Quantifying mixing of Rayleigh-Taylor turbulence

Accurate quantification of turbulent mixing induced by classical Rayleigh-Taylor instability is of fundamental importance for many natural phenomena and engineering applications. However, a systematic model to predict its evolution at different mixing levels and different density ratios ($R$) has not been established. In this paper, the mixing width is predicted by combining the principle of mass conservation and mean density profile. The mean density profile, as well as the mean profiles of mass fraction and molar/volume fraction, are predicted with $R$-invariant hybrid species profiles from asymptotic analysis. The unknown turbulent fluctuations are closed with the predicted mean quantities, yielding analytical predictions for mixing degree and mixed mass. The predictions agree very well with previous experiments and simulations, explaining the distinct differences that exist among the famous experiments.

Figure 1

Schematic diagram of RT mixing evolution. The $\overline{f}$ denotes an ensemble/plane average. The plane average is conducted over a plane perpendicular to the $x$-direction.

Figure 2

Variation of ${\alpha }_s/{\alpha }_b$ with density ratio $R$. The symbols give the results of implicit large-eddy simulations (ILES) [16] and experiments conducted by Dimonte et al. [21], Youngs et al. [20], and Kucherenko et al. [22], respectively. The lines show the predictions using the current model of Eq. (5) with a different parameter $c$.

Figure 3

Mean profiles of volume fraction at $R=3$ (inset) and $R=20$. The symbols give the results of ILES [16]. The lines show the predictions using the current model of Eq. (13) with a different parameter $c$.

Figure 4

Variation of $\overline{\mathrm{\Theta }}$ (inset) and $\overline{\mathrm{\Psi }}$ with Atwood number $A$. The symbols give the results of direct numerical simulation (DNS) [4, 18, 27]. The lines show the predictions using the current model of Eqs. (20) and (21) with different parameter $c$.