  The orientation dynamics of small anisotropic tracer particles in turbulent
flows is studied using direct numerical simulation (DNS) and results are
compared with Lagrangian stochastic models. Generalizing earlier analysis for
axisymmetric ellipsoidal particles (Parsa et al. 2012), we measure the
orientation statistics and rotation rates of general, triaxial ellipsoidal
tracer particles using Lagrangian tracking in DNS of isotropic turbulence.
Triaxial ellipsoids that are very long in one direction, very thin in another,
and of intermediate size in the third direction exhibit reduced rotation rates
that are similar to those of rods in the ellipsoid's longest direction, while
exhibiting increased rotation rates that are similar to those of axisymmetric
discs in the thinnest direction. DNS results differ significantly from the case
when the particle orientations are assumed to be statistically independent from
the velocity gradient tensor. They are also different from predictions of a
Gaussian process for the velocity gradient tensor, which does not provide
realistic preferred vorticity-strain-rate tensor alignments. DNS results are
also compared with a stochastic model for the velocity gradient tensor based on
the recent fluid deformation approximation (RFDA). Unlike the Gaussian model,
the stochastic model accurately predicts the reduction in rotation rate in the
longest direction of triaxial ellipsoids since this direction aligns with the
flow's vorticity, with its rotation perpendicular to the vorticity being
reduced. For disc-like particles, or in directions perpendicular to the longest
direction in triaxial particles, the model predicts {noticeably} smaller
rotation rates than those observed in DNS, a behavior that can be understood
based on the probability of vorticity orientation with the most contracting
strain-rate eigen-direction in the model.
