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Data-enabled discovery of specific and generalisable turbulence closures
Published online by Cambridge University Press: 25 July 2025
Abstract
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 Reynolds numbers outside the training set. The models outperform baseline Reynolds-averaged Navier–Stokes closures (e.g. the Spalart–Allmaras and shear stress transport models) in both a priori and a posteriori tests. These results demonstrate that explicit identification and retention of generalisable components is key to overcoming the generalisation challenge in machine-learned turbulence closures.
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References
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