Capturing velocity gradients and particle rotation rates in turbulence

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