Lagrangian analysis of materially conserved scalars is applied to the problem of turbulent transport in variable-density flows. The consequences of an additional material conserved quantity, the density, is generally not acknowledged and leads to significant and meaningfully different expressions for turbulent transport in the moment equations. The formal Lagrangian analysis produces gradient transport expressions substantially different from those obtained by the physically intuitive “argument by analogy” method used in computational models. Various intuitive arguments, in Favre and Reynolds averaged settings, are contrasted to the formal Lagrangian results. Using expressions from the formal analysis, we derive consistent gradient transport closures for the turbulent transport terms that appear in the first- and second-order Favre moment equations. Results for coupled multispecies turbulent transport are given. The analysis is limited to variable-density turbulence in which the dilatation of the fluctuating velocity is small. The results are applicable to turbulent combustion and to stellar convection problems in which the density fluctuations are on the order of the mean density.

中文翻译：

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变密度湍流中湍流输运的拉格朗日分析

物质守恒标量的拉格朗日分析应用于变密度流中的湍流输运问题。通常不认识到额外的材料守恒量（密度）的后果，并且导致了力矩方程中湍流输运的显着且有意义的不同表达式。形式上的拉格朗日分析产生的梯度输运表达式与通过计算模型中使用的物理直观“类推论”方法获得的梯度输运表达式完全不同。在法夫尔（Favre）和雷诺（Reynolds）平均设置下，各种直观的论证与正式的拉格朗日结果相反。使用形式分析中的表达式，我们为出现在第一阶和第二阶Favre矩方程中的湍流输运项导出一致的梯度输运闭塞。给出了耦合多物种湍流传输的结果。该分析仅限于变密度湍流，其中脉动速度的扩张很小。该结果适用于湍流燃烧和恒星对流问题，其中密度波动在平均密度的数量级上。