Fiber Orientation Fields in Turbulence

We study the orientation field of fibers in homogeneous isotropic turbulence. As small rod-like particles (referred to as fibers) are advected through a turbulent flow, they rotate and follow Jeffery’s equation, which may be used to calculate their orientations at any time in the flow. However, this method depends on the initial orientation chosen for each particle. Instead, we examine the preferential alignment of the particles, which is given by the largest stretching direction of the surrounding fluid. We calculate this using the left Cauchy-Green strain tensor, which measures the strain deformation undergone by the fluid over a finite time interval. The most extensional eigenvector of the left Cauchy-Green strain tensor gives the stretching direction and thus the preferential fiber orientation. This does not depend on the initial orientation of the particle. We show that the independence of initial conditions extends further: as we calculate this field using longer integration times (by considering earlier initial sampling times), the field converges to an invariant state. We visualize the spatial structures of the orientation field and observe, for the first time in 3D turbulence, surfaces across which the orientation rapidly rotates by π. These surfaces become thinner as we increase integration time, and create regions of very sharp change in the otherwise smooth orientation field. We measure these spatial structures statistically through the orientation structure function and demonstrate the fractal structure of the field caused by these alignment-inversion surfaces.