Bifurcations in penetrative Rayleigh-Bénard convection in a cylindrical container
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The bifurcations of penetrative Rayleigh-Bénard convection in cylindrical containers are studied by the linear stability analysis (LSA) combined with the direct numerical simulation (DNS) method. The working fluid is cold water near 4°C, where the Prandtl number Pr is 11.57, and the aspect ratio (radius/height) of the cylinder ranges from 0.66 to 2. It is found that the critical Rayleigh number increases with the increase in the density inversion parameter θm. The relationship between the normalized critical Rayleigh number (Rac(θm)/Rac(0)) and θm is formulated, which is in good agreement with the stability results within a large range of θm. The aspect ratio has a minor effect on Rac(θm)/Rac(0). The bifurcation processes based on the axisymmetric solutions are also investigated. The results show that the onset of axisymmetric convection occurs through a trans-critical bifurcation due to the top-bottom symmetry breaking of the present system. Moreover, two kinds of qualitatively different steady axisymmetric solutions are identified.
Key wordsbifurcation convection linear stability analysis (LSA)
density inversion parameter
Chinese Library ClassificationO357.1
2010 Mathematics Subject Classification76E20 34C23
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- DOEDEL, E. and TUCKERMAN, L. S. Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems, Springer Science and Business Media, New York, 453–466 (2012)Google Scholar