| Axisymmetry Breaking to Travelling Waves in the Cylinder with Partially Heated Sidewall |
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| 引用本文： | 马东军 孙德军 尹协远. Axisymmetry Breaking to Travelling Waves in the Cylinder with Partially Heated Sidewall[J]. 中国物理快报, 2006, 23(6): 1515-1518 |
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| 作者姓名： | 马东军 孙德军 尹协远 |
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| 作者单位： | School of Engineering Science, University of Science and Technology of China, Hefei 230027 |
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| 基金项目： | The authors wish to thank Professor Hamda BenHadid and Professor Daniel Henry, Ecole Centrale de Lyon/Université Claude Benard Lyon 1, for their helpful discussions of the numerical methods and results. |
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| 摘 要： | The transition from an axisymmetric stationary flow to three-dimensional time-dependent flows is carefully studied in a vertical cylinder partially heated from the side, with the aspect ratio A = 2 and Prandtl number Pτ=0.021. The flow develops from the steady toroidal pattern beyond the first instability threshold, breaks the axisymmetric state at a Rayleigh number near 2000, and transits to standing or travelling azimuthal waves. A new result is observed that a slightly unstable flow pattern of standing waves exists and will transit to stable travelling waves after a long time evolution. The onset of oscillations is associated with a supercritical Hopf bifurcation in a system with O（2） symmetry.
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| 关 键 词： | 行波 柱面 热边墙 不稳定性 雷利数 晶体学 |
| 修稿时间： | 2006-03-17 |
Axisymmetry Breaking to Travelling Waves in the Cylinder with Partially Heated Sidewall |
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| MA Dong-Jun,SUN De-Jun,YIN Xie-Yuan. Axisymmetry Breaking to Travelling Waves in the Cylinder with Partially Heated Sidewall[J]. Chinese Physics Letters, 2006, 23(6): 1515-1518 |
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| Authors: | MA Dong-Jun SUN De-Jun YIN Xie-Yuan |
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| Affiliation: | School of Engineering Science, University of Science and Technology of China, Hefei 230027 |
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| Abstract: | The transition from an axisymmetric stationary flow to three-dimensional time-dependent flows is carefully studied in a vertical cylinder partially heated from the side, with the aspect ratio A=2 and Prandtl number P4=0.021. The flow develops from the steady toroidal pattern beyond the first instability threshold, breaks the axisymmetric state at a Rayleigh number near 2000, and transits to standing or travelling azimuthal waves. A new result is observed that a slightly unstable flow pattern of standing waves exists and will transit to stable travelling waves after a long time evolution. The onset of oscillations is associated with a supercritical Hopf bifurcation in a system with O(2) symmetry. |
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| Keywords: | 44.25.+f 47.27.Te 47.20.Ky |
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