The role of the law of the wall in cross-scenario generalisation of data-driven models

An objective of turbulence model calibration or recalibration is to train a model on one flow and achieve improved performance across a broad class of flows that share similar underlying physics. Such cross-scenario generalisation remains a major challenge in data-driven turbulence modelling. Existing considerations – such as model-consistent training and Galilean invariance – have enabled only scenario-specific generalisation to cases resembling the training dataset. In this work, we demonstrate that preserving the law of the wall (LoW) enables the expected transfer of the learned physics from the training flow to a target flow that shares relevant physics with the training flow. We adopt the field inversion and machine learning (FIML) framework, using the one-equation Spalart–Allmaras (SA) model as the baseline. Two strategies are examined: a conventional, unconstrained FIML approach, and a constrained FIML framework. Both strategies use the full flow field without shielding; the constrained version deploys the learned coefficient on a LoW-preserving manifold. Training is limited to periodic-hill flows, while extrapolation tests include channel flow, periodic hills of different slopes, a backward-facing step, and the three-dimensional BeVERLI hill. For periodic-hill cases, unconstrained and constrained FIML exhibit comparable performance, indicating that LoW preservation is not essential for scenario-specific generalisation. In contrast, significant errors arise with unconstrained FIML in the very-high-Reynolds-number plane-channel case, whereas constrained FIML, by design, maintains the logarithmic law. This demonstrates that conventional FIML disrupts baseline model calibrations and may explain the lack of cross-scenario generalisation. Finally, in the backward-facing step and BeVERLI hill cases – two separated flows that share certain physical features with periodic hills but are absent from the training data – the constrained FIML framework delivers improved predictions over the baseline SA model, whereas unconstrained FIML results in no improvement and, in some cases, deterioration. These findings underscore that preserving the LoW can be important for achieving cross-scenario generalisability.