Bifurcations in penetrative Rayleigh-Bénard convection in a cylindrical container

doi:10.1007/s10483-019-2474-6

Abstract

Abstract: 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℃, 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 θ_m. The relationship between the normalized critical Rayleigh number (Ra_c(θ_m)/Ra_c(0)) and θ_m is formulated, which is in good agreement with the stability results within a large range of θ_m. The aspect ratio has a minor effect on Ra_c(θ_m)/Ra_c(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 words: impact torsional buckling, elastic cylindrical shell, perturbation analysis, initial imperfection sensitivity, bifurcation, convection, linear stability analysis (LSA)

2010 MSC Number:

76E20
34C23

Chuanshi SUN, Shuang LIU, Qi WANG, Zhenhua WAN, Dejun SUN. Bifurcations in penetrative Rayleigh-Bénard convection in a cylindrical container. Applied Mathematics and Mechanics (English Edition), 2019, 40(5): 695-704.

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