The law of the wall, regarded as one of the very few pieces of turbulence hypothesis, predicts the mean-velocity profile (MVP) in a wall-bound flow. For about nine decades, the underlying physics of the law is deemed to be governed by an ad hoc mixing-length hypothesis. Here, we seek the origin of the law, for the first time, with the aid of a new hypothesis, which we call the mixing-instability hypothesis. The hypothesis unveils the previously unknown universal scaling behavior for the amplitude of turbulent ripples or waves (that cause spontaneous stretching and shrinking of turbulent eddies) within the overlap layer and accurately maps the experimental data of the MVPs for moderate to extremely large Reynolds numbers. This study offers a new mechanism of the momentum transfer in a turbulent wall-bound flow, calling for a revision of the conventional mixing-length hypothesis, which has persisted in standard textbooks on turbulence for many decades.

中文翻译：

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墙的法则：一个新的视角

壁面定律被认为是极少数湍流假设之一，它预测了壁面流动中的平均速度剖面 (MVP)。在大约九年的时间里，该定律的基础物理学被认为是由一个特别的混合长度假设控制的。在这里，我们第一次借助一个新的假设来寻找定律的起源，我们称之为混合不稳定性假设。该假设揭示了重叠层内湍流波纹或波浪（导致湍流涡流的自发拉伸和收缩）幅度的先前未知的通用缩放行为，并准确地映射了 MVP 的实验数据，用于中到极大的雷诺数。这项研究提供了湍流壁面流动中动量传递的新机制，