Higher harmonic resonance of two-dimensional disturbances in Rayleigh-Bénard convection
- 1 January 1992
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 234 (-1) , 651-667
- https://doi.org/10.1017/s0022112092000958
Abstract
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).Keywords
This publication has 20 references indexed in Scilit:
- Kuramoto–Sivashinsky Dynamics on the Center–Unstable ManifoldSIAM Journal on Applied Mathematics, 1989
- Equilibrium characteristics of the secondary convection in a vertical fluid layer between two flat platesFluid Dynamics Research, 1987
- Subharmonic and asymmetric convection rollsZeitschrift für angewandte Mathematik und Physik, 1986
- Steady-state mode interactions in the presence of 0(2)-symmetryDynamics and Stability of Systems, 1986
- Some bifurcation diagrams for Taylor vortex flowsPhysics of Fluids, 1985
- Three-dimensional tertiary motions in a plane shear layerJournal of Fluid Mechanics, 1983
- Instabilities of convection rolls in a fluid of moderate Prandtl numberJournal of Fluid Mechanics, 1979
- Transition to time-dependent convectionJournal of Fluid Mechanics, 1974
- Instabilities of convection rolls in a high Prandtl number fluidJournal of Fluid Mechanics, 1971
- On the Stability of Two‐Dimensional Convection in a Layer Heated from BelowJournal of Mathematics and Physics, 1967