A Reynolds-averaged Navier-Stokes model is presented with the property that it admits self-consistent, high-order spatial profiles in simulations of two-fluid turbulent mixing layers. Whereas previous models have been limited by the assumption of a linear mixing profile, the present paper relaxes this assumption and, as a result, is shown to achieve much better agreement with experimental profiles. Similarity analysis is presented to derive constraints on model coefficients to enforce desired self-similar growth rates that are fully consistent with the high-order spatial profiles. Through this similarity analysis, it is shown that care must be taken in model construction, as it is possible to construct certain terms in such a way as to leave growth rates unconstrained. This model, termed the $k\text{−}\varphi \text{−}L\text{−}a\text{−}V$ model, is then applied in simulations of Rayleigh-Taylor, Richtmyer-Meshkov, and Kelvin-Helmholtz mixing layers. These simulations confirm that the expected growth parameters are recovered and high-order spatial profiles are maintained.

中文翻译：

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两流体湍流混合模型中的自洽高阶空间剖面

雷诺平均 Navier-Stokes 模型具有以下特性：它在模拟两流体湍流混合层时承认自洽的高阶空间剖面。尽管以前的模型受到线性混合曲线假设的限制，但本文放宽了这一假设，结果表明与实验曲线的一致性要好得多。提出了相似性分析以推导出对模型系数的约束，以强制执行与高阶空间剖面完全一致的所需自相似增长率。通过这种相似性分析，表明在构建模型时必须小心，因为可以以不限制增长率的方式构建某些项。该模型称为$克\text{-}\phi \text{-}升\text{-}\mathrm{一个}\text{-}伏$模型，然后应用于 Rayleigh-Taylor、Richtmyer-Meshkov 和 Kelvin-Helmholtz 混合层的模拟。这些模拟证实了预期的增长参数得到恢复并保持了高阶空间剖面。