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Bifurcations in penetrative Rayleigh-Bénard convection in a cylindrical container

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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°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.

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Abbreviations

θ m :

density inversion parameter

Ra :

Rayleigh number

Pr :

Prandtl number

T :

temperature

m :

wave number

a :

aspect ratio

θ :

dimensionless temperature

t :

dimensionless time

u :

dimensionless velocity

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Authors and Affiliations

  1. Department of Modern Mechanics, University of Science and Technology of China, Hefei, 230027, China

    Chuanshi Sun, Shuang Liu, Qi Wang, Zhenhua Wan & Dejun Sun

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  1. Chuanshi Sun
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  2. Shuang Liu
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  3. Qi Wang
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  4. Zhenhua Wan
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  5. Dejun Sun
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Correspondence to Dejun Sun.

Additional information

Citation: SUN, C. S., LIU, S., WANG, Q., WAN, Z. H., and SUN, D. J. Bifurcations in penetrative Rayleigh-Bénard convection in a cylindrical container. Applied Mathematics and Mechanics (English Edition) (2019) https://doi.org/10.1007/s10483-019-2474-6

Project supported by the National Natural Science Foundation of China (Nos. 11572314, 11621202, and 11772323) and the Fundamental Research Funds for the Central Universities

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Sun, C., Liu, S., Wang, Q. et al. Bifurcations in penetrative Rayleigh-Bénard convection in a cylindrical container. Appl. Math. Mech.-Engl. Ed. 40, 695–704 (2019). https://doi.org/10.1007/s10483-019-2474-6

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  • DOI: https://doi.org/10.1007/s10483-019-2474-6

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

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