Physics-informed data-driven inference of an interpretable equivariant LES model of incompressible fluid turbulence

Abstract

Restrictive phenomenological assumptions represent a major roadblock for the development of accurate subgrid-scale models of fluid turbulence. Specifically, these assumptions limit a model's ability to describe key quantities of interest, such as local fluxes of energy and enstrophy, in the presence of diverse coherent structures. This paper introduces a symbolic data-driven subgrid-scale model that requires no phenomenological assumptions and has no adjustable parameters, yet it outperforms leading LES models. A combination of a priori and a posteriori benchmarks shows that the model produces accurate predictions of various quantities including local fluxes across a broad range of two-dimensional turbulent flows. While the model is inferred using LES-style spatial coarse-graining, its structure is more similar to RANS models, as it employs an additional field to describe subgrid scales. We find that this field must have a rank-two tensor structure in order to correctly represent both the components of the subgrid-scale stress tensor and the various fluxes.