Symmetries and pattern selection in Rayleigh-Bénard convection

M. Golubitsky, James W Swift, E. Knobloch

Research output: Contribution to journalArticle

135 Citations (Scopus)

Abstract

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
Volume10
Issue number3
DOIs
StatePublished - 1984
Externally publishedYes

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Reflectional symmetry
Rayleigh
Convection
convection
Symmetry
Group theory
Hexagon
symmetry
hexagons
Boussinesq Approximation
Local Bifurcations
Regular Solution
Nondegeneracy
Boundary conditions
Group Theory
Bifurcation Diagram
Triangle
Horizontal
Boussinesq approximation
Bifurcation

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

Symmetries and pattern selection in Rayleigh-Bénard convection. / Golubitsky, M.; Swift, James W; Knobloch, E.

In: Physica D: Nonlinear Phenomena, Vol. 10, No. 3, 1984, p. 249-276.

Research output: Contribution to journalArticle

Golubitsky, M. ; Swift, James W ; Knobloch, E. / Symmetries and pattern selection in Rayleigh-Bénard convection. In: Physica D: Nonlinear Phenomena. 1984 ; Vol. 10, No. 3. pp. 249-276.
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