Manifolds, perimeters and speeds for active tracers and fronts in a two-dimensional flow

We study the motion of reaction fronts and swimming organisms in either a two-dimensional vortex array or disordered fluid flow. The reaction fronts are produced by the excitable Belousov-Zhabotinsky chemical reaction, and the swimming organisms are brine shrimp nauplii. Previous experiments have shown that the motion of both reaction fronts and swimming organisms in these flows are bounded by invariant manifolds (Burning and Swimming Invariant Manifolds – BIMs and SwIMs – respectively) that act as one-way barriers. We test theoretical predictions that the coarse-grained speed of a spreading reaction front is determined by its perimeter which is determined by the structure of the BIMs. We further test predictions that the spreading of an ensemble of swimmers in the flow – even those that tumble – is bounded by the same BIMs predicted for reaction fronts in the same flow.