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Abstract

Rotations of spheroidal particles immersed in turbulent flows reflect the combined effects
of fluid strain and vorticity, as well as the time history of these quantities along the
particle’s trajectory. Conversely, particle rotation statistics in turbulence provide a way
to characterise the Lagrangian properties of velocity gradients. Particle rotations are
also important for a range of environmental and industrial processes where particles of
various shapes and sizes are immersed in a turbulent flow. In this study, we investigate
the rotations of inertialess spheroidal particles that follow Lagrangian fluid trajectories.
We perform direct numerical simulations (DNS) of homogeneous isotropic turbulence
and investigate the dynamics of different particle shapes at different scales in turbulence
using a filtering approach.We find that the mean-square particle angular velocity is nearly
independent of particle shape across all scales from the Kolmogorov scale to the integral
scale. The particle shape does determine the relative split between different modes of
rotation (spinning vs tumbling), but this split is also almost independent of the filter scale
suggesting a Lagrangian scale-invariance in velocity gradients. We show how the split
between spinning and tumbling can be quantitatively related to the particle’s alignment
with respect to the fluid vorticity.