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Bifurcations in penetrative Rayleigh-Benard convection in a cylindrical container

Chuanshi Sun University of Science and Technology of China Shuang Liu University of Science and Technology of China Qi Wang University of Science and Technology of China Zhenhua Wan University of Science and Technology of China Dejun Sun University of Science and Technology of China

Fluid Dynamics and Shock Waves mathscidoc:2205.14001

Applied Mathematics and Mechanics-English Edition, 40, 2019.5
The bifurcations of penetrative Rayleigh-Benard 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 degrees 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 (m). The relationship between the normalized critical Rayleigh number (Ra-c((m))/Ra-c(0)) and (m) is formulated, which is in good agreement with the stability results within a large range of (m). The aspect ratio has a minor effect on Ra-c((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.
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@inproceedings{chuanshi2019bifurcations,
  title={Bifurcations in penetrative Rayleigh-Benard convection in a cylindrical container},
  author={Chuanshi Sun, Shuang Liu, Qi Wang, Zhenhua Wan, and Dejun Sun},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517140938795772214},
  booktitle={Applied Mathematics and Mechanics-English Edition},
  volume={40},
  year={2019},
}
Chuanshi Sun, Shuang Liu, Qi Wang, Zhenhua Wan, and Dejun Sun. Bifurcations in penetrative Rayleigh-Benard convection in a cylindrical container. 2019. Vol. 40. In Applied Mathematics and Mechanics-English Edition. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517140938795772214.
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