The motion, orientation, and control of self-propelled bodies in aqueous environments is an active field of scientific research. This field clearly has important engineering applications to, for example, swarms of autonomous underwater vehicles, collections of aerial drones, or swimming microrobots. This field is also important for understanding the fundamental physics of swimming organisms, such as bacteria, larvae, or even artificial colloidal particles. Many past studies focused on the interactions between bodies (agents) within a stationary ambient fluid; these interactions can lead to collective behavior like schooling, flocking, and group alignment. However, few studies have explored the motion of swimming agents in complicated flows that are caused by external disturbances. The current research will explore how isolated, self-propelled swimming agents are transported within such a flow. This is important for understanding swimming in the "real world", where swimmers often encounter nonnegligible, even turbulent, background flows. This work seeks to identify regions that are inaccessible to a swimmer, or accessible only after a long time. In many cases, these regions are delineated by geometric barriers that are not imposed by physical walls, but rather arise from subtle interactions between the dynamics of the swimmer and that of the flow. This work will develop techniques to predict where such barriers exist. These studies will be conducted in collaboration with a Bucknell University investigator, who is conducting experiments on bacteria in microfluidic flows.
For several decades it has been understood that invariant manifolds are the critical structures controlling the transport of passive tracers in fluids exhibiting chaotic advection. More recently, Lagrangian coherent structures have provided an analogous framework for passive advection in unsteady, aperiodic flows. The objective of this research is to extend these theories to agents that are both advected in the fluid and propelled under their own power. The passive invariant manifolds, and Lagrangian coherent structures, are no longer the most relevant objects. Rather, new objects called swimming invariant manifolds (SwIMs), which depend explicitly on the swimming speed, appear to be the key structures. This research will develop the theoretical framework for SwIMs, assess their importance to the transport of swimmers, and apply this framework to various scenarios, including: (i) swimmers of differing aspect ratios; (ii) steady, periodic, and aperiodic fluid flows; (iii) flows in 2D and 3D; (iv) hyperbolic versus elliptic flows; (v) the influence of stochastic effects in the swimmer's direction, and (vi) interactions between swimmers.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.