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Uncovering Townsend’s wall-attached eddies in low-Reynolds-number wall turbulence

Published online by Cambridge University Press:  26 February 2020

Cheng Cheng ,
Weipeng Li Open the ORCID record for Weipeng Li [Opens in a new window] ,
Adrián Lozano-Durán Open the ORCID record for Adrián Lozano-Durán [Opens in a new window]  and
Hong Liu
Cheng Cheng
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai200240, PR China
Weipeng Li*
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai200240, PR China
Adrián Lozano-Durán
Affiliation:
Center for Turbulence Research, Stanford University, CA94305, USA
Hong Liu
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai200240, PR China
*
†Email address for correspondence: [email protected]
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Abstract

A growing body of studies supports the existence of Townsend’s wall-attached eddies in wall turbulence under the condition of sufficiently high Reynolds numbers. In the present work, we uncover the signature of Townsend’s wall-attached eddies in low-Reynolds-number wall turbulence. To this end, we use a three-dimensional clustering methodology to identify the wall-attached structures of intense streamwise and spanwise velocity fluctuations in turbulent channel flows at four Reynolds numbers ($Re_{\unicode[STIX]{x1D70F}}=186$, 358, 547 and 934). The statistical properties of the structures, such as their geometric self-similarity, population density and statistical moments, are investigated and compared with the predictions of the attached-eddy model. Particular attention is paid to the asymmetries between high- and low-speed wall-attached streaky structures, and we show that the former are a closer representation of the wall-attached eddies. This observation is ascribed to the differences between the sweep and ejection events associated with the streaks. We also examine the Reynolds-number effects on the statistical properties of the structures, and find that the signature of attached eddies can be observed within the Reynolds-number range under scrutiny. Our approach paves the way to cost-efficient model development and flow prediction using computationally more affordable simulations at low Reynolds numbers.

JFM classification

Boundary Layers: Boundary layer structure Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 889 , 25 April 2020 , A29
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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