The influence of initial perturbation power spectra on the growth of a turbulent mixing layer induced by Richtmyer-Meshkov instability

Abstract

This paper investigates the influence of different broadband perturbations on the evolution of a Richtmyer--Meshkov turbulent mixing layer initiated by a Mach 1.84 shock traversing a perturbed interface separating gases with a density ratio of 3:1. Both the bandwidth of modes in the interface perturbation, as well as their relative amplitudes, are varied in a series of carefully designed numerical simulations at grid resolutions up to $3.2\times 10^9$ cells. Three different perturbations are considered, characterised by a power spectrum of the form $P(k)\propto k^m$ where $m=-1$, $-2$ and $-3$. The growth of the mixing layer is shown to strongly depend on the initial conditions, with the growth rate exponent $\theta$ found to be $0.5$, $0.63$ and $0.75$ for each value of $m$ at the highest grid resolution. The asymptotic values of the molecular mixing fraction $\Theta$ are also shown to vary significantly with $m$; at the latest time considered $\Theta$ is $0.56$, $0.39$ and $0.20$ respectively. Turbulent kinetic energy (TKE) is also analysed in both the temporal and spectral domains. The temporal decay rate of TKE is found not to match the predicted value of $n=2-3\theta$, which is shown to be due to a time-varying {normalised dissipation rate $C_{\epsilon }$}. In spectral space, the data follow the theoretical scaling of $k^{(m+2)/2}$ at low wavenumbers and tend towards $k^{-3/2}$ and $k^{-5/3}$ scalings at high wavenumbers for the spectra of transverse and normal velocity components respectively. The results represent a significant extension of previous work on the Richtmyer--Meshkov instability evolving from broadband initial perturbations and provide useful benchmarks for future research.

References in corpus (3)

• Late-time growth rate, mixing and anisotropy in the multimode narrowband Richtmyer--Meshkov Instability: the $\theta$-Group Collaboration
• Turbulent transport and mixing in the multimode narrowband Richtmyer-Meshkov instability
• Direct numerical simulation of the multimode narrowband Richtmyer-Meshkov instability

Cited by in corpus (2)

• Reynolds number dependence of turbulence induced by the Richtmyer-Meshkov instability using direct numerical simulations
• Impact of transverse strain on linear, transitional and self-similar turbulent mixing layers