Formulating turbulence closures using sparse regression with embedded form invariance

A data-driven framework for formulation of closures of the Reynolds-average Navier-Stokes (RANS) equations is presented. In recent years, the scientific community has turned to machine learning techniques to translate data into improved RANS closures. While the body of work in this area has primarily leveraged neural networks (NNs), we alternately leverage a sparse regression framework. This methodology has two important properties: (1) The resultant model is in a closed, algebraic form, allowing for direct physical inferences to be drawn and naive integration into existing computational fluid dynamics solvers, and (2) Galilean invariance can be guaranteed by thoughtful tailoring of the feature space. Our approach is demonstrated for two classes of flows: homogeneous free shear turbulence and turbulent flow over a wavy wall. The model learned based upon the wavy wall configuration is then validated against flow over a backward-facing step. This work demonstrates similar performance to that of modern NNs but with the added benefits of interpretability, increased ease of use and dissemination, and robustness to sparse and noisy training data sets.