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Scalings of scale-by-scale turbulence energy in non-homogeneous turbulence

Published online by Cambridge University Press:  10 March 2022

J.G. Chen Open the ORCID record for J.G. Chen [Opens in a new window]  and
J.C. Vassilicos Open the ORCID record for J.C. Vassilicos [Opens in a new window]
J.G. Chen
Affiliation:
Univ. Lille, CNRS, ONERA, Arts et Metiers Institute of Technology, Centrale Lille, UMR 9014 – LMFL – Laboratoire de Mécanique des Fluides de Lille – Kampé de Fériet, F-59000 Lille, France
J.C. Vassilicos*
Affiliation:
Univ. Lille, CNRS, ONERA, Arts et Metiers Institute of Technology, Centrale Lille, UMR 9014 – LMFL – Laboratoire de Mécanique des Fluides de Lille – Kampé de Fériet, F-59000 Lille, France
*
†Email address for correspondence: [email protected]
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Abstract

A theory of non-homogeneous turbulence is developed and applied to boundary-free shear flows. The theory introduces assumptions of inner and outer similarity for the non-homogeneity of two-point statistics, and predicts power-law scalings of second-order structure functions that have some similarities with but also some differences from Kolmogorov scalings. These scalings arise as a consequence of these assumptions, of the general interscale and interspace energy balance, and of an inner–outer equivalence hypothesis for turbulence dissipation. They reduce to the usual Kolmogorov scalings in stationary homogeneous turbulence. Comparisons with structure function data from three qualitatively different turbulent wakes provide support for the theory's predictions but also raise new questions for future research.

JFM classification

Turbulent Flows: Turbulence theory Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 938 , 10 May 2022 , A7
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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