Chaotic advection in a two-dimensional flow: Lévy flights and anomalous diffusion

Abstract

Long-term particle tracking is used to study chaotic transport experimentally in laminar, chaotic, and turbulent flows in an annular tank that rotates sufficiently rapidly to insure two-dimensionality of the flow. For the laminar and chaotic velocity fields, the flow consists of v flow regimes, tracer particles stick for long times to remnants of invariant surfaces around the vortices, then make long excursions (“flights”) in the jet regions. The probability distributions for the flight time durations exhibit power-law rather than exponential decays, indicating that the parrticle trajectories are described mathematically as Lévy flights (i.e. the trajectories have infinite mean square displacement per flight). Sticking time probability distributions are also characterized by power laws, as found in previous numerical studies. The mixing of an ensemble of tracer particles is superdiffusive: the variance of the displacement grows with time as t λ with 1<λ<2. The dependence of the diffusion exponent λ and the scaling of the probability distributions are investigated for periodic and chaotic flow regimes, and the results are found to be consistent with theoretical predictions relating Lévy flights and anomalous diffusion. For a turbulent flow, the Lévy flight description no longer applies, and mixing no longer appears superdiffusive.