Abstract: The
local statistical and geometric structure of
threedimensional 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 selfstretching term accounts for the
development of wellknown nonGaussian statistics
and geometric alignment trends. The nonlocal
pressure and viscous effects are accounted for by a
closure that models the material deformation history
of fluid elements. The system is forced with a
simple, white in time, Gaussian noise. The resulting
stochastic system reproduces many statistical and
geometric trends observed in numerical and
experimental 3D turbulent flows. Examples include
the nonGaussian statistics of velocity gradient
components, the preferential aligment of vorticity,
nearly lognormal statistics of the dissipation, the
teardrop shape of the socalled `RQ' joint
probability density and anomalous relative scaling
of velocity derivatives.
[LECTURE SLIDES]
