### Abstract

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

Pages (from-to) | 4076-4088 |

Number of pages | 13 |

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

Volume | 51 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1 May 1995 |

### Keywords

- basin boundaries
- scattering
- attractors
- transients
- systems

### Cite this

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

*51*(5), 4076-4088. https://doi.org/10.1103/PhysRevE.51.4076

**Fractal boundaries in open hydrodynamical flows : Signatures of chaotic saddles.** / Péntek, Áron; Toroczkai, Zoltán; Tél, Tamás; Grebogi, Celso; Yorke, James A.

Research output: Contribution to journal › Article

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 51, no. 5, pp. 4076-4088. https://doi.org/10.1103/PhysRevE.51.4076

}

TY - JOUR

T1 - Fractal boundaries in open hydrodynamical flows

T2 - Signatures of chaotic saddles

AU - Péntek, Áron

AU - Toroczkai, Zoltán

AU - Tél, Tamás

AU - Grebogi, Celso

AU - Yorke, James A.

PY - 1995/5/1

Y1 - 1995/5/1

N2 - We introduce the concept of fractal boundaries in open hydrodynamical flows based on two gedanken experiments carried out with passive tracer particles colored differently. It is shown that the signature for the presence of a chaotic saddle in the advection dynamics is a fractal boundary between regions of different colors. The fractal parts of the boundaries found in the two experiments contain either the stable or the unstable manifold of this chaotic set. We point out that these boundaries coincide with streak lines passing through appropriately chosen points. As an illustrative numerical experiment, we consider a model of the von Kármán vortex street, a time periodic two-dimensional flow of a viscous fluid around a cylinder.

AB - We introduce the concept of fractal boundaries in open hydrodynamical flows based on two gedanken experiments carried out with passive tracer particles colored differently. It is shown that the signature for the presence of a chaotic saddle in the advection dynamics is a fractal boundary between regions of different colors. The fractal parts of the boundaries found in the two experiments contain either the stable or the unstable manifold of this chaotic set. We point out that these boundaries coincide with streak lines passing through appropriately chosen points. As an illustrative numerical experiment, we consider a model of the von Kármán vortex street, a time periodic two-dimensional flow of a viscous fluid around a cylinder.

KW - basin boundaries

KW - scattering

KW - attractors

KW - transients

KW - systems

U2 - 10.1103/PhysRevE.51.4076

DO - 10.1103/PhysRevE.51.4076

M3 - Article

VL - 51

SP - 4076

EP - 4088

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 -