Mixed mass of classical Rayleigh-Taylor mixing at arbitrary density ratios

The accurate prediction of mixed mass induced by turbulent Rayleigh-Taylor mixing is of fundamental importance for many natural phenomena and engineering applications; however, no quantitative theory based on it has been established yet. In this study, we establish a quantitative theory to predict its evolution at arbitrary density ratios by combining the theory of density-ratio-invariant mean species profiles, which was recently developed by us, and the closure model for the turbulent fluctuations presented in this letter. The transformation formula between mixed mass and mixing width is obtained; in addition, the quantitative variation of normalized mixed mass with respect to the density ratio is derived. The theoretical results agreed very well with the direct numerical simulations at varied density ratios. The study sheds light on the quantitative prediction of mixed mass in practical engineering applications such as inertial confinement fusion.