Density-ratio-invariant mean-species profile of classical Rayleigh-Taylor mixing

Accurately predicting profiles of mean-mass fraction Y¯ and mean-molar/volume fraction φ¯ (equivalent to renormalized mean density ρ¯) of turbulent mixing induced by Rayleigh-Taylor instability at different density ratio R is of fundamental importance for many natural phenomena and engineering applications but has not been quantified yet. Based on asymptotic analysis, we give an R-invariant hybrid profiles C(X)FY¯+(1-F)φ¯ with A(R-1)/(R+1) and F(1+A)(1-X)/2 and derive the analytical expression of C(X), where X [0,1] is a mixing-width-rescaled dimensionless coordinate. The invariance are validated by both experiments and simulations. Consequently, combining the R invariance of C(X) and the relation of φ¯=Y¯/[Y¯+(1-Y¯)R] derived from definitions, the mean profiles of density, mass fraction, and molar/volume fraction at different density ratios are accurately predicted.