The рарег discusses the ргвЫеш of gas-dynamic instability and the corresponding turbulent mixing as well as the numerical methods of its solving. The authors consider the problem of the turbulent mixing in the two-layer cylinder-shaped targets (based on the three-layer predicted intercept area). They also analyze three means of accelerating the contact boundary surface. The paper introduces similarity criteria and major dimension-less parameters defining the process of radiation and magnetic gas-dynamic instability.