  The local statistical and geometric structure of three-dimensional turbulent
flow can be described by properties of the velocity gradient tensor. A
stochastic model is developed for the Lagrangian time evolution of this tensor,
in which the exact nonlinear self-stretching term accounts for the development
of well-known non-Gaussian statistics and geometric alignment trends. The
non-local pressure and viscous effects are accounted for by a closure that
models the material deformation history of fluid elements. The resulting
stochastic system reproduces many statistical and geometric trends observed in
numerical and experimental 3D turbulent flows, including anomalous relative
scaling.
