Exact Expansion Law for Richtmyer-Meshkov Turbulent Mixing Zone

Development of the Richtmyer-Meshkov instability leads to mixing of two substances separated by contact boundary. Mixture of two fluids is confined between two mixing fronts. Universal asymptotics follows the transition stage at late time. Functions which describe the fronts penetration asymptoticaly transform to power law dependences. Mixing is acompanied by cascade of enlarging of dominant scale of a turbulent mixing zone. The exponents of the power laws are: 2/5 for 2D and 1/3 for 3D cases. These exact exponents are calculated in our work. They are determined by the mechanism of redistribution of momentum from small into the large scales.