Symmetries and pattern selection in Rayleigh-Bénard convection

M. Golubitsky, J. W. Swift, E. Knobloch

Research output: Contribution to journalArticlepeer-review

147 Scopus citations


This paper describes the process of pattern selection between rolls and hexagons in Rayleigh-Bénard convection with reflectional symmetry in the horizontal midplane. This symmetry is a consequence of the Boussinesq approximation, provided the boundary conditions are the same on the top and bottom plates. All possible local bifurcation diagrams (assuming certain non-degeneracy conditions) are found using only group theory. The results are therefore applicable to other systems with the same symmetries. Rolls, hexagons, or a new solution, regular triangles, can be stable depending on the physical system. Rolls are stable in ordinary Rayleigh-Bénard convection. The results are compared to those of Buzano and Golubitsky [1] without the midplane reflection symmetry. The bifurcation behavior of the two cases is quite different, and a connection between them is established by considering the effects of breaking the reflectional symmetry. Finally, the relevant experimental results are described.

Original languageEnglish (US)
Pages (from-to)249-276
Number of pages28
JournalPhysica D: Nonlinear Phenomena
Issue number3
StatePublished - Mar 1984

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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