  We present simultaneous experimental measurements of the dynamics of
anisotropic particles transported by a turbulent flow and the velocity gradient
tensor of the flow surrounding them. We track both rod-shaped particles and
small spherical flow tracers using stereoscopic particle tracking. By using
scanned illumination, we are able to obtain a high enough seeding density of
tracers to measure the full velocity gradient tensor near the rod. The
alignment of rods with the vorticity and the eigenvectors of the strain rate
show agreement with numerical simulations. A full description of the tumbling
of rods in turbulence requires specifying a seven-dimensional joint probability
density function (PDF) of five scalars characterizing the velocity gradient
tensor and two scalars describing the relative orientation of the rod. If these
seven parameters are known, then Jeffery's equation specifies the rod tumbling
rate and any statistic of rod rotations can be obtained as a weighted average
over the joint PDF. To look for a lower-dimensional projection to simplify the
problem, we explore conditional averages of the mean-squared tumbling rate. The
conditional dependence of the mean-squared tumbling rate on the magnitude of
both the vorticity and the strain rate is strong, as expected, and similar.
There is also a strong dependence on the orientation between the rod and the
vorticity, since a rod aligned with the vorticity vector tumbles due to strain
but not vorticity. When conditioned on the alignment of the rod with the
eigenvectors of the strain rate, the largest tumbling rate is obtained when the
rod is oriented at a certain angle to the eigenvector that corresponds to the
smallest eigenvalue, because this particular orientation maximizes the
contribution from both the vorticity and strain.
