### Abstract

We investigate the evolution of particle ensembles in open chaotic hydrodynamical flows. Active processes of the type A+B-->2B and A+B-->2C are considered in the limit of weak diffusion. As an illustrative advection dynamics we consider a model of the von 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 Ln 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. [S1063-651X(99)04905-3].

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

Pages (from-to) | 5468-5481 |

Number of pages | 14 |

Journal | Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 59 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 1999 |

### Keywords

- open hydrodynamical flows
- leapfrogging vortex pairs
- Gonyaulax-Polyedra Stein
- Red Tide Dinoglagellate
- advection
- turbulence
- scattering
- boundaries
- transport
- diffusion

### Cite this

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*59*(5), 5468-5481. https://doi.org/10.1103/PhysRevE.59.5468

**Chemical or biological activity in open chaotic flows.** / Karolyi, Gyorgy; Pentek, Aron; Toroczkai, Zoltan; Tel, Tamas; Grebogi, Celso.

Research output: Contribution to journal › Article

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 59, no. 5, pp. 5468-5481. https://doi.org/10.1103/PhysRevE.59.5468

}

TY - JOUR

T1 - Chemical or biological activity in open chaotic flows

AU - Karolyi, Gyorgy

AU - Pentek, Aron

AU - Toroczkai, Zoltan

AU - Tel, Tamas

AU - Grebogi, Celso

PY - 1999/5

Y1 - 1999/5

N2 - We investigate the evolution of particle ensembles in open chaotic hydrodynamical flows. Active processes of the type A+B-->2B and A+B-->2C are considered in the limit of weak diffusion. As an illustrative advection dynamics we consider a model of the von 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 Ln 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. [S1063-651X(99)04905-3].

AB - We investigate the evolution of particle ensembles in open chaotic hydrodynamical flows. Active processes of the type A+B-->2B and A+B-->2C are considered in the limit of weak diffusion. As an illustrative advection dynamics we consider a model of the von 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 Ln 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. [S1063-651X(99)04905-3].

KW - open hydrodynamical flows

KW - leapfrogging vortex pairs

KW - Gonyaulax-Polyedra Stein

KW - Red Tide Dinoglagellate

KW - advection

KW - turbulence

KW - scattering

KW - boundaries

KW - transport

KW - diffusion

U2 - 10.1103/PhysRevE.59.5468

DO - 10.1103/PhysRevE.59.5468

M3 - Article

VL - 59

SP - 5468

EP - 5481

JO - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 5

ER -