Fractality, chaos, and reactions in imperfectly mixed open hydrodynamical flows

We investigate the dynamics of tracer particles in time-dependent open flow s. If the advection is passive the tracer dynamics is shown to be typically transiently chaotic. This implies the appearance of stable fractal pattern s, so-called unstable manifolds, traced out by ensembles of particles. Next , the advection of chemically or biologically active tracers is investigate d. Since the tracers spend a long time in the vicinity of a fractal curve, the unstable manifold, this fractal structure serves as a catalyst for the active process. The permanent competition between the enhanced activity alo ng the unstable manifold and the escape dac: to advection results in a stea dy state of constant production rate. This observation provides a possible solution for the so-called "paradox of plankton", that several competing pl ankton species are able to coexists in spite of the competitive exclusion p redicted by classical studies. We point out that the derivation of the reac tion (or population dynamics) equations is analog to that of the macroscopi c transport equations based on a microscopic kinetic theory whose support i s a fractal subset of the full phase space. (C) 1999 Elsevier Science B.V. All rights reserved.