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 existed among the famous experiments.

中文翻译：

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量化瑞利-泰勒湍流的混合

对于许多自然现象和工程应用而言，由经典的瑞利-泰勒不稳定性引起的湍流混合的精确定量是至关重要的。但是，有一个系统模型可以预测其在不同混合水平和不同密度比下的演化（$\mathrm{[R}$）尚未建立。本文通过结合质量守恒原理和平均密度分布来预测混合宽度。可以预测平均密度分布以及质量分数和摩尔/体积分数的平均分布$\mathrm{[R}$渐进分析得出的不变杂种物种概况。未知的湍流波动被预测的平均量封闭，从而产生混合度和混合质量的分析预测。这些预测与先前的实验和模拟非常吻合，从而解释了著名实验之间存在的明显差异。