The Alignment of Rods and Disks in Turbulence

We study the orientation and rotational dynamics of anisotropic particles in homogenous isotropic turbulence. By analyzing direct numerical simulation (DNS) data at Taylor-microscale Reynolds number of Rλ = 180, we quantify the preferential alignment between particle orientations and vorticity, as well as alignment with principal stretching directions defined by the Cauchy-Green strain tensor. This tensor quantifies stretching experienced by material elements in turbulence and provides a natural basis for studying particle alignment in turbulence. While previous work has focused primarily on thin rods, we extend the study to oblate disks. Both rods and disks are a specific class of anisotropic particles known as axisymmetric ellipsoids. These particles are defined by their aspect ratio (α), the ratio of their length (L) to their diameter, (d). Rods have an aspect ratio of α > 1 while disks have an aspect ratio of α < 1. The case of α = 1 is a sphere. In this thesis, we compare the preferential alignments of rods with disks in turbulence. Rods preferentially align with vorticity as a result of both quantities independently aligning with the strongest extensional stretching direction, as defined by the maximum Cauchy-Green eigenvector, êL1. In contrast, disks orient perpendicular to vorticity and preferentially align with the strongest compressional stretching direction, as defined by the smallest Cauchy-Green eigenvector, êL3. Furthermore, we study the relationship between the principle stretching eigenframe defined by the eigenvectors of the Cauchy-Green strain tensor and the principle rate of stretching eigenframe defined by the eigenvectors of the strain-rate tensor, the symmetric part of the velocity gradient tensor.