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

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 of the integral width and mixed mass is shown to marginally depend on the initial Reynolds number Re0, as does the minimum value of the molecular mixing fraction. The decay rates of turbulent kinetic energy and its dissipation rate are shown to decrease with increasing Re0, while the spatial distribution of these quantities is biased towards the spike side of the layer. The normalised dissipation rate and scalar dissipation rate are calculated and are observed to be approaching a high Reynolds number limit. By fitting an appropriate functional form, the asymptotic value of these two quantities is estimated as 1.54 and 0.66. Finally, an evaluation of the mixing transition criterion for unsteady flows is performed, showing that even for the highest Re0 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 -3/2.