Scaling approaches for mean velocity in two-dimensional, fully-developed, turbulent wall jets developing on flat surfaces, have invariably reckoned on the nozzle initial conditions as scaling parameters. This choice, however, does not square with the notion of self similarity which essentially involves "local" scales. We demonstrate that the mean velocity data across different facilities scale remarkably well with the "local" parameters rather than the nozzle parameters i.e. self similarity prevails. Data further suggest existence of two distinct layers, the wall (inner) layer and the jet (outer) layer, with each layer having its own universal scaling independent of the local Reynolds number $Re_{\tau}$. Analysis suggests that the scale-aware overlap of these universal layers renders the overlap velocity profile $Re_{\tau}$-dependent. An intermediate variable effectively absorbs this $Re_{\tau}$-dependence and yields a universal power-law profile for mean velocity in the overlap layer; experimental data strongly support these outcomes.

中文翻译：

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二维湍流壁射流中的标度平均速度

在平面上发展的二维、完全发展、湍流壁射流中平均速度的缩放方法总是将喷嘴初始条件视为缩放参数。然而，这种选择与本质上涉及“局部”尺度的自我相似性的概念并不相符。我们证明了不同设施的平均速度数据与“本地”参数而不是喷嘴参数的比例非常好，即自相似占优势。数据进一步表明存在两个不同的层，壁（内）层和喷射（外）层，每一层都有自己的通用缩放，独立于局部雷诺数 $Re_{\tau}$。分析表明，这些通用层的尺度感知重叠呈现重叠速度剖面 $Re_{\tau}$ 相关。一个中间变量有效地吸收了这种 $Re_{\tau}$ 依赖性，并产生了重叠层中平均速度的通用幂律分布；实验数据有力地支持了这些结果。