M. Golubitsky, J.W. Swift and E. Knobloch
Symmetries and pattern selection in Rayleigh-Benard convection
Physica. 10D (1984) 249-276.
This paper describes the process of pattern selection between rolls and hexagons in Rayleigh-Benard 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-Benard convection. The results are compared to those of Buzano and Golubitsky 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.