LI Zhen, LIAN Xin-yu. Seven-Mode Truncation and Chaotic Characteristics of Kolmogorov Flow Model[J]. Applied Mathematics and Mechanics, 2013, 34(3): 318-326. doi: 10.3879/j.issn.1000-0887.2013.03.011
Citation: LI Zhen, LIAN Xin-yu. Seven-Mode Truncation and Chaotic Characteristics of Kolmogorov Flow Model[J]. Applied Mathematics and Mechanics, 2013, 34(3): 318-326. doi: 10.3879/j.issn.1000-0887.2013.03.011

Seven-Mode Truncation and Chaotic Characteristics of Kolmogorov Flow Model

doi: 10.3879/j.issn.1000-0887.2013.03.011
  • Received Date: 2012-12-10
  • Rev Recd Date: 2013-01-07
  • Publish Date: 2013-03-15
  • To provide a mathematical description of the chaotic behavior in Kolmogorov flow model,with k=3was researched,NavierStokes equation was truncated by seven basic modes and a new sevendimensional chaotic system described by ordinary differential equations was obtained. The basic dynamical behaviors and chaotic behaviors were simulated numerically according to control parameter changes and the chaotic characteristics were analyzed. The result verifies that the mathematical object which accounts for turbulence is attributed to lowdimensional chaotic attractors and this is helpful to understand turbulent flow.
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  • [1]
    陈奉苏.混沌学及其应用[M].北京:中国电力出版社,1998.(CHEN Feng-su. Chaos Theory and Application [M]. Beijing: China Electric Power Press, 1998.(in Chinese))
    [2]
    邹恩, 李祥飞, 陈建国.混沌控制及其优化应用[M].长沙:国防科技大学出版社,2002.(ZOU En, LI Xiang-fei, CHEN Jian-guo.Chaos Control and Optimization Application [M]. Changsha: National University of Defense Technology Press, 2002.(in Chinese))
    [3]
    张化光, 王智良, 黄玮.混沌系统的控制理论[M].沈阳:东北大学出版社,2003.(ZHANG Hua-guang, WANG Zhi-liang, HUANG Wei. Control Theory of Chaotic System [M]. Shenyang: Northeastern University Press, 2003.(in Chinese))
    [4]
    郭光, 严绍瑾, 张培昌.大气边界层湍流的混沌特性[J].南京气象学院学报, 1992, 15(4): 476-484.(GUO Guang, YAN Shao-jin, ZHANG Pei-chang. The chaotic characteristics of the atmospheric boundary layer turbulence[J]. Journal of Nanjing Institute of Meteorology,1992, 15(4): 476-484.(in Chinese))
    [5]
    Long-Jye Sheu, Lap-Mou Tam, Juhn-Horng Chen, Hsien-Keng Chen, Kuang-Tai Lin,Yuan Kang. Chaotic convection of viscoelastic fluids in porous media[J]. Chaos, Solitons and Fractals,2008, 37(1): 113-124.
    [6]
    Evstigneev N M, Magnitskii N A, Sidorov S V. On the nature of turbulence in a problem on the motion of a fluid behind a ledge[J].Differential Equations,2009, 45(1): 68-72.
    [7]
    CAI Feng-chun, ZANG Feng-gang, LIANG Yan-xian. Nonlinear dynamic behaviors of a cracked hinged-hinged pipe conveying pulsating fluid[J]. Journal of Vibration and Shock,2012, 31(4): 162-167.
    [8]
    刘兆存, 金忠青.湍流理论若干问题研究进展[J].水利水电科技进展, 1995, 15(4): 12-15.(LIU Zhao-cun, JIN Zhong-qing. Progress of some problems in the theory of turbulence[J]. Advances in Science and Technology of Water Resources,1995, 15(4): 12-15.(in Chinese))
    [9]
    Carlo Ferrarioa, Arianna Passerini, Gudrun Thoter. Generalization of the Lorenz model to the two-dimensional convection of secondgrade fluids[J]. International Journal of Non-Linear Mechanics,2004, 39(4): 581-591.
    [10]
    Roy D, Musielak Z E. Generalized Lorenz models and their routes to chaos—Ⅰ: energy-conserving vertical mode truncations[J].Chaos, Solitons and Fractals,2007, 32(3): 1038-1052.
    [11]
    CHEN Zhi-min, Price W G. Transition to chaos in a fluid motion system[J].Chaos, Solitons and Fractals,2005, 26(4): 1195-1202.
    [12]
    Arnold V I, Meshalkin L D. Kolmogorov’s seminar on selected problems of analysis [J].Russ Math Surv,1960, 15(1): 247-250.
    [13]
    CHEN Zhimin, Price W G. Onset of chaotic Kolmogorov flows resulting from interacting oscillatory modes[J]. Commun Math Phys,2005, 256(3): 737-766.
    [14]
    Reynolds O. An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous and of the law of resistance in a parallel channel[J]. Philos Trans Roy Soc,1883, 174: 935-982.
    [15]
    CHEN Zhi-min. Bifurcations of a steadystate solution to the two-dimensional Navier-Stokes equations[J].Commun Math Phys,1999, 201(1): 117-138.
    [16]
    CHEN Zhi-min, Price W G. Time-dependent periodic NavierStokes flow in a two-dimensional torus[J]. Commun Math Phys,1996, 179(3): 577-597.
    [17]
    吴舒辞.自动控制技术[M].北京:中国林业出版社, 2000.(WU Shu-ci.Automatic Control Technology [M]. Beijing: China Forestry Press, 2000.(in Chinese))
    [18]
    刘宗华.混沌动力学基础及其应用[M].北京:高等教育出版社, 2006.(LIU Zong-hua. Fundamentals and Applications of Chaotic Dynamics [M]. Beijing: Higher Education Press, 2006.(in Chinese))
    [19]
    Graef J R, Spikes P W. On the nonlinear limit-point/limit-circle problem[J]. Nonlinear Analysis: Theory, Methods and Applications,1983, 7(8): 851-871.
    [20]
    Landau L. On the problem of turbulence [J]. C R Acad Sci URSS,1944, 44: 311-315.
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