Bifurcation analysis to Rayleigh-Bénard convection in finite box with up-down symmetry

Pages: 383 - 393, Volume 5, Issue 2, June 2006

doi:10.3934/cpaa.2006.5.383       Abstract        Full Text (4289.7K)       Related Articles

Toshiyuki Ogawa - Graduate School of Engineering Science, Osaka University, 560-8531 Toyonaka, Japan (email)

Abstract: Rayleigh-Bénard convection in a small rectangular domain is studied by the standard bifurcation analysis. The dynamics on the center manifold is calculated up to 3rd order. By this normal form, it is possible to determine the local bifurcation structures in principle. One can easily imagine that mixed mode solutions such as hexagonal, patchwork-quilt patterns are unstable from the knowledge of amplitude equation:Ginzburg-Landau equation. However they are not necessarily similar to each other in a small rectangular domain. Several non-trivial stable mixed mode patterns are introduced.

Keywords:  Rayleigh-Bénard convection, bifurcation analysis, normal form.
Mathematics Subject Classification:  35B32, 37G05 ,76E06.

Received: February 2005;      Revised: June 2005;      Published: March 2006.