Data-enabled discovery of specific and generalisable turbulence closures

作者：Zhongxin Yang, Xianglin Shan, Xiang I. A. Yang, Weiwei Zhang · 发表于：Journal of Fluid Mechanics · 年份：2025 · DOI：10.1017/jfm.2025.10332 · 被引用次数：15 · 研究领域：Fluid Dynamics and Turbulent Flows、Wind and Air Flow Studies、Fluid Dynamics and Vibration Analysis

Turbulence closures are essential for predictive fluid flow simulations in both natural and engineering systems. While machine learning offers promising avenues, existing data-driven turbulence models often fail to generalise beyond their training datasets. This study identifies the root cause of this limitation as the conflation of generalisable flow physics and dataset-specific behaviours. We address this challenge using symbolic regression, which yields interpretable, white-box expressions. By decomposing the learned corrections into inner-layer, outer-layer and pressure-gradient components, we isolate universal physics from flow-specific features. The model is trained progressively using high-fidelity datasets for plane channel flows, zero-pressure-gradient turbulent boundary layers (ZPGTBLs), and adverse pressure-gradient turbulent boundary layers (PGTBLs). For example, direct application of a model trained on channel flow data to ZPGTBLs results in incorrect skin friction predictions. However, when only the generalisable inner-layer component is retained and combined with an outer-layer correction specific to ZPGTBLs, predictions improve significantly. Similarly, a pressure-gradient correction derived from PGTBL data enables accurate modelling of aerofoil flows with both favourable and adverse pressure gradients. The resulting symbolic corrections are compact, interpretable, and generalise across configurations – including unseen geometries such as aerofoils and Reynold...