Chaotic advection, diffusion, and reactions in open flows

We review and generalize recent results on advection of particles in open t ime-periodic hydrodynamical flows. First, the problem of passive advection is considered, and its fractal and chaotic nature is pointed out. Next, we study the effect of weak molecular diffusion or randomness of the flow. Fin ally, we investigate the influence of passive advection on chemical or biol ogical activity superimposed on open flows. The nondiffusive approach is sh own to carry some features of a weak diffusion, due to the finiteness of th e reaction range or reaction velocity. (C) 2000 American Institute of Physi cs. [S1054-1500(00)02001-2].