Towards a physical interpretation of machine-learned turbulence models

This study aims at obtaining a physical understanding of the existing machine-learning turbulence models. We apply three established methods, i.e., tensor-basis neural networks (TBNN), physics-informed machine learning (PIML), and field inversion & machine learning (FIML), to the one-equation Spalart-Allmaras model, the two-equation Wilcox k-omega model, and the seven-equation full Reynolds stress model. The machine learning corrections are trained against plane channel flow and temporally-evolving mixing layer flow. The goal is to assess if the ML methods can preserve the law of the wall. Our results show that FIML preserves the law of the wall for the one- and two-equation models and improve the predictions of the seven-equation model in the context of channel flow---although the improvement offered by FIML is not entirely physical. TBNN and PIML, on the other hand, do not preserve the law of the wall, which proves to be a consequence of the choice of inputs.