An Accurate and Interpretable Data-Driven Turbulence Model (Part 1 Discovery and Formulation)

Constructing accurate, stable and generalizable turbulence models that work over a wide range of parameters and flow regimes has been a challenge for over half a century. Most modelling approaches rely on strong physical assumptions that are only satisfied under certain conditions (e.g., in the absence of strong coherent structures). These assumptions usually lead to models that do not generalize well, are unstable, and/or fail to capture key statistics. To address these problems, we use a data-driven framework (SPIDER), which makes no specific physical assumptions, and dimensional analysis to infer an equivariant turbulence model. This model comprises a closure term that incorporates the dependence of the subgrid-scale stress tensor on small scales and an explicit evolution equation for the Reynolds stress tensor describing small scales. The closure is interpretable as a version of a higher-order nonlinear gradient model which allows one to infer the explicit dependence of the coefficients on the filter scale, the filtering operator, and molecular viscosity.