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Skin-friction generation by attached eddies in turbulent channel flow

Published online by Cambridge University Press:  03 November 2016

Matteo de Giovanetti ,
Yongyun Hwang  and
Haecheon Choi
Matteo de Giovanetti
Affiliation:
Department of Aeronautics, Imperial College London, South Kensington SW7 2AZ, UK
Yongyun Hwang*
Affiliation:
Department of Aeronautics, Imperial College London, South Kensington SW7 2AZ, UK
Haecheon Choi
Affiliation:
Department of Mechanical and Aerospace Engineering, Seoul National University, Seoul 08826, South Korea
*
†Email address for correspondence: y.hwang@imperial.ac.uk
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Abstract

Despite a growing body of recent evidence on the hierarchical organization of the self-similar energy-containing motions in the form of Townsend’s attached eddies in wall-bounded turbulent flows, their role in turbulent skin-friction generation is currently not well understood. In this paper, the contribution of each of these self-similar energy-containing motions to turbulent skin friction is explored up to $Re_{\unicode[STIX]{x1D70F}}\simeq 4000$. Three different approaches are employed to quantify the skin-friction generation by the motions, the spanwise length scale of which is smaller than a given cutoff wavelength: (i) FIK (Fukagata, Iwamoto, Kasagi) identity in combination with the spanwise wavenumber spectra of the Reynolds shear stress; (ii) confinement of the spanwise computational domain; (iii) artificial damping of the motions to be examined. The near-wall motions are found to continuously reduce their role in skin-friction generation on increasing the Reynolds number, consistent with the previous finding at low Reynolds numbers. The largest structures given in the form of very-large-scale and large-scale motions are also found to be of limited importance: due to a non-trivial scale interaction process, their complete removal yields only a 5–8 % skin-friction reduction at all of the Reynolds numbers considered, although they are found to be responsible for 20–30 % of total skin friction at $Re_{\unicode[STIX]{x1D70F}}\simeq 2000$. Application of all the three approaches consistently reveals that the largest amount of skin friction is generated by the self-similar motions populating the logarithmic region. It is further shown that the contribution of these motions to turbulent skin friction gradually increases with the Reynolds number, and that these coherent structures are eventually responsible for most of turbulent skin-friction generation at sufficiently high Reynolds numbers.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulence theory Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 808 , 10 December 2016 , pp. 511 - 538
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© 2016 Cambridge University Press 

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