Growth rate of a shocked mixing layer with known initial perturbations

Abstract

AbstractWe derive a growth-rate model for the Richtmyer–Meshkov mixing layer, given arbitrary but known initial conditions. The initial growth rate is determined by the net mass flux through the centre plane of the perturbed interface immediately after shock passage. The net mass flux is determined by the correlation between the post-shock density and streamwise velocity. The post-shock density field is computed from the known initial perturbations and the shock jump conditions. The streamwise velocity is computed via Biot–Savart integration of the vorticity field. The vorticity deposited by the shock is obtained from the baroclinic torque with an impulsive acceleration. Using the initial growth rate and characteristic perturbation wavelength as scaling factors, the model collapses the growth-rate curves and, in most cases, predicts the peak growth rate over a range of Mach numbers ($1. 1\leq {M}_{i} \leq 1. 9$), Atwood numbers ($- 0. 73\leq A\leq - 0. 35$ and $0. 22\leq A\leq 0. 73$), adiabatic indices ($1. 40/ 1. 67\leq {\gamma }_{1} / {\gamma }_{2} \leq 1. 67/ 1. 09$) and narrow-band perturbation spectra. The mixing layer at late times exhibits a power-law growth with an average exponent of $\theta = 0. 24$.