Deep Learning Emulation of Subgrid-Scale Processes in Turbulent Shear Flows

Deep neural networks (DNNs) are developed from a data set obtained from the dynamic Smagorinsky model to emulate the subgrid-scale (SGS) viscosity (nu(sgs)) and diffusivity (kappa(sgs)) for turbulent stratified shear flows encountered in the oceans and the atmosphere. These DNNs predict nu(sgs) and kappa(sgs) from velocities, strain rates, and density gradients such that the evolution of the kinetic energy budget and density variance budget terms is similar to the corresponding values obtained from the original dynamic Smagorinsky model. These DNNs also compute nu(sgs) and kappa(sgs) similar to 2-4 times quicker than the dynamic Smagorinsky model resulting in a similar to 2-2.5 times acceleration of the entire simulation. This study demonstrates the feasibility of deep learning in emulating the subgrid-scale (SGS) phenomenon in geophysical flows accurately in a cost-effective manner. In a broader perspective, deep learning-based surrogate models can present a promising alternative to the traditional parameterizations of the subgrid-scale processes in climate models. Plain Language Summary Large eddy simulations (LES) are commonly used to simulate various oceanic and atmospheric flows. In LES, the large eddies are resolved, whereas the small-scale turbulent features, which are the primary sources of mixing, are parameterized using physical models. A deep learning-based surrogate LES model is developed from the data set obtained from such a physical model, the dynamic Smagorinsky model, at moderate Reynolds number and resolution. When this surrogate LES model is deployed for 10 times higher Reynolds number at a relatively higher and lower resolution, it was able to capture all the qualitative and quantitative features of the flow accurately at a cheaper computational cost. The effectiveness of deep learning-based surrogate models to emulate the small-scale processes is a promising area of research and can potentially be extended for various subgrid-scale parameterizations in climate and earth science models.