Turbulent mixing induced by Richtmyer-Meshkov instability

Turbulent mixing development, induced by shock wave passage through the interface, has been studied on the basis of two semi-empirical models. The process of transition from randam initial perturbations to turbulence is a rather complicated one, but proceeds in a finite time. Here it is assumed that the shock wave passage through the initial zone of “roughness” leads to the instantaneous development of mixing. An expression for the turbulent kinetic energy, transfered by shock wave, has been derived. The value of this energy is determined by a non-dimensional parameter which is equivalent to the Richardson number. The analytical solution describing the turbulent kinetic energy decay and the change of mixing zone width in time has been obtained. The analytical form of the solutions allows to compare the models with the existing experimental results. Comparison of the theoretical results with Zaitzev’s experimental data is given for the impulsive acceleration.