Capturing small scale dynamics of turbulent velocity and scalar fields using deep learning

The notion of small scale universality, captured for instance by the statistics of velocity gradients, is central to our understanding and modeling of turbulent flows. Similarly, when considering associated scalar transport and mixing processes, the statistics of scalar gradients are of equal importance. However, obtaining statistics of velocity and scalar gradients from direct numerical simulations at practical Reynolds numbers and Schmidt numbers is still beyond the capability of current supercomputers. In this work, we use a deep learning framework to model gradient dynamics by utilizing physics-informed tensor-based neural networks. We learn from a massive direct numerical simulation database at various Reynolds numbers and demonstrate that our model can predict statistics at higher unseen Reynolds numbers. Likewise, we illustrate extensions to passive scalar mixing at high Schmidt numbers. Our work demonstrates that prohibitively expensive direct numerical simulations at increasingly high Reynolds and Schmidt numbers can possibly be avoided, and the small scale dynamics of turbulence can be adequately modeled from existing datasets.