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arXiv · 2610.35276

Physics-Constrained Symbolic Regression for Mean-Velocity and Mixing-Length Scaling in Zero-Pressure-Gradient Turbulent Boundary Layers

Xianglin Shan·Weiwei Zhang
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Abstract

Developing interpretable full-profile relations for mean velocity and effective mixing length remains challenging because the near-wall, overlap, and outer regions exhibit distinct scaling behaviors. In this paper, physics-constrained symbolic regression is used to construct analytical relations for incompressible zero-pressure-gradient turbulent boundary layers. Classical logarithmic and Prandtl mixing-length scalings provide the starting points, while the regression identifies near-wall transition functions under asymptotic constraints and Reynolds-number-dependent outer corrections. The resulting expressions retain the prescribed leading-order near-wall exponents, reproduce the principal overlap-region behavior, and describe finite-Reynolds-number variations. The mean-velocity relation agrees well with 35 profiles from direct numerical simulations, large-eddy simulations, and experiments spanning friction Reynolds numbers from 252 to 72,526, while the mixing-length relation captures the principal trends in the simulation-derived data. These results illustrate how physical scaling knowledge can guide symbolic regression toward compact, interpretable analytical descriptions of canonical wall turbulence.

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Xianglin Shan, Weiwei Zhang. 2026-10-26. Physics-Constrained Symbolic Regression for Mean-Velocity and Mixing-Length Scaling in Zero-Pressure-Gradient Turbulent Boundary Layers. https://arxiv.org/abs/2610.35276

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