Development of turbulent mixing induced by the Richtmyer–Meshkov instability

Turbulent mixing development, induced by passing shock waves through the interface, has been studied on the basis of two semiempirical models. The process of transition from random initial perturbations to turbulence is rather complex, but it proceeds in a finite time. The shock waves passing through the initial zone of “roughness” are believed to lead to the instant developing of mixing. The expression for the rubulent kinetic energy, transfered by the arriving shock wave, has been derived. The value of this energy is determined by the non-dimensional parameter value which is equivalent to the Richardson number. The analytical solution, describing the decay of the turbulent kinetic energy and changing the mixing zone width in time has been obtained. The analytical form of the constructed solutions allows to make a comparison between the models and to choose constants as a result of comparing with the known experiments. The obtained approximated solution correlates well with numerical computations, perfomed by the code TURINB.