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On the normalized dissipation parameter $C_{\unicode[STIX]{x1D716}}$ in decaying turbulence

Published online by Cambridge University Press:  15 March 2017

L. Djenidi Open the ORCID record for L. Djenidi [Opens in a new window] ,
N. Lefeuvre ,
M. Kamruzzaman  and
R. A. Antonia
L. Djenidi*
Affiliation:
Discipline of Mechanical Engineering, School of Engineering, University of Newcastle, Newcastle, 2308 NSW, Australia
N. Lefeuvre
Affiliation:
Discipline of Mechanical Engineering, School of Engineering, University of Newcastle, Newcastle, 2308 NSW, Australia
M. Kamruzzaman
Affiliation:
Discipline of Mechanical Engineering, School of Engineering, University of Newcastle, Newcastle, 2308 NSW, Australia
R. A. Antonia
Affiliation:
Discipline of Mechanical Engineering, School of Engineering, University of Newcastle, Newcastle, 2308 NSW, Australia
*
†Email address for correspondence: [email protected]
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Abstract

The Reynolds number dependence of the non-dimensional mean turbulent kinetic energy dissipation rate $C_{\unicode[STIX]{x1D716}}=\overline{\unicode[STIX]{x1D716}}L/u^{\prime 3}$ (where $\unicode[STIX]{x1D716}$ is the mean turbulent kinetic energy dissipation rate, $L$ is an integral length scale and $u^{\prime }$ is the velocity root-mean-square) is investigated in decaying turbulence. Expressions for $C_{\unicode[STIX]{x1D716}}$ in homogeneous isotropic turbulent (HIT), as approximated by grid turbulence, and in local HIT, as on the axis of the far field of a turbulent round jet, are developed from the Navier–Stokes equations within the framework of a scale-by-scale energy budget. The analysis shows that when turbulence decays/evolves in compliance with self-preservation (SP), $C_{\unicode[STIX]{x1D716}}$ remains constant for a given flow condition, e.g. a given initial Reynolds number. Measurements in grid turbulence, which does not satisfy SP, and on the axis in the far field of a round jet, which does comply with SP, show that $C_{\unicode[STIX]{x1D716}}$ decreases in the former case and remains constant in the latter, thus supporting the theoretical results. Further, while $C_{\unicode[STIX]{x1D716}}$ can remain constant during the decay for a given initial Reynolds number, both the theory and measurements show that it decreases towards a constant, $C_{\unicode[STIX]{x1D716},\infty }$ , as $Re_{\unicode[STIX]{x1D706}}$ increases. This trend, in agreement with existing data, is not inconsistent with the possibility that $C_{\unicode[STIX]{x1D716}}$ tends to a universal constant.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulence theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 817 , 25 April 2017 , pp. 61 - 79
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© 2017 Cambridge University Press 

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