Barriers, chutes and long-range transport of active tracers in vortex flows*

We present experiments on the effects of imposed, two-dimensional, laminar flows on the motion of self-propelled tracers. The self-propelled particles are motile algae microbes (tetraselmis and euglena) or brine shrimp (artemia) nauplii, and the flow is a time-independent chain or array of vortices, driven magnetohydrodynamically. The trajectories of the swimming organisms in the flows are analyzed in terms of a theory of "swimming invariant manifolds" (SwIMs). These SwIMs separate trajectories into distinct regions in a three-dimensional phase space determined by the x and y coordinates and swimming directions of the microbes. Projected into physical, x-y space, the edges of the SwIMs act as one-way barriers through which the active tracers can cross in one-direction only. This theory is a generalization of a theory of "burning invariant manifolds" (BIMs) that have previously been shown to act as one-way barriers that block the motion of propagating reaction fronts in laminar flows. The SwIMs also combine to produce "chutes" that carry microbes between adjacent vortices.  We measure the growing variance of an ensemble for different microbe swimming speeds and interpret those results in terms of the SwIM geometry and the coexistence of ordered and chaotic trajectories of the swimming microbes.