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In this investigation, a data-driven turbulence closure framework isintroduced and deployed for the sub-grid modelling of Kraichnan turbulence. Thenovelty of the proposed method lies in the fact that snapshots fromhigh-fidelity numerical data are used to inform artificial neural networks forpredicting the turbulence source term through localized grid-resolvedinformation. In particular, our proposed methodology successfully establishes amap between inputs given by stencils of the vorticity and the streamfunctionalong with information from two well-known eddy-viscosity kernels. Through thiswe predict the sub-grid vorticity forcing in a temporally and spatially dynamicfashion. Our study is both a-priori and a-posteriori in nature. In the former,we present an extensive hyper-parameter optimization analysis in addition tolearning quantification through probability density function based validationof sub-grid predictions. In the latter, we analyse the performance of ourframework for flow evolution in a classical decaying two-dimensional turbulencetest case in the presence of errors related to temporal and spatialdiscretization. Statistical assessments in the form of angle-averaged kineticenergy spectra demonstrate the promise of the proposed methodology for sub-gridquantity inference. In addition, it is also observed that some measure ofa-posteriori error must be considered during optimal model selection forgreater accuracy. The results in this article thus represent a promisingdevelopment in the formalization of a framework for generation ofheuristic-free turbulence closures from data.

Sub-grid modelling for two-dimensional turbulence using neural networks