Statistics of long-wavelength fluctuations and the expansion rate of Richtmyer-Meshkov turbulence zone

The important problem of Richtmyer-Meshkov turbulence (RMT) is solved. Much work has been devoted to the experimental, numerical (direct numerical simulation), and semiphenomenological (turbulent diffusion and bubble envelope models) analysis of RMT. All of them were of approximate character. They considered the evolution of a mixing layer, and its average thickness $h(t)$ was found. Then, the approximate value of the most important exponent $\theta (h \propto t^{\theta}$) was judged from the slope of the $h(t)$ curve in the $\ln t, \ln h$ coordinates. In this work, the theoretical approach for the exact determination of $\theta$ is developed.