Accumulation and alignment of elongated gyrotactic swimmers in turbulence

Abstract

We study the dynamics of gyrotactic swimmers in turbulence, whose orientation is governed by gravitational torque and local fluid velocity gradient. The gyrotaxis strength is measured by the ratio of the Kolmogorov time scale to the reorientation time scale due to gravity, and a large value of this ratio means the gyrotaxis is strong. By means of direct numerical simulations, we investigate the effects of swimming velocity and gyrotactic stability on spatial accumulation and alignment. Three-dimensional Voronoï analysis is used to study the spatial distribution and time evolution of the particle concentration. We study spatial distribution by examining the overall preferential sampling, where clusters and voids (subsets of particles that have small and large Voronoï volumes, respectively) form. Compared with the ensemble particles, the preferential sampling of clusters and voids is found to be more pronounced. The clustering of fast swimmers lasts much longer than slower swimmers when the gyrotaxis is strong and intermediate, but an opposite trend emerges when the gyrotaxis is weak. In addition, we study the preferential alignment with the Lagrangian stretching direction, with which passive slender rods have been known to align. We show that the Lagrangian alignment is reduced by the swimming velocity when the gyrotaxis is weak, while the Lagrangian alignment is enhanced for the regime in which gyrotaxis is strong.