In experiments and numerical simulations we measure angles between the symmetry axes of small spheroids advected in turbulence (passive directors). Since turbulent strains tend to align nearby spheroids, one might think that their relative angles are quite small. We show that this intuition fails in general because angles between the symmetry axes of nearby particles are anomalously large. We identify two mechanisms that cause this phenomenon. First, the dynamics evolves to a fractal attractor despite the fact that the fluid velocity is spatially smooth at small scales. Second, this fractal forms steps akin to scar lines observed in the director patterns for random or chaotic two-dimensional maps.

• Received 9 October 2017
• Revised 21 May 2018

DOI:https://doi.org/10.1103/PhysRevFluids.4.054602

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society