Bifurcation to oscillations in three-dimensional Rayleigh-Bénard convection

  • Three-dimensional bouyancy-driven convection in a horizontal fluid layer with stress-free boundary conditions at the top and bottom and periodic boundary conditions in the horizontal directions is investigated by means of numerical simulation and bifurcation-analysis techniques. The aspect ratio is fixed to a value of 2√2 and the Prandtl number to a value of 6.8. Two-dimensional convection rolls are found to be stable up to a Rayleigh number of 17 950, where a Hopf bifurcation leads to traveling waves. These are stable up to a Rayleigh number of 30 000, where a secondary Hopf bifurcation generates modulated traveling waves. We pay particular attention to the symmetries of the solutions and symmetry breaking by the bifurcations.

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Author:Stefan Scheel, Norbert Seehafer
Series (Serial Number):NLD Preprints (paper 039)
Document Type:Preprint
Year of Completion:1997
Publishing Institution:Universität Potsdam
Release Date:2007/07/03
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Zentrale und wissenschaftliche Einrichtungen / Interdisziplinäres Zentrum für Dynamik komplexer Systeme
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik