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Boundedness of the velocity derivative skewness in various turbulent flows

Published online by Cambridge University Press:  28 September 2015

R. A. Antonia ,
S. L. Tang ,
L. Djenidi  and
L. Danaila
R. A. Antonia
Affiliation:
School of Engineering, University of Newcastle, NSW 2308, Australia
S. L. Tang
Affiliation:
School of Engineering, University of Newcastle, NSW 2308, Australia Institute for Turbulence-Noise-Vibration Interaction and Control, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, PR China
L. Djenidi*
Affiliation:
School of Engineering, University of Newcastle, NSW 2308, Australia
L. Danaila
Affiliation:
CORIA CNRS UMR 6614, Université de Rouen, 76801 Saint Etienne du Rouvray, France
*
†Email address for correspondence: lyazid.djenidi@newcastle.edu.au
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Abstract

The variation of $S$, the velocity derivative skewness, with the Taylor microscale Reynolds number $\mathit{Re}_{{\it\lambda}}$ is examined for different turbulent flows by considering the locally isotropic form of the transport equation for the mean energy dissipation rate $\overline{{\it\epsilon}}_{iso}$. In each flow, the equation can be expressed in the form $S+2G/\mathit{Re}_{{\it\lambda}}=C/\mathit{Re}_{{\it\lambda}}$, where $G$ is a non-dimensional rate of destruction of $\overline{{\it\epsilon}}_{iso}$ and $C$ is a flow-dependent constant. Since $2G/\mathit{Re}_{{\it\lambda}}$ is found to be very nearly constant for $\mathit{Re}_{{\it\lambda}}\geqslant 70$, $S$ should approach a universal constant when $\mathit{Re}_{{\it\lambda}}$ is sufficiently large, but the way this constant is approached is flow dependent. For example, the approach is slow in grid turbulence and rapid along the axis of a round jet. For all the flows considered, the approach is reasonably well supported by experimental and numerical data. The constancy of $S$ at large $\mathit{Re}_{{\it\lambda}}$ has obvious ramifications for small-scale turbulence research since it violates the modified similarity hypothesis introduced by Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82–85) but is consistent with the original similarity hypothesis (Kolmogorov, Dokl. Akad. Nauk SSSR, vol. 30, 1941, pp. 299–303).

JFM classification

Turbulent Flows: Turbulence theory Turbulent Flows: Turbulent Flows
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Journal of Fluid Mechanics , Volume 781 , 25 October 2015 , pp. 727 - 744
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© 2015 Cambridge University Press 

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