Coherent Structures in 3D Stretching Alignment Fields

We study the emergent structures of stretching alignment fields in 3D flows in order to better understand stretching and folding in turbulence. We numerically study a 3D sine flow and determine magnitudes and directions of stretching from the Cauchy Green strain tensors. From previous work in 2D, interest areas have been identified at alignment inversion sites where we see large gradients in the stretching orientation director field. In three dimensions, these alignment inversions can occur in several different types related to the twist and bend walls exhibited in nematic liquid crystals but with additional inversion geometries inherent with the triaxial ellipsoids caused by 3D fluid deformation. We find that different types of inversions continuously transform from one to another along a single inversion surface. These surfaces become sharper with time and, in turbulence, could be the geometric structures responsible for the rapid curvature growth rate at later times observed by Qi et al. [1] as well as the fractal orientation fields observed by Zhao et al. [2]

[1] Y. Qi, C. Meneveau, G. A. Voth, and R. Ni, Phys. Rev. Lett. 130 (2023)

[2] L. Zhao et al., Phys. Rev. Fluids 4 (2019)