Gyrotactic suppression and emergence of chaotic trajectories of swimming particles in three-dimensional flows

Abstract

We study the effects of imposed {three-dimensional flows} on the trajectories and mixing of gyrotactic swimming micro-organisms, and identify new phenomena not seen in flows restricted to two dimensions. Through numerical simulation of Taylor--Green and ABC flows, we explore the role that the flow and the cell shape play in determining the long-term configuration of the cells' trajectories, which often take the form of multiple sinuous and helical `plume-like' structures, even in the chaotic ABC flow. This gyrotactic suppression of Lagrangian chaos persists even in the presence of random noise. Analytical solutions for a number of cases reveal the how plumes form and the nature of the competition between torques acting on individual cells. \note{Furthermore, studies of Lyapunov exponents reveal that as the ratio of cell swimming speed relative to the flow speed increases from zero, the initial chaotic trajectories are first suppressed and then give way to a second unexpected window of chaotic trajectories at speeds greater than unity, before suppression of chaos at high relative swimming speeds.