### 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 language | English |
---|---|

Pages (from-to) | 1605-1614 |

Number of pages | 10 |

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

Volume | 59 |

Issue number | 2 |

Publication status | Published - Feb 1999 |

### Keywords

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

### Cite this

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

*59*(2), 1605-1614.

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

Research output: Contribution to journal › Article

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 59, no. 2, pp. 1605-1614.

}

TY - JOUR

T1 - Tracer dynamics in a flow of driven vortices

AU - Witt, A

AU - Braun, R

AU - Feudel, F

AU - Grebogi, C

AU - Kurths, J

PY - 1999/2

Y1 - 1999/2

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].

KW - OPEN HYDRODYNAMICAL FLOWS

KW - LINEAR-ARRAY

KW - CHAOTIC ADVECTION

KW - COMPLEXITY

KW - INSTABILITY

KW - BOUNDARIES

M3 - Article

VL - 59

SP - 1605

EP - 1614

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 - 2

ER -