Random Walks and L Evy Ights Observed in Uid Ows

We use a rapidly rotating tank lled with water to study the random walks of tracer particles in two di erent ows: one with coherent structures (vortices and jets), and one without (weakly turbulent). Most random walks, such as those taken by dye molecules di using by Brownian motion, obey the Central Limit Theorem; their motion can be characterized by a di usion constant. The random walks in our experiment with coherent structures are L evy ights: random walks with in nite mean square step size. L evy ights are particularly interesting as the Central Limit Theorem does not apply to them; the e ective di usion constant becomes in nite. Tracer particles in the weakly turbulent ow di use normally. We discuss our observations and mathematical descriptions of transport in situations with L evy ights.