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Reynolds number dependence of turbulence induced by the Richtmyer–Meshkov instability using direct numerical simulations

Published online by Cambridge University Press:  11 December 2020

M. Groom Open the ORCID record for M. Groom [Opens in a new window]  and
B. Thornber Open the ORCID record for B. Thornber [Opens in a new window]
M. Groom*
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, University of Sydney, Sydney, NSW2006, Australia
B. Thornber
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, University of Sydney, Sydney, NSW2006, Australia
*
†Email address for correspondence: [email protected]
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Abstract

This paper investigates the Reynolds number dependence of a turbulent mixing layer evolving from the Richtmyer–Meshkov instability using a series of direct numerical simulations of a well-defined narrowband initial condition for a range of different Reynolds numbers. The growth rate exponent $\theta$ of the integral width and mixed mass is shown to marginally depend on the initial Reynolds number $Re_0$, as does the minimum value of the molecular mixing fraction $\varTheta$. The decay rates of turbulent kinetic energy and its dissipation rate are shown to decrease with increasing $Re_0$, while the spatial distribution of these quantities is biased towards the spike side of the layer. The normalised dissipation rate $C_{\epsilon }$ and scalar dissipation rate $C_{\chi }$ are calculated and are observed to be approaching a high Reynolds number limit. By fitting an appropriate functional form, the asymptotic values of these two quantities are estimated as $C_{\epsilon }=1.54$ and $C_{\chi }=0.66$. Finally, an evaluation of the mixing transition criterion for unsteady flows is performed, showing that, even for the highest $Re_0$ case, the turbulence in the flow is not yet fully developed. This is despite the observation of a narrow inertial range in the turbulent kinetic energy spectra, with a scaling close to $k^{-3/2}$, where k is the radial wavenumber.

JFM classification

Compressible Flows: Shock waves Instability: Transition to turbulence Mixing: Turbulent mixing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 908 , 10 February 2021 , A31
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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