Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact Publication 14-CNA-017 Anomalous Diffusion in Fast Cellular Flows at Intermediate Time Scales Gautam IyerDepartment of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213gautam@math.cmu.edu Alexei NovikovDepartment of Mathematics Pennsylvania State University State College PA 16802anovikov@math.psu.eduAbstract: 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