Symmetries and pattern selection in Rayleigh-Bénard convection
type: Item
instance of: scholarly article
title: Symmetries and pattern selection in Rayleigh-Bénard convection
zbMATH Open document ID: 0599.76098
DOI: 10.1016/0167-2789(84)90179-9
published in: Physica D
publication date: 1984-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 76Rxx
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 3968195
zbMATH Keywords: process of pattern selection
zbMATH Keywords: rolls
zbMATH Keywords: hexagons
zbMATH Keywords: Rayleigh-Bénard convection
zbMATH Keywords: Boussinesq approximation
zbMATH Keywords: boundary conditions
zbMATH Keywords: local bifurcation diagrams
author: Martin Golubitsky
author: James W. Swift
author: Edgar Knobloch
MaRDI profile type: Publication
full work available at URL: 0167-2789(84)90179-9
OpenAlex ID: W2100386495
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description: scientific article; zbMATH DE number 3968195