Modeling of structural uncertainties in Reynolds-averaged Navier-Stokes closures

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Machine Learning-augmented Predictive Modeling of Turbulent Separated Flows over Airfoils (2016, methodology): “[20] introduced ad hoc but realizable perturbations to the nondimensional Reynolds stress anisotropy tensor aij to quantify structural errors in eddy viscosity models.”
Turbulence Modeling in the Age of Data (2018, methodology): “Emory et al. (2013) and Gorl´e et al. (2014) speciﬁed a spatial ﬁeld for the eigenvalue perturbations based on the assumed limitations of RANS models, while Wang et al. (2016b) and Xiao et al. (2017) used a non-stationary Gaussian process to encode the same empirical knowledge.”
Quantification of model uncertainty in RANS simulations: A review (2018, methodology): “[54] specified a spatial field for the eigenvalue perturbations based on the empirical understanding on the performance of the RANS model for the particular”
Physics-informed machine learning approach for augmenting turbulence models: A comprehensive framework (2017, methodology): “Following [8, 43], we formulate the Reynolds stress discrepancies as six physically interpretable components (i.”