O(2)-symmetric bifurcation theory for convection rolls
type: Item
instance of: scholarly article
title: O(2)-symmetric bifurcation theory for convection rolls
zbMATH Open document ID: 0625.76051
DOI: 10.1016/0167-2789(87)90042-X
author: Dieter Armbruster
published in: Physica D
publication date: 1987-01-01T00:00:00Z
review text: The interaction of two steady state modes for the two-dimensional Bénard problem with lateral periodic boundary conditions (p.b.c) and free horizontal boundary conditions is considered. The p.b.c generate an action of O(2) on the Navier-Stokes equations. The Boussinesq approximation induces an additional Z(2)-symmetry. The O(2)\(\times Z(2)\) equivariant bifurcation equations are determined and two fifth order terms are identified. Two types of mixed mode solutions and a travelling wave solution are found. Using MACSYMA, the fifth order terms are calculated and the stability of the solutions to phase perturbations depending on the Prandtl number is determined.
Mathematics Subject Classification ID: 76E15
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 4016459
zbMATH Keywords: two-dimensional convection rolls
zbMATH Keywords: symmetry
zbMATH Keywords: steady state modes
zbMATH Keywords: two- dimensional Bénard problem
zbMATH Keywords: lateral periodic boundary conditions
zbMATH Keywords: free horizontal boundary conditions
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: Boussinesq approximation
zbMATH Keywords: bifurcation equations
zbMATH Keywords: MACSYMA
describes a project that uses: MACSYMA
MaRDI profile type: Publication
cites work: Subharmonic and asymmetric convection rolls
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cites work: Q3738294
cites work: Group representation theory, bifurcation theory and pattern formation
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full work available at URL: 0167-2789(87)90042-x
OpenAlex ID: W2017896395
description: scientific article; zbMATH DE number 4016459