Hwang, Y., Willis, A.P. and Cossu, C. (2016) Invariant solutions of minimal large-scale structures in turbulent channel flow for Re_τ up to 1000. Journal of Fluid Mechanics, 802. R1. ISSN 0022-1120
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., 2015, 782, p515) have computed invariant solutions for the large-scale structures in turbulent Couette flow at Reτ ≃ 128 using an over-damped LES with the Smagorinsky model to account for the effect of the surrounding small-scale motions. Here, we extend this approach to an order of magnitude higher Reynolds numbers 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) energetically emerge. 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 Lx = 3.0h streamwise and Lz = 1.5h spanwise) with midplane reflection symmetry at least up to Reτ ≃ 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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 Cambridge University Press. This is an author produced version of a paper subsequently published in Journal of Fluid Mechanics. Article available under the terms of the CC-BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/). |
Keywords: | low-dimensional models; nonlinear dynamical systems; turbulent boundary layers |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 11 Jul 2016 13:16 |
Last Modified: | 04 May 2020 13:59 |
Published Version: | http://dx.doi.org/10.1017/jfm.2016.470 |
Status: | Published |
Publisher: | Cambridge University Press (CUP) |
Refereed: | Yes |
Identification Number: | 10.1017/jfm.2016.470 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:102233 |