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Non-universal scaling transition of momentum cascade in wall turbulence

Published online by Cambridge University Press:  24 May 2019

Xi Chen Open the ORCID record for Xi Chen [Opens in a new window] ,
Fazle Hussain Open the ORCID record for Fazle Hussain [Opens in a new window]  and
Zhen-Su She Open the ORCID record for Zhen-Su She [Opens in a new window]
Xi Chen*
Affiliation:
Department of Mechanical Engineering, Texas Tech University, TX 79409, USA
Fazle Hussain*
Affiliation:
Department of Mechanical Engineering, Texas Tech University, TX 79409, USA
Zhen-Su She*
Affiliation:
State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics, College of Engineering, Peking University, Beijing 100871, China
*
†Email addresses for correspondence: [email protected], [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected], [email protected]
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Abstract

As a counterpart of energy cascade, turbulent momentum cascade (TMC) in the wall-normal direction is important for understanding wall turbulence. Here, we report an analytic prediction of non-universal Reynolds number ($Re_{\unicode[STIX]{x1D70F}}$) scaling transition of the maximum TMC located at $y_{p}$. We show that in viscous units, $y_{p}^{+}$ (and $1+\overline{u^{\prime }v^{\prime }}_{p}^{+}$) displays a scaling transition from $Re_{\unicode[STIX]{x1D70F}}^{3/7}$ ($Re_{\unicode[STIX]{x1D70F}}^{-6/7}$) to $Re_{\unicode[STIX]{x1D70F}}^{3/5}$ ($Re_{\unicode[STIX]{x1D70F}}^{-3/5}$) in turbulent boundary layer, in sharp contrast to that from $Re_{\unicode[STIX]{x1D70F}}^{1/3}$ ($Re_{\unicode[STIX]{x1D70F}}^{-2/3}$) to $Re_{\unicode[STIX]{x1D70F}}^{1/2}$ ($Re_{\unicode[STIX]{x1D70F}}^{-1/2}$) in a channel/pipe, countering the prevailing view of a single universal near-wall scaling. This scaling transition reflects different near-wall motions in the buffer layer for small $Re_{\unicode[STIX]{x1D70F}}$ and log layer for large $Re_{\unicode[STIX]{x1D70F}}$, with the non-universality being ascribed to the presence/absence of mean wall-normal velocity $V$. Our predictions are validated by a large set of data, and a probable flow state with a full coupling between momentum and energy cascades beyond a critical $Re_{\unicode[STIX]{x1D70F}}$ is envisaged.

JFM classification

Turbulent Flows: Turbulence theory
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 871 , 25 July 2019 , R2
Copyright
© 2019 Cambridge University Press 

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