The 1: 2 Mode Interaction in Rayleigh-BéNard convection with Weakly Broken midplane Symmetry

The effects of weak breaking of the midplane reflection symmetry on the 1:2 steady state mode interaction in Rayleigh–Bénard convection are discussed in a PDE setting. Effects of this type arise from the inclusion of non-Boussinesq terms or due to small differences in the boundary conditions at the top and bottom of the convecting layer. The latter provides the simplest realization, and captures all qualitative effects of such symmetry breaking. The analysis is performed for two Prandtl numbers, σ = 10 and σ = 0.1, representing behavior typical of large and low Prandtl numbers, respectively.