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Characteristic scales of Townsend’s wall-attached eddies

Lozano-Durán, Adrián and Bae, Hyunji Jane (2019) Characteristic scales of Townsend’s wall-attached eddies. Journal of Fluid Mechanics, 868 . pp. 698-725. ISSN 0022-1120. https://resolver.caltech.edu/CaltechAUTHORS:20190508-161433596

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Abstract

Townsend (The Structure of Turbulent Shear Flow, 1976, Cambridge University Press) proposed a structural model for the logarithmic layer (log layer) of wall turbulence at high Reynolds numbers, where the dominant momentum-carrying motions are organised into a multiscale population of eddies attached to the wall. In the attached-eddy framework, the relevant length and velocity scales of the wall-attached eddies are the friction velocity and the distance to the wall. In the present work, we hypothesise that the momentum-carrying eddies are controlled by the mean momentum flux and mean shear with no explicit reference to the distance to the wall and propose new characteristic velocity, length and time scales consistent with this argument. Our hypothesis is supported by direct numerical simulation of turbulent channel flows driven by non-uniform body forces and modified mean velocity profiles, where the resulting outer-layer flow structures are substantially altered to accommodate the new mean momentum transfer. The proposed scaling is further corroborated by simulations where the no-slip wall is replaced by a Robin boundary condition for the three velocity components, allowing for substantial wall-normal transpiration at all length scales. We show that the outer-layer one-point statistics and spectra of this channel with transpiration agree quantitatively with those of its wall-bounded counterpart. The results reveal that the wall-parallel no-slip condition is not required to recover classic wall-bounded turbulence far from the wall and, more importantly, neither is the impermeability condition at the wall.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1017/jfm.2019.209DOIArticle
https://arxiv.org/abs/1901.04613arXivDiscussion Paper
ORCID:
AuthorORCID
Lozano-Durán, Adrián0000-0001-9306-0261
Bae, Hyunji Jane0000-0001-6789-6209
Additional Information:© 2019 Cambridge University Press. Received 16 January 2019; revised 4 March 2019; accepted 8 March 2019; first published online 16 April 2019. This work was supported by NASA under grant no. NNX15AU93A and by ONR under grant no. N00014-16-S-BA10. The authors thank Professor P. Moin, Professor J. Jiménez, Dr P. Johnson and Dr M. Cho for their insightful comments on previous versions of the manuscript.
Group:GALCIT
Funders:
Funding AgencyGrant Number
NASANNX15AU93A
Office of Naval Research (ONR)N00014-16-S-BA10
Subject Keywords:turbulence simulation, turbulence theory, turbulent boundary layers
Record Number:CaltechAUTHORS:20190508-161433596
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190508-161433596
Official Citation:Lozano-Durán, A., & Bae, H. (2019). Characteristic scales of Townsend’s wall-attached eddies. Journal of Fluid Mechanics, 868, 698-725. doi:10.1017/jfm.2019.209
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:95358
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:08 May 2019 23:46
Last Modified:19 Mar 2021 20:40

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