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arXiv · 2402.02237

Wall-wake laws for the mean velocity and the turbulence

Alexander J. Smits
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Abstract

A new wall-wake law is proposed for the streamwise turbulence in the outer region of a turbulent boundary layer. The formulation pairs the logarithmic part of the profile (with a slope A_1 and additive constant B_1) to an outer linear part, and it accurately describes over 95% of the boundary layer profile at high Reynolds numbers. Once the slope A_1 is fixed, B_1 is the only free parameter determining the fit. Most importantly, B_1 is shown to be proportional to the wake factor in the wall-wake law for the mean velocity, revealing a previously unsuspected connection between the turbulence and the mean flow.

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Alexander J. Smits. 2024-02-03. Wall-wake laws for the mean velocity and the turbulence. https://doi.org/10.1017/jfm.2024.519

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