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

Velocity gradient tensor, Aij = partial derivative u(i)/partial derivative x(j), in a turbulence flow field is modelled by separating the treatment of intermittent magnitude (A = root A(ij)A(ij)) from that of the more universal normalised velocity gradient tensor, b(ij) = A(ij)/A. The boundedness and compactness of the b(ij)-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.