An Accurate and Interpretable Data-Driven Turbulence Model (Part 2 Modeling and Validation)

Existing LES and RANS turbulence models struggle to provide a description of turbulence that is accurate in both a priori and a posteriori sense in many key statistics. One such prominent statistic that models fail to capture are the backscatter of enstrophy and energy, as most models aim to only describe average inter-scale fluxes and generally fail to describe the spatial and temporal structure of these fluxes for flow regimes featuring strong coherent structures. Here we regularize and interpret the version of the data-driven equivariant model described in part 1, and show that it is not only numerically stable and generalizable, but provides an accurate description of a variety of key turbulence metrics such as fluxes (particularly the strength and localization of backscatter events), integral quantities (such as total energy), spectrum, and correlations substantially matching or outperforming popular models, such as ones based on the eddy viscosity assumption.