Subgrid modelling for two-dimensional turbulence using neural networks

Abstract

In this investigation, a data-driven turbulence closure framework is introduced and deployed for the subgrid modelling of Kraichnan turbulence. The novelty of the proposed method lies in the fact that snapshots from high-fidelity numerical data are used to inform artificial neural networks for predicting the turbulence source term through localized grid-resolved information. In particular, our proposed methodology successfully establishes a map between inputs given by stencils of the vorticity and the streamfunction along with information from two well-known eddy-viscosity kernels. Through this we predict the subgrid vorticity forcing in a temporally and spatially dynamic fashion. Our study is botha priorianda posterioriin nature. In the former, we present an extensive hyper-parameter optimization analysis in addition to learning quantification through probability-density-function-based validation of subgrid predictions. In the latter, we analyse the performance of our framework for flow evolution in a classical decaying two-dimensional turbulence test case in the presence of errors related to temporal and spatial discretization. Statistical assessments in the form of angle-averaged kinetic energy spectra demonstrate the promise of the proposed methodology for subgrid quantity inference. In addition, it is also observed that some measure ofa posteriorierror must be considered during optimal model selection for greater accuracy. The results in this article thus represent a promising development in the formalization of a framework for generation of heuristic-free turbulence closures from data.