Tracer dynamics in a flow of driven vortices

A Witt, R Braun, F Feudel, C Grebogi, J Kurths

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

From numerical computations of the two-dimensional Navier-Stokes equations, we derive a low-dimensional stream-function model that captures the essential properties of the dynamics of an array of driven vortices in time-periodic regime. Using this analytical model, we study the Lagrangian dynamics of passive tracers and show that it is essentially controlled by the existence of a chaotic saddle. We obtain its stable and unstable manifolds, which in turn, yield an approximation of the chaotic saddle in terms of their intersections. By introducing symbolic dynamics, the spatiotemporal properties of the flow, including an alternative approximation of the chaotic saddle, are described in terms of measures of complexity. [S1063-651X(99)03102-5].

Original languageEnglish
Pages (from-to)1605-1614
Number of pages10
JournalPhysical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume59
Issue number2
Publication statusPublished - Feb 1999

Keywords

  • OPEN HYDRODYNAMICAL FLOWS
  • LINEAR-ARRAY
  • CHAOTIC ADVECTION
  • COMPLEXITY
  • INSTABILITY
  • BOUNDARIES

Cite this

Tracer dynamics in a flow of driven vortices. / Witt, A ; Braun, R ; Feudel, F ; Grebogi, C ; Kurths, J .

In: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 59, No. 2, 02.1999, p. 1605-1614.

Research output: Contribution to journalArticle

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AU - Braun, R

AU - Feudel, F

AU - Grebogi, C

AU - Kurths, J

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N2 - From numerical computations of the two-dimensional Navier-Stokes equations, we derive a low-dimensional stream-function model that captures the essential properties of the dynamics of an array of driven vortices in time-periodic regime. Using this analytical model, we study the Lagrangian dynamics of passive tracers and show that it is essentially controlled by the existence of a chaotic saddle. We obtain its stable and unstable manifolds, which in turn, yield an approximation of the chaotic saddle in terms of their intersections. By introducing symbolic dynamics, the spatiotemporal properties of the flow, including an alternative approximation of the chaotic saddle, are described in terms of measures of complexity. [S1063-651X(99)03102-5].

AB - From numerical computations of the two-dimensional Navier-Stokes equations, we derive a low-dimensional stream-function model that captures the essential properties of the dynamics of an array of driven vortices in time-periodic regime. Using this analytical model, we study the Lagrangian dynamics of passive tracers and show that it is essentially controlled by the existence of a chaotic saddle. We obtain its stable and unstable manifolds, which in turn, yield an approximation of the chaotic saddle in terms of their intersections. By introducing symbolic dynamics, the spatiotemporal properties of the flow, including an alternative approximation of the chaotic saddle, are described in terms of measures of complexity. [S1063-651X(99)03102-5].

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KW - LINEAR-ARRAY

KW - CHAOTIC ADVECTION

KW - COMPLEXITY

KW - INSTABILITY

KW - BOUNDARIES

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

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