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URN: urn:nbn:de:kobv:517-opus-14564
URL: http://opus.kobv.de/ubp/volltexte/2007/1456/

Braun, Robert ; Feudel, Fred ; Seehafer, Norbert

Bifurcations and chaos in an array of forced vortices

Dokument 1.pdf (2.155 KB)

Kurzfassung auf Englisch

We have studied the bifurcation structure of the incompressible two-dimensional Navier-Stokes equations with a special external forcing driving an array of 8×8 counterrotating vortices. The study has been motivated by recent experiments with thin layers of electrolytes showing, among other things, the formation of large-scale spatial patterns. As the strength of the forcing or the Reynolds number is raised the original stationary vortex array becomes unstable and a complex sequence of bifurcations is observed. The bifurcations lead to several periodic branches, torus and chaotic solutions, and other stationary solutions. Most remarkable is the appearance of solutions characterized by structures on spatial scales large compared to the scale of the forcing. We also characterize the different dynamic regimes by means of tracers injected into the fluid. Stretching rates and Hausdorff dimensions of convected line elements are calculated to quantify the mixing process. It turns out that for time-periodic velocity fields the mixing can be very effective.

PACS - Klassifikation 47.54.+r , 47.27.Cn , 47.52.+j , 47.20.Ky
Institut 1: Institut für Physik und Astronomie
Institut 2: Interdisziplinäres Zentrum Dynamik komplexer Systeme
DDC-Sachgruppe: Physik
Dokumentart: c Preprint (Vorabdruck)
Schriftenreihe: NLD Preprints
Band Nummer: paper 037
Sprache: Englisch
Erstellungsjahr: 1997
Publikationsdatum: 29.06.2007

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