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Scaling of the turbulent energy dissipation correlation function

Published online by Cambridge University Press:  27 March 2020

S. L. Tang Open the ORCID record for S. L. Tang [Opens in a new window] ,
R. A. Antonia ,
L. Djenidi Open the ORCID record for L. Djenidi [Opens in a new window]  and
Y. Zhou
S. L. Tang*
Affiliation:
Institute for Turbulence-Noise-Vibration Interaction and Control Harbin Institute of Technology, Shenzhen518055, PR China Digital Engineering Laboratory of Offshore Equipment, Shenzhen518055, PR China
R. A. Antonia
Affiliation:
School of Engineering, University of Newcastle, NSW 2308, Australia
L. Djenidi
Affiliation:
School of Engineering, University of Newcastle, NSW 2308, Australia
Y. Zhou
Affiliation:
Institute for Turbulence-Noise-Vibration Interaction and Control Harbin Institute of Technology, Shenzhen518055, PR China Digital Engineering Laboratory of Offshore Equipment, Shenzhen518055, PR China
*
†Email address for correspondence: [email protected]
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Abstract

We examine the scaling of the two-point correlation function for $\unicode[STIX]{x1D716}$, the energy dissipation rate, over a range of values of the separation $r$ between the two points and the Taylor microscale Reynolds number $Re_{\unicode[STIX]{x1D706}}$. The correlation function is estimated from hot-wire measurements in grid turbulence, along the axes of wakes and jets, and along the centreline of a fully developed channel flow. When $Re_{\unicode[STIX]{x1D706}}$ exceeds a value of approximately 300, a condition which is achieved for both plane and circular jets, the correlation function collapses over nearly all values of $r$ when the normalization uses Kolmogorov scales. However, there is no collapse in either the power-law range or dissipative range when the normalization is on the integral (or external) length scale, which indicates that there is no self-similarity based on external scales. Although the maximum value of $Re_{\unicode[STIX]{x1D706}}$ is not much larger than $10^{3}$, the behaviour of the energy dissipation correlation function on the axes of plane and circular jets seems consistent with the first similarity hypothesis of Kolmogorov (Dokl. Akad. Nauk SSSR, vol. 30, 1941, pp. 299–303) but not with the revised phenomenology of Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82–85).

JFM classification

Turbulent Flows: Turbulence theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 891 , 25 May 2020 , A26
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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