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

Velocity gradient tensor, Aᵢⱼ≡ ∂ uᵢ/∂ xⱼ , in a turbulence flow field is modelled by separating the treatment of intermittent magnitude ( A = √ AᵢⱼAᵢⱼ ) from that of the more universal normalised velocity gradient tensor, bᵢⱼ ≡ Aᵢⱼ/A . The boundedness and compactness of the bᵢⱼ -space along with its universal dynamics allow 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 data over a wide range of velocity-gradient features and Reynolds numbers.