Transport of Swimmers in a Periodic Vortex Lattice: A Theoretical Study with Noise*

There is a large body of research on the dynamics of tracer particles in fluid flows. Most of this research focusses on the passive case, where small particles are advected by the flow. Less is known about active self-propelled tracer particles. This research is a theoretical study of the nonlinear dynamics of rigid ellipsoidal self-propelled particles (swimmers) in a two dimensional periodic vortex lattice. The system is treated with and without noise. Deterministic swimmers can undergo ballistic transport at low swimming speeds, while the motion is chaotic at high swimming speeds. The symmetries of the flow are used to produce a Poincare surface of section. Due to time reversal symmetry, periodic orbits of the Poincare map are surrounded by ballistic tori; these orbits undergo a period-doubling cascade that destroys the stable islands. These bifurcations are correlated with a ballistic to diffusive transition in ensemble simulations. Monte-Carlo simulations are used to test the robustness of these results to noise.