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Non-dimensional energy dissipation rate near the turbulent/non-turbulent interfacial layer in free shear flows and shear free turbulence

Published online by Cambridge University Press:  18 July 2019

Tomoaki Watanabe Open the ORCID record for Tomoaki Watanabe [Opens in a new window] ,
Carlos B. da Silva Open the ORCID record for Carlos B. da Silva [Opens in a new window]  and
Koji Nagata Open the ORCID record for Koji Nagata [Opens in a new window]
Tomoaki Watanabe*
Affiliation:
Department of Aerospace Engineering, Nagoya University, Nagoya 464-8603, Japan
Carlos B. da Silva
Affiliation:
Instituto Superior Técnico, Universidade de Lisboa, Lisboa 1049-001, Portugal
Koji Nagata
Affiliation:
Department of Aerospace Engineering, Nagoya University, Nagoya 464-8603, Japan
*
†Email address for correspondence: watanabe.tomoaki@c.nagoya-u.jp
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Abstract

The non-dimensional dissipation rate $C_{\unicode[STIX]{x1D700}}=\unicode[STIX]{x1D700}L/u^{\prime 3}$, where $\unicode[STIX]{x1D700}$, $L$ and $u^{\prime }$ are the viscous energy dissipation rate, integral length scale of turbulence and root-mean-square of the velocity fluctuations, respectively, is computed and analysed within the turbulent/non-turbulent interfacial (TNTI) layer using direct numerical simulations of a planar jet, mixing layer and shear free turbulence. The TNTI layer that separates the turbulent and non-turbulent regions exists at the edge of free shear turbulent flows and turbulent boundary layers, and comprises both the viscous superlayer and turbulent sublayer regions. The computation of $C_{\unicode[STIX]{x1D700}}$ is made possible by the introduction of an original procedure, based on local volume averages within spheres of radius $r$, combined with conditional sampling as a function of the location with respect to the TNTI layer. The new procedure allows for a detailed investigation of the scale dependence of several turbulent quantities near the TNTI layer. An important achievement of this procedure consists in permitting the computation of the turbulent integral scale within the TNTI layer, which is shown to be approximately constant. Both the non-dimensional dissipation rate and turbulent Reynolds number $Re_{\unicode[STIX]{x1D706}}$ vary in space within the TNTI layer, where two relations are observed: $C_{\unicode[STIX]{x1D700}}\sim Re_{\unicode[STIX]{x1D706}}^{-1}$ and $C_{\unicode[STIX]{x1D700}}\sim Re_{\unicode[STIX]{x1D706}}^{-2}$. Specifically, whereas the viscous superlayer and part of the turbulent sublayer display $C_{\unicode[STIX]{x1D700}}\sim Re_{\unicode[STIX]{x1D706}}^{-2}$, the remaining of the turbulent sublayer exhibits $C_{\unicode[STIX]{x1D700}}\sim Re_{\unicode[STIX]{x1D706}}^{-1}$, which is consistent with non-equilibrium turbulence (Vassilicos, Annu. Rev. Fluid Mech. vol. 47, 2015, pp. 95–114).

JFM classification

Wakes/Jets: Jets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 875 , 25 September 2019 , pp. 321 - 344
Copyright
© 2019 Cambridge University Press 

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