Symmetry breaking bifurcations for the magnetohydrodynamic equations with helical forcing

  • We have studied the bifurcations in a three-dimensional incompressible magnetofluid with periodic boundary conditions and an external forcing of the Arnold-Beltrami-Childress (ABC) type. Bifurcation-analysis techniques have been applied to explore the qualitative behavior of solution branches. Due to the symmetry of the forcing, the equations are equivariant with respect to a group of transformations isomorphic to the octahedral group, and we have paid special attention to symmetry-breaking effects. As the Reynolds number is increased, the primary nonmagnetic steady state, the ABC flow, loses its stability to a periodic magnetic state, showing the appearance of a generic dynamo effect; the critical value of the Reynolds number for the instability of the ABC flow is decreased compared to the purely hydrodynamic case. The bifurcating magnetic branch in turn is subject to secondary, symmetry-breaking bifurcations. We have traced periodic and quasi- periodic branches until they end up in chaotic states. In particular detail we have analyzWe have studied the bifurcations in a three-dimensional incompressible magnetofluid with periodic boundary conditions and an external forcing of the Arnold-Beltrami-Childress (ABC) type. Bifurcation-analysis techniques have been applied to explore the qualitative behavior of solution branches. Due to the symmetry of the forcing, the equations are equivariant with respect to a group of transformations isomorphic to the octahedral group, and we have paid special attention to symmetry-breaking effects. As the Reynolds number is increased, the primary nonmagnetic steady state, the ABC flow, loses its stability to a periodic magnetic state, showing the appearance of a generic dynamo effect; the critical value of the Reynolds number for the instability of the ABC flow is decreased compared to the purely hydrodynamic case. The bifurcating magnetic branch in turn is subject to secondary, symmetry-breaking bifurcations. We have traced periodic and quasi- periodic branches until they end up in chaotic states. In particular detail we have analyzed the subgroup symmetries of the bifurcating periodic branches, which are closely related to the spatial structure of the magnetic field.show moreshow less

Download full text files

Export metadata

  • Export Bibtex
  • Export RIS
  • Export XML

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Fred Feudel, Norbert Seehafer, Barak Galanti, Sten Rüdiger
URN:urn:nbn:de:kobv:517-opus-14317
Series (Serial Number):NLD Preprints (paper 031)
Document Type:Preprint
Language:English
Date of Publication (online):2007/06/20
Year of Completion:1996
Publishing Institution:Universität Potsdam
Release Date:2007/06/20
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
90.00.00 GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS (for more detailed headings, see the Geophysics Appendix) / 95.00.00 Fundamental astronomy and astrophysics; instrumentation, techniques, and astronomical observations / 95.30.-k Fundamental aspects of astrophysics (see also section 26 Nuclear astrophysics) / 95.30.Qd Magnetohydrodynamics and plasmas (see also 52.30.Cv and 52.72.+v-in physics of plasmas)