What is the `canonical structure' of turbulent flows
remains an important and multifaceted fundamental question
in turbulence research. One facet relates to typical
local deformations of fluid elements in the neighborhood
of Lagrangian tracers. These deformations are described by
the velocity gradient tensor. Its properties determine, for
instance, if the deformation produces vorticity stretching
along a particular direction (possibly yielding tubular
vortex structures), or to produce structures that are
flattened out in one direction while expanding in the
other two (possibly yielding pancake-like objects).

On the basis of recent three-dimensional measurements in
turbulent duct flow using holographic PIV techniques
(Tao, Katz & Meneveau, J. Fluid Mech. 2002), we
consider the dynamics of the velocity gradient tensor
filtered at inertial-range scales. In addition to
self-interactions and the filtered pressure Hessian, the
evolution of the filtered velocity gradient tensor is
determined by the subgrid-scale stress tensor. The
measurements  show that the SGS stresses have significant
effects on velocity gradient evolution, e.g. along the so-called
Vieillefosse tail they oppose the formation of a finite-time
singularity that occurs in Restricted Euler dynamics. Motivated by
practical modeling needs in the context of large eddy
simulations, we examine the behavior of various closures
for the subgrid stresses.  Analysis of the Smagorinsky,
nonlinear, and mixed models show that all reproduce the
real SGS stress effect along the Vieillefosse tail, but
that they fail in several other regions. An attempt is
made to optimize the mixed model by letting the two model
coefficients be functions of the two invariants R and Q.
Some recent wind-tunnel measurements will also be presented,
in which the classic Comte-Bellot & Corrsin experiment in
decaying isotropic turbulence is repeated at a much higher Reynolds
number, using an active grid in the same wind tunnel.