Evaluation of joint probability density function descriptions for three-layer Rayleigh-Taylor mixing

Simulations of a three-layer Rayleigh-Taylor mixing problem are presented. The simulations are conducted in a heavy-light-heavy configuration, where one of the two interfaces is unstable, and a heavy-intermediate-light configuration, where both interfaces are unstable. Each of the two configurations are further considered in a high- and low-Reynolds number regime. The joint probability density function (PDF) of species concentration from the simulation data is then compared against model PDFs that have been proposed to describe the species concentration distribution in three-component mixing. PDFs considered include the Dirichlet distribution, which is a multivariate generalization of the beta distribution that has been shown to accurately describe two-component mixing, as well as more complicated PDFs with increased generality. Qualitative and quantitative comparisons of the model PDFs and simulation data as a function of time and problem configuration are presented. Notably, the Dirichlet distribution does not appear to accurately describe the data in general, and more complicated PDFs appear to be necessary.