A higher harmonic resonance with wavenumber ratio of 1:3 is found to take place in Rayleigh-Bénard convection under rigid-rigid boundary conditions. Bifurcation diagrams for two-dimensional motion are obtained for various values of the Prandtl number P. It is found that a pure mode and mixed mode solutions exist as nonlinear equilibrium states of primary roll solutions for relatively high-Prandtl-number fluids (P ≥ 0.13) while the pure mode, mixed modes, travelling wave and modulated wave solutions exist for relatively low-Prandtl-number fluids (P ≤ 0.12).
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