reynolds number, to Taylor–Couette flow. In doing so, we find that also the transversal structure function of the spanwise velocity component exhibits the same universal behaviour across all flow types considered. We further demonstrate that these observations are consistent with predictions developed based on an attached-eddy hypothesis. These considerations also yield a possible explanation for the efficacy of the ESS framework by showing that it relaxes the self-similarity assumption for the attached-eddy contributions. By taking the effect of streamwise alignment into account, the attached-eddy model predicts different behaviour for structure functions in the streamwise and in the spanwise directions and that this effect cancels in the ESS framework – both consistent with the data. Moreover, it is demonstrated here that also the additive constants, which were previously believed to be flow dependent, are indeed universal at least in turbulent boundary layers and pipe flow where high Reynolds number data are currently available.

JFM classification

Turbulent Flows: Rotating turbulence Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 830 , 10 November 2017 , pp. 797 - 819
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© 2017 Cambridge University Press 

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