Richtmyer–Meshkov instability of an interface between two media due to passage of two successive shocks

The instability of a free surface of aluminum after passage of two shocks that follow one after the other at a certain time interval is studied numerically. The first shock is rather strong (the postshock pressure is about 75 GPa). It is shown that if at the moment when the second shock arrives at the free surface, the perturbation evolution is nonlinear, then, in contrast to the linear stage, the change in the growth rate of the amplitude depends weakly on the wavelength of the initial perturbation. A formula is proposed which describes the effect of the second shock on the amplitude growth rate and in which the main structure of Richtmyer's formula is preserved. It is demonstrated that the parameters of the second shock that ensure freezing of the instability can be determined using only the growth rate of the amplitude.