The mean stress is one of the most important quantities of interest in turbulent boundary layers. The governing equations for the mean flow are used to derive a relation between the mean total stress and the mean velocity in a zero pressure gradient turbulent boundary layer, allowing the mean shear stress to be written as a function of wall-normal distance. The relation contains an unknown term, which is modeled using a linear function of the wall-normal distance, inspired by existing data sets. The model for the mean total stress requires the wall-normal mean velocity profile, which requires modeling if not available. The existing data sets and scaling arguments are used to obtain a simple and compact fit for the mean wall-normal velocity, which is subsequently used to obtain a simple model for the mean total stress. The model shows good agreement with the available simulation and experimental data for a large range of Reynolds number.

中文翻译：

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湍流边界层中平均应力的简单模型

在湍流边界层中，平均应力是最重要的关注量之一。平均流量的控制方程式用于推导零压力梯度湍流边界层中的平均总应力与平均速度之间的关系，从而允许将平均剪应力写为壁面法向距离的函数。该关系包含一个未知项，该项使用墙法线距离的线性函数建模，该函数受现有数据集的启发。平均总应力模型需要壁法向平均速度分布图，如果不可用，则需要建模。现有数据集和缩放参数用于获得平均壁法线速度的简单且紧凑的拟合，随后将其用于获得平均总应力的简单模型。