Manifolds, swimming microbes and propagating fronts in a vortex array flow

We present experiments that measure the speeds of moving fronts and swimming organisms in a two-dimensional, vortex array flow. The fronts in these experiments are produced by the excitable Belousov-Zhabotinsky (BZ) reaction, and the swimming organisms are either tumbling brine shrimp nauplii or an active dye composed of swimming Tetraselmis microbes. The motion of the reaction fronts is determined by burning invariant manifolds (BIMs) that have been previously shown to act as one-way barriers. These BIMs serve to roughen the front, with rougher, more folded fronts (with larger perimeter L_f) for smaller non-dimensional propagation speed V₀/U, where V₀ is the speed at which fronts move in the absence of a flow and U is the maximum flow speed. We test predictions that the coarsened front speed scales linearly with the roughness L_f/L_a where L_a is the circumference of a circle with the same overall area as the roughened front. Swimming organisms in the same flow are also bound by the same BIMs, even if the organism is tumbling.