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Invariant solutions of minimal large-scale structures in turbulent channel flow for $Re_{\unicode[STIX]{x1D70F}}$ up to 1000

Published online by Cambridge University Press:  01 August 2016

Yongyun Hwang ,
Ashley P. Willis  and
Carlo Cossu Open the ORCID record for Carlo Cossu [Opens in a new window]
Yongyun Hwang*
Affiliation:
Department of Aeronautics, Imperial College London, South Kensington, London SW7 2AZ, UK
Ashley P. Willis
Affiliation:
School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH, UK
Carlo Cossu
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT), CNRS Université de Toulouse, Allée du Pr. Camille Soula, F-31400 Toulouse, France
*
†Email address for correspondence: y.hwang@imperial.ac.uk
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Abstract

Understanding the origin of large-scale structures in high-Reynolds-number wall turbulence has been a central issue over a number of years. Recently, Rawat et al. (J. Fluid Mech., vol. 782, 2015, pp. 515–540) have computed invariant solutions for the large-scale structures in turbulent Couette flow at $Re_{\unicode[STIX]{x1D70F}}\simeq 128$ using an overdamped large-eddy simulation with the Smagorinsky model to account for the effect of the surrounding small-scale motions. Here, we extend this approach to Reynolds numbers an order of magnitude higher in turbulent channel flow, towards the regime where the large-scale structures in the form of very-large-scale motions (long streaky motions) and large-scale motions (short vortical structures) emerge energetically. We demonstrate that a set of invariant solutions can be computed from simulations of the self-sustaining large-scale structures in the minimal unit (domain of size $L_{x}=3.0h$ streamwise and $L_{z}=1.5h$ spanwise) with midplane reflection symmetry at least up to $Re_{\unicode[STIX]{x1D70F}}\simeq 1000$ . By approximating the surrounding small scales with an artificially elevated Smagorinsky constant, a set of equilibrium states are found, labelled upper- and lower-branch according to their associated drag. It is shown that the upper-branch equilibrium state is a reasonable proxy for the spatial structure and the turbulent statistics of the self-sustaining large-scale structures.

JFM classification

Nonlinear Dynamical Systems: Low-dimensional models Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Turbulent Flows: Turbulent boundary layers

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Type
Rapids
Information
Journal of Fluid Mechanics , Volume 802 , 10 September 2016 , R1
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© 2016 Cambridge University Press 

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