HIGHER HARMONIC RESONANCE OF 2-DIMENSIONAL DISTURBANCES IN RAYLEIGH-BENARD CONVECTION

A higher harmonic resonance with wavenumber ratio of 1:3 is found to take place in Rayleigh-Benard 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 greater-than-or-equal-to 0.13) while the pure mode, mixed modes, travelling wave and modulated wave solutions exist for relatively low-Prandtl-number fluids (P less-than-or-equal-to 0.12).