Mixing and Chaos in Open Flows

We review the theoretical and experimental knowledge of mixing in open flows displaying chaotic advection, from a point of view of dynamical systems theory. We show that the chaotic saddle and its stable and unstable manifolds constitute the skeleton around which the dynamics are organized, and that their fractal properties govern advection and mixing in open flows. The effects of KAM islands on the mixing are examined, as well as the interplay between molecular diffusion and chaotic advection. We discuss the appropriate definition of mixing in practical situations and present experiments motivated by industrial applications. We also discuss applications of these concepts to plankton dynamics in the oceans.