Physics-Constrained Symbolic Regression for Mean-Velocity and Mixing-Length Scaling in Zero-Pressure-Gradient Turbulent Boundary Layers
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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BibTeX
@misc{shan2026physicsconstrained,
title = {{Physics-Constrained Symbolic Regression for Mean-Velocity and Mixing-Length Scaling in Zero-Pressure-Gradient Turbulent Boundary Layers}},
author = {Xianglin Shan and Weiwei Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35276},
eprint = {2610.35276},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35276},
}
RIS
TY - UNPB
TI - Physics-Constrained Symbolic Regression for Mean-Velocity and Mixing-Length Scaling in Zero-Pressure-Gradient Turbulent Boundary Layers
AU - Xianglin Shan
AU - Weiwei Zhang
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35276
UR - https://arxiv.org/abs/2610.35276
AB - 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.
ER -