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Higher harmonic resonance of two-dimensional disturbances in Rayleigh- Bénard convection. (English) Zbl 0744.76053
Summary: 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 $\left(P\ge 0·13\right)$ while the pure mode, mixed modes, travelling wave and modulated wave solutions exist for relatively low-Prandtl-number fluids $\left(P\le 0·12\right)$.
##### MSC:
 76E15 Convective instability (fluid mechanics) 76R10 Free convection (fluid mechanics) 76E30 Nonlinear effects (fluid mechanics)