The role of the law of the wall in enabling generalization of data-driven turbulence models

We conduct a law-of-the-wall (LoW) constrained augmentation of the Spalart-Allmaras (SA) model within the framework of field inversion and machine learning (FIML). In contrast to conventional FIML approaches, our method explicitly imposes constraints to preserve the LoW—a key calibration of the SA model. The augmented model is trained using data from the flow over periodic hills and tested on plane channel flow, flat-plate boundary layer, backward-facing step, and three-dimensional BeVERLI hill to evaluate generalizability. Results show that preserving the LoW not only maintains model performance in the plane channel flow and flat-plate boundary layer but also improves generalizability to flows where non-equilibrium effects dominate and the LoW appears irrelevant. Specifically, the constrained FIML approach yields more accurate predictions of the separation bubble size and skin friction in the backward-facing step and the BeVERLI hill case—both of which are challenging for RANS models. In contrast, unconstrained FIML performs worse compared to the baseline SA model in these scenarios. These results suggest that the limited generalizability of existing data-driven models is not an inherent limitation of the FIML framework. More importantly, they underscore the value of preserving baseline model calibrations to ensure the generalizability of data-driven turbulence models.