TY - JOUR

T1 - O(2)-symmetric bifurcation theory for convection rolls

AU - Armbruster, D.

N1 - Funding Information:
This work was initiated by F. Busse. I am grateful for his advice and the hospitalitya t the University of Bayreuth.T he financial support by the SFB 213 in Bayreuth,t he Stiftung Volkswag-enwerk,t he NSF (Grant MSM 8509481)a nd the U.S. Army ResearchO ffice is acknowledged.

PY - 1987/8

Y1 - 1987/8

N2 - The interaction of two steady state modes for the two-dimensional Benard 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) × 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.

AB - The interaction of two steady state modes for the two-dimensional Benard 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) × 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.

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U2 - 10.1016/0167-2789(87)90042-X

DO - 10.1016/0167-2789(87)90042-X

M3 - Article

AN - SCOPUS:0000578457

VL - 27

SP - 433

EP - 439

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 3

ER -