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 × 1 0 9 cells. Three different perturbations are considered, characterised by a power spectrum of the form P ( k ) ∝ 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 θ 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 Θ are also shown to vary significantly with m ; at the latest time considered Θ 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 θ , which is shown to be due to a time-varying normalised dissipation rate C ϵ . 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.