Turbulence modeling of stratified turbulence using a constrained artificial neural network

For large eddy simulations (LES) of stratified turbulence in the strongly stratified regime, an artificial neural network (ANN) with five hidden layers is used to construct a sub-grid scale (SGS) model. The ANN is assessed by comparing it to the Smagorinsky model, the dynamic Smagorinsky model, the gradient model, and filtered direct numerical simulation data. In the a priori test, the SGS model using ANN performed better than the Smagorinsky model and the gradient model in terms of the correlation coefficient and relative error of the energy transfer rate. However, the ANN does not provide sufficient energy dissipation when it is applied to LES with a larger filter width because it overpredicts backscatter. To address this problem, we also trained a constrained ANN using a custom loss function that penalizes excessive backscatter. It is shown that the constrained ANN successfully predicts less backscatter, maintaining the high correlation coefficient without ad hoc clipping. These results show that ANN is a promising tool for realizing a highly accurate and stable SGS model for stratified turbulence.