O(2)-symmetric bifurcation theory for convection rolls
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.
scientific article; zbMATH DE number 4016459