Periodic Stream Lines in the Three-Dimensional Square Cell Pattern

LI Ji-bin; DUAN Wan-suo

Volume 22 Issue 2

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 2001 > 22(2): 191-198

LI Ji-bin, DUAN Wan-suo. Periodic Stream Lines in the Three-Dimensional Square Cell Pattern[J]. Applied Mathematics and Mechanics, 2001, 22(2): 191-198.

Citation:

LI Ji-bin, DUAN Wan-suo. Periodic Stream Lines in the Three-Dimensional Square Cell Pattern[J]. Applied Mathematics and Mechanics, 2001, 22(2): 191-198.

Citation:

LI Ji-bin, DUAN Wan-suo. Periodic Stream Lines in the Three-Dimensional Square Cell Pattern[J]. Applied Mathematics and Mechanics, 2001, 22(2): 191-198.

PDF( 323 KB)

Periodic Stream Lines in the Three-Dimensional Square Cell Pattern

Center for Nonlinear Science Studies, Kunming University of Science and Technology, Kunming 650093, P. R. China

Received Date: 1999-11-05
Rev Recd Date: 2000-10-03
Publish Date: 2001-02-15

Abstract

Abstract

By using the theory of the generalized perturbed Hamiltonian systems, it is shown that there exist periodic stream lines in the three-dimensional square cell pattern of Rayleigh-Benard convection. The result means that our method enables this three-dimensional flow pattern to be described in an unambiguous manner, and some experimental results of other authors can be explained.
- Rayleigh-Benard convection,
- periodic solutions,
- Hamiltonian systems,
- square cell pattern

FullText(HTML)

References(7)

References

[1]	Jenkins D R.Interpretation of shadowgraph patterns in Rayleigh-Benard convection[J].J Fluid Mech,1988,190:451-469.
[2]	Stuart J T.On the cellular patterns in thermal convection[J].J Fluid Mech,1964,18:481-498.
[3]	李继彬,赵晓华,刘正荣.广义哈密顿系统理论及其应用[M].北京:科学出版社,1994.
[4]	LI Ji-bin,Christie J R,Gopalsamy K.Perturbed generalized Hamiltonian systems and some advection models[J].Bull Austral Math Soc,1998,57:1-24.
[5]	Palm E.On the tendency towards hexagonal cells in steady convection[J].J Fluid Mech,1960,8:183-192.
[6]	Zaslavsky G M,Sageer R Z,Vsikov D A,et al.Weak Chaos and Quasi-Regular Patterns[M].Cambridge:Cambridge University Press,1991.
[7]	Stuart J T.The Lagrangian picture of fluid motion and its implication for flow structures[J].IMA J Appl Math,1991,46:147-163.

Relative Articles

[1]	LI Changtong. Analysis of the Predator-Prey Model With Nonlinear Impulsive Control[J]. Applied Mathematics and Mechanics, 2020, 41(5): 568-580. doi: 10.21656/1000-0887.400226
[2]	LIU Xiaomei, ZHOU Gang, ZHU Shuai. A Highly Precise Symplectic Direct Integration Method Based on Phase Errors for Hamiltonian Systems[J]. Applied Mathematics and Mechanics, 2019, 40(6): 595-608. doi: 10.21656/1000-0887.390249
[3]	JIANG Xian-hong, DENG Zi-chen, ZHANG Kai, WANG Jia-qi. A Symplectic Approach for Boundary-Value Problems of Linear Hamiltonian Systems[J]. Applied Mathematics and Mechanics, 2017, 38(9): 988-998. doi: 10.21656/1000-0887.370365
[4]	HU Biao, NING Li-zhong, NING Bi-bo, TIAN Wei-li, WU Hao, NING Jing-hao. Effects of Horizontal Flow on Perturbation Growth and Convection Periodicity[J]. Applied Mathematics and Mechanics, 2017, 38(10): 1103-1111. doi: 10.21656/1000-0887.370314
[5]	LI Can-hua, CHEN Chuan-miao. Ultraconvergence for Averaging Discontinuous Finite Elements and Its Applications in Hamiltonian System[J]. Applied Mathematics and Mechanics, 2011, 32(7): 883-894. doi: 10.3879/j.issn.1000-0887.2011.07.011
[6]	XU Chang-jin, TANG Xian-hua, LIAO Mao-xin. Local Hopf Bifurcation and Global Existence of Periodic Solutions in a TCP System[J]. Applied Mathematics and Mechanics, 2010, 31(6): 745-755. doi: 10.3879/j.issn.1000-0887.2010.06.012
[7]	XU Zi-xiang, ZHOU De-yun, DENG Zi-chen. Numerical Method Based on Hamilton System and Symplectic Algorithm to Differential Games[J]. Applied Mathematics and Mechanics, 2006, 27(3): 305-310.
[8]	JIA Yi-feng, CHEN Yu-fu, XU Zhi-qiang. Application of Wu Elimination Method to Constrained Dynamics[J]. Applied Mathematics and Mechanics, 2006, 27(10): 1226-1234.
[9]	YUAN Yu-bo, PU Dong-mei, LI Shu-min. Bifurcations of Travelling Wave Solutions in Variant Boussinesq Equations[J]. Applied Mathematics and Mechanics, 2006, 27(6): 716-726.
[10]	LI Guo-cheng, XUE Xiao-ping, SONG Shi-ji. On the Periodic Solutions of Differential Inclusions and Applications[J]. Applied Mathematics and Mechanics, 2004, 25(2): 150-158.
[11]	CAO Xian-bing. On the Existence of Periodic Solutions for Nonlinear System With Multiple Delays[J]. Applied Mathematics and Mechanics, 2003, 24(1): 105-110.
[12]	HUANG Zheng-hong. On Cauchy Problems for the RLW Equation in Two Space Dimensions[J]. Applied Mathematics and Mechanics, 2002, 23(2): 157-164.
[13]	LIU Jun. Research of the Periodic Motion and Stability of Two-Degree-of-Freedom Nonlinear Oscillating Systems[J]. Applied Mathematics and Mechanics, 2002, 23(10): 1093-1100.
[14]	WANG Mao-nan, XU Zhen-yuan. On the Homoclinic Orbits in a Class of Two-Degree of Freedom Systems Under the Resonance Conditions[J]. Applied Mathematics and Mechanics, 2001, 22(3): 295-306.
[15]	MA Shi-wang, WANG Zhi-cheng, YU Jian-she. The Existence of Periodic Solutions for Nonlinear Systems of First-Order Differential Equations at Resonance[J]. Applied Mathematics and Mechanics, 2000, 21(11): 1156-1164.
[16]	Cemil Tun, . On the Boundedness and Periodicity of the Solutions of a Certain Vector Differential Equation of Third-Order[J]. Applied Mathematics and Mechanics, 1999, 20(2): 153-160.
[17]	Huang Xiankai, Dong Qinxi. On the Existence of Periodic Solutions to Higher Dimensional Periodic System with Delay[J]. Applied Mathematics and Mechanics, 1999, 20(8): 847-850.
[18]	Gao Puyun. A New Method for the Construction of Integrable Hamiltonian Systems[J]. Applied Mathematics and Mechanics, 1996, 17(10): 933-938.
[19]	Zhang Diming, Li Lin, Huang Hai. Stability Analysis of Linear and Nonlinear Periodic Convection in Thermohaline Double-Diffusive Systems[J]. Applied Mathematics and Mechanics, 1996, 17(9): 821-828.
[20]	Ma Wen-xiu. A Hierarchy of Liouville Integrable Finite-Dimensional Hamiltonian Systems[J]. Applied Mathematics and Mechanics, 1992, 13(4): 349-357.