Nonlinear Science Webinar - Wednesday, April 8, 3:00-4:00pm EST at Georgia Tech, https://gatech.bluejeans.com/7678987299
April 8, 2020 - 3:00pm to 4:00pm
at Georgia Tech, https://gatech.bluejeans.com/7678987299
UNIVERSITY OF CALIFORNIA, MERCED
The transport and mixing of passive tracers in a fluid can be understood in terms of a passive tracer’s phase-space geometry: the invariant solutions and invariant manifolds of the passive tracer equations of motion. In this talk, I will describe our ongoing work on extending this phase-space perspective to explain the transport of a particular type of active tracer: the rigid ellipsoidal microswimmer. In our model, microswimmers swim at a fixed speed in the local fluid frame and rotate due to flow gradients at a rate determined by their shape. We determine the phase-space structures governing transport in two model fluid flows and examine the influence of swimmer speed and shape. In the first example, a linear hyperbolic flow, we find that the fixed points and their invariant manifolds form one-way barriers to the swimmers, while the swimmer parameters play a minor role. In the second example, a spatially periodic vortex array, we focus on the trapping of swimmers in vortices. We identify a stable periodic orbit surrounded by invariant tori as the main cause of trapping for a wide range of swimmer parameters. We show that this periodic orbit undergoes a sequence of bifurcations, both local and global, which sheds light on the sensitive dependence of trapping probability on swimmer speed and shape and accurately predicts the parameters at which the trapping probability vanishes.