Date of Original Version

1-21-2015

Type

Article

Rights Management

The final publication is available at Springer via http://dx.doi.org/10.1007/s00440-015-0617-9

Abstract or Description

It is well known that on long time scales the behaviour of tracer particles diffusing in a cellular flow is effectively that of a Brownian motion. This paper studies the behaviour on “intermediate” time scales before diffusion sets in. Various heuristics suggest that an anomalous diffusive behaviour should be observed. We prove that the variance on intermediate time scales grows like O(t√). Hence, on these time scales the effective behaviour can not be purely diffusive, and is consistent with an anomalous diffusive behaviour.

DOI

10.1007/s00440-015-0617-9

Included in

Mathematics Commons

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Published In

Probability Theory and Related Fields, 2015, 1-34.