Fractality, Chaos, and Reactions in Imperfectly Mixed Open Hydrodynamics Flows

A Pentek, G Karolyi, I Scheuring, T Tel, Z Toroczkai* (Corresponding Author), J Kadtke, C Grebogi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


We investigate the dynamics of tracer particles in time-dependent open flows. If the advection is passive the tracer dynamics is shown to be typically transiently chaotic. This implies the appearance of stable fractal patterns, so-called unstable manifolds, traced out by ensembles of particles. Next, the advection of chemically or biologically active tracers is investigated. 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 along the unstable manifold and the escape due to advection results in a steady state of constant production rate. This observation provides a possible solution for the so-called “paradox of plankton”, that several competing plankton species are able to coexists in spite of the competitive exclusion predicted by classical studies. We point out that the derivation of the reaction (or population dynamics) equations is analog to that of the macroscopic transport equations based on a microscopic kinetic theory whose support is a fractal subset of the full phase space.
Original languageEnglish
Pages (from-to)120-131
Number of pages12
JournalPhysica. A, Statistical Mechanics and its Applications
Issue number1-2
Early online date20 Dec 1999
Publication statusPublished - Dec 1999
EventNATO Advanced Research Workshop: Applications of Statistical Physics - Budapest, Hungary
Duration: 19 May 199922 May 1999

Bibliographical note

This research has been supported by the NSF-MRSEC at University of Maryland, by the NSF-DMR, by ONR(physics), CNPq/NSF-INT, by the DOE, by the US-Hungarian Science and Technology Joint Fund under Project numbers 286 and 501, by the Hungarian Science Foundation T019483, T025793, T029789, and F029637, by the Hungarian-British Intergovernmental Science and Technology Cooperation Program GB-66/95, and by the Hungarian Ministry of Culture and Education under grant number 0391/1997.


  • leapfrogging vortex pairs
  • Gonyaulax-Polyedra Stein
  • Red Tide Dinoflagellate
  • Stokes-Flow
  • advection
  • scattering
  • turbulence
  • kinematics
  • boundaries
  • transport


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