Doohan, P., Willis, A. orcid.org/0000-0002-2693-2952 and Hwang, Y. (2019) Shear stress-driven flow : the state space of near-wall turbulence as Reτ → ∞. Journal of Fluid Mechanics, 874. pp. 606-638. ISSN 0022-1120
Abstract
An inner-scaled, shear stress-driven flow is considered as a model of independent near-wall turbulence as Re τ → ∞. In this limit, the model is applicable to the near-wall region and the lower part of the logarithmic layer of various parallel shear flows, including turbulent Couette flow, Poiseuille flow and Hagen-Poiseuille flow. The model is validated against damped Couette flow and there is excellent agreement between the velocity statistics and spectra for y + < 40. A near-wall flow domain of similar size to the minimal unit is analysed from a dynamical systems perspective. The edge and fifteen invariant solutions are computed, the first discovered for this flow configuration. Through continuation in the spanwise width L + z , the bifurcation behaviour of the solutions over the domain size is investigated. The physical properties of the solutions are explored through phase portraits, including the energy input and dissipation plane, and streak, roll and wave energy space. Finally, a Reynolds number is defined in outer units and the high-Re asymptotic behaviour of the equilibria is studied. Three lower branch solutions are found to scale consistently with vortex-wave interaction (VWI) theory, with wave forcing localising around the critical layer.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 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: | Turbulent Flows; Nonlinear Dynamical Systems |
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: | 21 Jun 2019 09:42 |
Last Modified: | 26 Jun 2020 08:33 |
Status: | Published |
Publisher: | Cambridge University Press |
Refereed: | Yes |
Identification Number: | 10.1017/jfm.2019.472 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:147136 |