Leveraging deep learning to predict small scale dynamics of turbulence at higher unseen Reynolds numbers

Turbulent flows in nature and engineering are characterized by a wide range of interacting scales, which must all be resolved for an accurate direct numerical simulation of the problem. However, despite ever improving supercomputing capabilities, such simulations in all circumstances are still not feasible and modeling remains unavoidable. In this regard, the notion of small scale universality, captured by velocity gradient statistics (for instance), has been very useful. Similarly, when considering the mixing and transport of scalars by turbulence, the statistics of scalar gradients are treated in the same spirit. In recent years, deep learning algorithms have emerged as promising modeling tools because of their ability to directly learn from data. Here, we present such an analysis in which tensor-based deep neural networks are utilized to model the gradient dynamics of velocity and scalars in turbulence. We learn from a massive direct numerical simulation database at various Reynolds numbers and demonstrate that our model can predict statistics at higher, yet unseen, Reynolds numbers. Likewise, extensions to turbulent mixing are illustrated. Our work demonstrates that prohibitively expensive simulations can be avoided and the small scale dynamics of turbulence can be adequately modeled from the already available datasets.