Bifurcations and chaos in an array of forced vortices

  • 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 veWe 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.show moreshow less

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Metadaten
Author:Robert Braun, Fred Feudel, Norbert Seehafer
URN:urn:nbn:de:kobv:517-opus-14564
Series (Serial Number):NLD Preprints (paper 037)
Document Type:Preprint
Language:English
Date of Publication (online):2007/06/29
Year of Completion:1997
Publishing Institution:Universität Potsdam
Release Date:2007/06/29
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Wissenschaftliche Einrichtungen / Interdisziplinäres Zentrum Dynamik komplexer Systeme
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
PACS Classification:40.00.00 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS / 47.00.00 Fluid dynamics (for fluid dynamics of quantum fluids, see section 67; see also section 83 Rheology; for sound generation by fluid flow, see 43.28.Ra-in Acoustics Appendix) / 47.20.-k Flow instabilities (see also 47.15.Fe Stability of laminar flows) / 47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
40.00.00 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS / 47.00.00 Fluid dynamics (for fluid dynamics of quantum fluids, see section 67; see also section 83 Rheology; for sound generation by fluid flow, see 43.28.Ra-in Acoustics Appendix) / 47.27.-i Turbulent flows / 47.27.Cn Transition to turbulence
40.00.00 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS / 47.00.00 Fluid dynamics (for fluid dynamics of quantum fluids, see section 67; see also section 83 Rheology; for sound generation by fluid flow, see 43.28.Ra-in Acoustics Appendix) / 47.52.+j Chaos in fluid dynamics (see also 05.45.-a Nonlinear dynamics and chaos in Statistical physics, thermodynamics, and nonlinear dynamical systems)