Journal of Fluid Mechanics

Higher harmonic resonance of two-dimensional disturbances in Rayleigh-Bénard convection

Jiro  Mizushima a1 and Kaoru  Fujimura a2
a1 Faculty of Education, Wakayama University, Wakayama 640, Japan
a2 Japan Atomic Energy Research Institute, Tokai-mura, Ibaraki 319-11, Japan

Article author query
mizushima j   [Google Scholar] 
fujimura k   [Google Scholar] 


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 [greater-than-or-equal] 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] 0.12).

(Published Online April 26 2006)
(Received November 5 1990)
(Revised July 30 1991)