Chemical or biological activity in open chaotic flows

György Károlyi, Áron Péntek, Zoltán Toroczkai, Tamás Tél, Celso Grebogi

Research output: Contribution to journalArticle

54 Citations (Scopus)

Abstract

We investigate the evolution of particle ensembles in open chaotic hydrodynamical flows. Active processes of the type [Formula Presented] and [Formula Presented] are considered in the limit of weak diffusion. As an illustrative advection dynamics we consider a model of the von Kármán vortex street, a time-periodic two-dimensional flow of a viscous fluid around a cylinder. We show that a fractal unstable manifold acts as a catalyst for the process, and the products cover fattened-up copies of this manifold. This may account for the observed filamental intensification of activity in environmental flows. The reaction equations valid in the wake are derived either in the form of dissipative maps or differential equations depending on the regime under consideration. They contain terms that are not present in the traditional reaction equations of the same active process: the decay of the products is slower while the productivity is much faster than in homogeneous flows. Both effects appear as a consequence of underlying fractal structures. In the long time limit, the system locks itself in a dynamic equilibrium state synchronized to the flow for both types of reactions. For particles of finite size an emptying transition might also occur leading to no products left in the wake.

Original languageEnglish
Pages (from-to)5468-5481
Number of pages14
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume59
Issue number5
DOIs
Publication statusPublished - Jan 1 1999

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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