### Abstract

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 dac: 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. (C) 1999 Elsevier Science B.V. All rights reserved.

Original language | English |
---|---|

Pages (from-to) | 120-131 |

Number of pages | 12 |

Journal | Physica. A, Statistical Mechanics and its Applications |

Volume | 274 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 1 Dec 1999 |

### Keywords

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

### Cite this

*Physica. A, Statistical Mechanics and its Applications*,

*274*(1-2), 120-131. https://doi.org/10.1016/S0378-4371(99)00408-2

**Fractality, chaos, and reactions in imperfectly mixed open hydrodynamical flows.** / Pentek, A ; Karolyi, G ; Scheuring, I ; Tel, T ; Toroczkai, Z ; Kadtke, J ; Grebogi, C .

Research output: Contribution to journal › Article

*Physica. A, Statistical Mechanics and its Applications*, vol. 274, no. 1-2, pp. 120-131. https://doi.org/10.1016/S0378-4371(99)00408-2

}

TY - JOUR

T1 - Fractality, chaos, and reactions in imperfectly mixed open hydrodynamical flows

AU - Pentek, A

AU - Karolyi, G

AU - Scheuring, I

AU - Tel, T

AU - Toroczkai, Z

AU - Kadtke, J

AU - Grebogi, C

PY - 1999/12/1

Y1 - 1999/12/1

N2 - 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 dac: 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. (C) 1999 Elsevier Science B.V. All rights reserved.

AB - 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 dac: 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. (C) 1999 Elsevier Science B.V. All rights reserved.

KW - leapfrogging vortex pairs

KW - Gonyaulax-Polyedra Stein

KW - Red Tide Dinoflagellate

KW - Stokes-Flow

KW - advection

KW - scattering

KW - turbulence

KW - kinematics

KW - boundaries

KW - transport

U2 - 10.1016/S0378-4371(99)00408-2

DO - 10.1016/S0378-4371(99)00408-2

M3 - Article

VL - 274

SP - 120

EP - 131

JO - Physica. A, Statistical Mechanics and its Applications

JF - Physica. A, Statistical Mechanics and its Applications

SN - 0378-4371

IS - 1-2

ER -