Abstract
In systems with midplane reflection symmetry the dominant spatial resonance is the 1:3 resonance. Numerical continuation is used to study this and other $1:2k+1$ resonances in two-dimensional convection between no-slip perfectly conducting horizontal plates. Periodic boundary conditions are imposed in the horizontal. These resonances influence the process of wave number selection at moderate Rayleigh numbers through the generation of hybrid solutions, and thereby modify the Eckhaus picture of wave number selection. Unlike the better known mixed modes the hybrid solutions have the same symmetry as a pair of primary rolls. Both hybrid and symmetry-breaking mixed modes are computed and their linear stability properties with respect to perturbations preserving different spatial periods are determined. A complete description of the effects of midplane reflection on wave number selection emerges. Only steady solutions are considered and the Prandtl number is fixed at $\ensuremath{\sigma}=10$.
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