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Length scales and the turbulent/non-turbulent interface of a temporally developing turbulent jet

Published online by Cambridge University Press:  04 September 2023

S. Er Open the ORCID record for S. Er [Opens in a new window] ,
J.-P. Laval Open the ORCID record for J.-P. Laval [Opens in a new window]  and
J.C. Vassilicos Open the ORCID record for J.C. Vassilicos [Opens in a new window]
S. Er*
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.-P. Laval
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 addresses for correspondence: sarp.er.etu@univ-lille.fr, john-christos.vassilicos@centralelille.fr
†Email addresses for correspondence: sarp.er.etu@univ-lille.fr, john-christos.vassilicos@centralelille.fr
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Abstract

The temporally developing self-similar turbulent jet is fundamentally different from its spatially developing namesake because the former conserves volume flux and has zero cross-stream mean flow velocity whereas the latter conserves momentum flux and does not have zero cross-stream mean flow velocity. It follows that, irrespective of the turbulent dissipation's power-law scalings, the time-local Reynolds number remains constant, and the jet half-width $\delta$, the Kolmogorov length $\eta$ and the Taylor length $\lambda$ grow identically as the square root of time during the temporally developing self-similar planar jet's evolution. We predict theoretically and confirm numerically by direct numerical simulations that the mean centreline velocity, the Kolmogorov velocity and the mean propagation speed of the turbulent/non-turbulent interface (TNTI) of this planar jet decay identically as the inverse square root of time. The TNTI has an inner structure over a wide range of closely spatially packed iso-enstrophy surfaces with fractal dimensions that are well defined over a range of scales between $\lambda$ and $\delta$, and that decrease with decreasing iso-enstrophy towards values close to $2$ at the viscous superlayer. The smallest scale on these isosurfaces is approximately $\eta$, and the length scales between $\eta$ and $\lambda$ contribute significantly to the surface area of the iso-enstrophy surfaces without being characterised by a well-defined fractal dimension. A simple model is sketched for the mean propagation speeds of the iso-enstrophy surfaces within the TNTI of temporally developing self-similar turbulent planar jets. This model is based on a generalised Corrsin length, on the multiscale geometrical properties of the TNTI, and on a proportionality between the turbulent jet volume's growth rate and the growth rate of $\delta$. A prediction of this model is that the mean propagation speed at the outer edge of the viscous superlayer is proportional to the Kolmogorov velocity multiplied by the $1/4$th power of the global Reynolds number.

JFM classification

Wakes/Jets: Jets Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 970 , 10 September 2023 , A33
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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