Publication 14-CNA-017

Anomalous Diffusion in Fast Cellular Flows at Intermediate Time Scales

Gautam Iyer
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
gautam@math.cmu.edu

Alexei Novikov
Department of Mathematics
Pennsylvania State University
State College PA 16802
anovikov@math.psu.edu

Abstract: 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 $O(\sqrt t)$. Hence, on these time scales the effective behaviour can not be purely diffusive, and is consistent with an anomalous diffusive behaviour.

Get the paper in its entirety as  14-CNA-017.pdf

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