Chaos and dynamic trapping of swimming microbes in a vortex chain flow*

We present experiments of the motion of swimming Tetraselmis algae microbes in a two-dimensional, vortex chain flow. For microbes swimming with small speed v₀, simulated trajectories of idealized swimmers can be either chaotic or ordered, depending on the location in the flow. In the experiments, the slow-swimming microbes follow trajectories that appear to be chaotic, but which become dynamically trapped temporarily to ghosts of the ordered region in the flow. The long-range transport in this case is subdiffusive with variance <x²> ~ t^γ with γ < 1.  For larger swimming speeds, the simulated island of ordered trajectories disappears, resulting in long-range transport that is diffusive (γ = 1).We calculate Lagrangian-averaged trajectories (LATs) from the experimental data and use the LATs to measure trapping time probability distributions P(t). We find regimes with P(t) ~ t^-η with η < 2 for small v₀, consistent with the measured subdiffusion.