  Turbulent fluid flows exhibit a complex small-scale structure with frequently
occurring extreme velocity gradients. Particles probing such swirling and
straining regions respond with an intricate shape-dependent orientational
dynamics, which sensitively depends on the particle history. Here, we
systematically develop a reduced-order model for the small-scale dynamics of
turbulence, which captures the velocity gradient statistics along particle
paths. An analysis of the resulting stochastic dynamical system allows
pinpointing the emergence of non-Gaussian statistics and non-trivial temporal
correlations of vorticity and strain, as previously reported from experiments
and simulations. Based on these insights, we use our model to predict the
orientational statistics of anisotropic particles in turbulence, enabling a
host of modeling applications for complex particulate flows.
