ABSTRACT We address the important point of the proportionality between the longitudinal integral lengthscale (L) and the characteristic mean flow width (δ) using experimental data of an axisymmetric wake and a turbulent planar jet. This is a fundamental hypothesis when deriving the self-similar scaling laws in free shear flow. We show that L/δ is indeed constant, at least in a range of streamwise distances between 15 and 50 times the characteristic inlet dimension. We revisit turbulence closure models such as the Prandtl mixing length and the eddy viscosity in the light of the non-equilibrium dissipation scaling. We show that the mixing length model does not comply with the scalings stemming from the non-equilibrium version of the theory even if it does comply with the theory’s equilibrium version. Similarly, the eddy viscosity model holds in the case of the non-equilibrium version of the theory provided that the eddy viscosity is constant everywhere. We conclude by comparing the results of the different models with each other and with experimental data and with an improved model (following Townsend) that corrects for the eddy viscosity by considering the intermittency of the flow.

中文翻译：

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湍流自由剪切流中的长度尺度

摘要 我们使用轴对称尾流和湍流平面射流的实验数据解决了纵向积分长度尺度 (L) 和特征平均流宽度 (δ) 之间比例关系的重要问题。这是导出自由剪切流中的自相似标度定律时的基本假设。我们表明 L/δ 确实是恒定的，至少在特征入口尺寸的 15 到 50 倍之间的流向距离范围内。我们根据非平衡耗散比例重新审视湍流闭合模型，例如 Prandtl 混合长度和涡流粘度。我们表明，即使混合长度模型确实符合理论的平衡版本，它也不符合源自理论的非平衡版本的标度。相似地，涡粘度模型适用于理论的非平衡版本，前提是涡粘度在任何地方都是恒定的。我们通过将不同模型的结果相互比较并与实验数据和改进的模型（在 Townsend 之后）进行比较来得出结论，该模型通过考虑流动的间歇性来校正涡流粘度。