Characteristics of turbulent mixing at late stage of the Richtmyer-Meshkov instability

We present a model for the mixing width, h, at self-similar stage of the Richtmyer-Meshkov instability (RMI). The derivation of the model is based on the formula of the growth rate of mixing width [Gao et al., Phys. Fluids 28, 114101, (2016)], which is essentially equals to the first principle (Navior-Stokes equation). The model predicts that, in the self-similar mixing stage of the RMI h² is linearly proportional to time. This is substantially different from the classical h ∼ τ^θ description. The linearity is validated by various experimental and numerical data. The exponent, θ, in the classical relation is also discussed according to the present model.