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

• Published in: Journal of fluid mechanics 2021-02, Vol.908, Article A31
• Main Authors: Groom, M., Thornber, B.
• Format: Article
• Language: English
• Subjects: Algorithms; Collaboration; Computational fluid dynamics; Decay rate; Dependence; Direct numerical simulation; Energy; Energy spectra; Fluid flow; Fluid mechanics; Growth rate; High Reynolds number; JFM Papers; Kinetic energy; Narrowband; Numerical analysis; Reynolds number; Richtmeyer-Meshkov instability; Scaling; Simulation; Spatial distribution; Turbulence; Turbulent flow; Turbulent mixing; Unsteady flow; Wavelengths
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2020.913

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.