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Scale-by-scale non-equilibrium with Kolmogorov-like scalings in non-homogeneous stationary turbulence

Published online by Cambridge University Press:  03 April 2024

P. Beaumard Open the ORCID record for P. Beaumard [Opens in a new window] ,
P. Bragança Open the ORCID record for P. Bragança [Opens in a new window] ,
C. Cuvier Open the ORCID record for C. Cuvier [Opens in a new window] ,
K. Steiros Open the ORCID record for K. Steiros [Opens in a new window]  and
J.C. Vassilicos Open the ORCID record for J.C. Vassilicos [Opens in a new window]
P. Beaumard
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
P. Bragança
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
C. Cuvier
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
K. Steiros
Affiliation:
Department of Aeronautics, Imperial College London, London SW7 2AZ, UK
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: john-christos.vassilicos@cnrs.fr
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Abstract

An improved version of the non-equilibrium theory of non-homogeneous turbulence of Chen & Vassilicos (J. Fluid Mech., vol. 938, 2022, A7) predicts that an intermediate range of length scales exists where the interscale turbulence transfer rate, the two-point interspace turbulence transport rate and the two-point pressure gradient velocity correlation term in the two-point small-scale turbulent energy equation are all proportional to the turbulence dissipation rate and independent of length scale. Particle image velocimetry measurements in a field of view under the turbulence-generating impellers in a baffled water tank support these predictions and show that the measured small-scale turbulence is significantly non-homogeneous. The particle image velocimetry measurements also suggest that the rate with which large scales lose energy to the small scales in the two-point large-scale turbulent energy equation also appears to be approximately proportional to the turbulence dissipation rate and independent of length scale in the same intermediate range and that this rate may not balance the interscale turbulence transfer rate in the two-point small-scale turbulent energy equation because of turbulent energy transport caused by the non-homogeneity.

JFM classification

Turbulent Flows: Turbulence theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 984 , 10 April 2024 , A35
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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