Fractal boundaries in open hydrodynamical flows: Signatures of chaotic saddles

Áron Péntek, Zoltán Toroczkai, Tamás Tél, Celso Grebogi, James A. Yorke

Research output: Contribution to journalArticle

78 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)4076-4088
Number of pages13
JournalPhysical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume51
Issue number5
DOIs
Publication statusPublished - 1 May 1995

Keywords

  • basin boundaries
  • scattering
  • attractors
  • transients
  • systems

Cite this

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

In: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 51, No. 5, 01.05.1995, p. 4076-4088.

Research output: Contribution to journalArticle

@article{1691adc6ce9440f094e386bca0f9a254,
title = "Fractal boundaries in open hydrodynamical flows: Signatures of chaotic saddles",
abstract = "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 K{\'a}rm{\'a}n vortex street, a time periodic two-dimensional flow of a viscous fluid around a cylinder.",
keywords = "basin boundaries, scattering, attractors, transients, systems",
author = "{\'A}ron P{\'e}ntek and Zolt{\'a}n Toroczkai and Tam{\'a}s T{\'e}l and Celso Grebogi and Yorke, {James A.}",
year = "1995",
month = "5",
day = "1",
doi = "10.1103/PhysRevE.51.4076",
language = "English",
volume = "51",
pages = "4076--4088",
journal = "Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics",
issn = "1063-651X",
publisher = "American Physical Society",
number = "5",

}

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 -