Data-driven model for Lagrangian evolution of velocity gradients in incompressible turbulent flows

Abstract

Velocity gradient tensor, $A_{ij}\equiv \partial u_i/\partial x_j$, in a turbulence flow field is modeled by separating the treatment of intermittent magnitude ($A = \sqrt{A_{ij}A_{ij}}$) from that of the more universal normalized velocity gradient tensor, $b_{ij} \equiv A_{ij}/A$. The boundedness and compactness of the $b_{ij}$-space along with its universal dynamics allows for the development of models that are reasonably insensitive to Reynolds number. The near-lognormality of the magnitude $A$ is then exploited to derive a model based on a modified Ornstein-Uhlenbeck process. These models are developed using data-driven strategies employing high-fidelity forced isotropic turbulence data sets. A posteriori model results agree well with direct numerical simulation (DNS) data over a wide range of velocity-gradient features.