The <i>law of the wall</i>: A new perspective
Sk Zeeshan Ali, Subhasish Dey
Abstract
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.