Dynamical systems tools prove to be instrumental for analyzing the transport properties of simple (time periodic) fluid flows in the limit of vanishing molecular diffusion. In particular, the unstable manifolds of hyperbolic stagnation points divide the space and govern the motion of fluid particles. Hence, the geometrical properties of the unstable and stable manifolds determine the transport of passive scalars. These considerations may explain the combined effects of chaotic advection and molecular diffusion on the finite time transport of a fixed initial distribution of scalars. Moreover, there are some universal properties of the frequency dependence of such transport problems in a broad class of time periodic flows. The relation to recent works on a-periodic flows and geophysical applications will be discussed.
Joint work with A. Poje.