M. Golubitsky, J. 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.