Machine Learning assisted modeling of velocity gradient dynamics in turbulent flows

The evolution of nonlinear turbulent processes like energy cascading, scalar mixing, and intermittency is highly dependent on the evolution process of velocity gradients. Accessing the velocity gradient evolution through simple dynamic models has many advantages over direct numerical simulations (DNS) and experimental methods. Indeed. such velocity gradient models can be directly used as closure models for Lagrangian probability density function (PDF) methods. Modeling the velocity gradient dynamics needs modeling of the two terms the pressure Hessian tensor and the viscous term which are nonlocal and mathematically unclosed. In this work, the TBNN architecture is used to model the pressure Hessian term. The TBNN model is trained with the locally normalized incompressible isotropic DNS data. Using a local normalization strategy enables our model to integrate the pressure hessian term in the velocity gradient evolution equation. The current model performance is evaluated based on known turbulent characteristics observed in DNS results. The performance of the new model is also compared with the existing velocity gradient models of incompressible as well as compressible flows. The model is showing a significant improvement over the existing models.