Chemical or biological activity in open chaotic flows

We investigate the evolution of particle ensembles in open chaotic hydrodyn amical flows. Active processes of the type A+B-->2B and A+B-->2C are consid ered in the limit of weak diffusion. As an illustrative advection dynamics we consider a model of the von vortex street, a time-periodic two-dimension al flow of a viscous fluid around a cylinder. We show that a fractal unstab le manifold acts as a catalyst for the process, and the products cover fatt ened-up copies of this manifold. This may account for the observed filament al intensification of activity in environmental flows. The reaction equatio ns valid in the wake are derived either in the form of dissipative maps or differential equations depending on the regime under consideration. They co ntain terms that are not present Ln the traditional reaction equations of t he same active process: the decay of the products is slower while the produ ctivity is much faster than in homogeneous flows. Both effects appear as a consequence of underlying fractal structures. In the long time limit, the s ystem locks itself in a dynamic equilibrium state synchronized to the flow for both types of reactions. For particles of finite size an emptying trans ition might also occur leading to no products left in the wake. [S1063-651X (99)04905-3].