Determinism and invariant measures for diffusing passive scalars advected by unsteady random shear flows

Abstract

We study a complicated fluid flow generated by a robotic arm moving randomly back and forth that is shown to stir a tracer in an unexpectedly simple way. One might expect that such random motions would lead to highly random observations. But it turns out that after a certain, fixed amount of time, a broad class of random motions leads to an enhanced non-random, deterministic tracer spreading rate. Looking closer, the tracer shows non-Gaussian random fluctuations which are explicitly computed.