A data-driven approach to model enstrophy transfers in large eddy simulation of forced two-dimensional turbulence

Abstract

Contemporary research on the application of data-driven techniques to modeling subgrid closure in two-dimensional turbulence has been limited. Furthermore, the incorporation of the enstrophy cascade and other two-dimensional turbulence-specific physics has received insufficient attention. To address these gaps, a novel physics-based shallow feed-forward neural network framework was designed in this study to model subgrid closure in three selected cases of forced two-dimensional turbulence with a forcing that provides energy and enstrophy at a particular wavenumber. As a novel approach, we trained our framework to learn the subgrid vorticity transport vector from a set of appropriate resolved flow variables. Another framework used in recent works which directly learned the subgrid forcing field was also investigated. Both frameworks were assessed using a priori and a posteriori tests for two selected filter widths. Both frameworks performed accurately for the lower filter width but less accurately for the higher filter width. However, we demonstrate that our new framework has wider usefulness for model diagnosis. Ad hoc clipping procedures were used to make the models more generalizable to higher filter widths, and stable and consistent a posteriori tests were observed for all test cases and filter widths when the subgrid forcing field was modified to enhance the model's subgrid dissipative characteristics. In contrast, modifying the enstrophy fluxes did not perform as consistently. These findings demonstrate the potential of the novel physics-based framework for improving subgrid modeling in two-dimensional turbulence.