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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
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.
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- © The Author(s), 2020. Published by Cambridge University Press
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