全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...

混沌理论与大气边界层湍流研究

DOI: 10.11867/j.issn.1001-8166.2000.02.0178, PP. 178-183

Keywords: 混沌,分数维,大气边界层,湍流

Full-Text   Cite this paper   Add to My Lib

Abstract:

简述了混沌理论的发展及其判别方法,阐明混沌理论的建立给大气科学中的湍流研究带来了新的启示;介绍了近期混沌理论在大气边界层湍流研究中的应用结果,这些结果表明大气边界层湍流具有很强的混沌特性,且存在低维奇怪吸引子。最后提出了有待进一步研究的问题。

References

[1]  〔15〕Berge P Y Pomeau, Vidal C. Order within Chaos〔M〕. New York:John Wiley and Sons Inc,1984.329p.
[2]  〔16〕Mandelbrot B B. The Fractal Geometry of Nature〔M〕. San Francisco:Freeman,1983.
[3]  〔17〕Falconer K. Fractal Geometery: Mathematical Foundation and Applications〔M〕. New York:Wiley,1990.
[4]  〔18〕Grassberger P, Procaccia I. Characterization of strange attrators〔J〕.Phys Rev.Lett, 1983,50:346~349.
[5]  〔19〕Eckmann J P, Ruelle D. Ergodic theory of chaos and strange attractors〔J〕. Rev Mod Phys,1985,57:617~656.
[6]  〔20〕Guckenheimer J, Holmes P. Nonlinear Oscillations,Dynamical Systems and Bifurcations of Vector Fields〔M〕.New York:Springer-Verlag,1983.453pp.
[7]  〔21〕Kolmogorov A N. A new metric invariant of transient dynamical systems and automorphisms in Lebesguepaces〔J〕.Dokl Akad Nauk SSSR,1958,119:861~864(Sov Phys Dokl,112:426~429).
[8]  〔22〕Wolf A,Swift J. Progress in computing Lyapunov exponents from experimental data〔A〕. In:Holton C W, Reichl L E,eds. Statistical Physics and Chaos in Fusion Plasmas〔C〕.New York: Wiley Pub,1984.
[9]  〔23〕杨培才.湍流运动与非线性科学理论〔J〕.力学进展,1994,27(2):205~219.
[10]  〔24〕Packard N H. Geometry from a time series〔J〕. Phy Rev Lett,1980, 45: 712.
[11]  〔25〕Takens F. Detecting strange attractor in turbulence〔J〕.Le ture Notes in Math,1981, 898: 336.
[12]  〔26〕方兆本.走出混沌〔M〕.长沙:湖南教育出版社,1995.71~81.
[13]  〔27〕刘秉正.非线性动力学与混沌基础〔M〕.长春:东北师范大学出版社,1994.70~90.
[14]  〔28〕Theiler J, Eubank S. Don' t bleach chaotic data〔J〕. Chaos,1993, 3: 771.
[15]  〔29〕Ababrbanel H D I, Kennel M B. Local false nearest neigh-bors and dynamical dimensions from observed chaotic data〔J〕. Phys Rev, 1993,E47: 3 057.
[16]  〔30〕Kantz H. A robust method to estimate the maximal lyapunov exponent of a time series〔J〕. Phys Rev,1994, A185: 77.
[17]  〔31〕Farmer J D. Predicting chaotic time series〔J〕. Phys Rev Lett,1987,59:845.
[18]  〔32〕Orcutt K F, Arritt R W. Comparative fractal dimension for daytime and nocturnal surface layer turbulence〔A〕. 11th Symp Boundayr Layer & Turb〔C〕. Charlotte: NC Amer Meterol Soc, 1995.
[19]  〔33〕Ababrbanel H D I. Analysis of Observed Chaotic Data〔M〕.New York: Springer,1996.108~115.
[20]  〔49〕Wolf A,Swift J B, Swinney HL,et al. Determining lyapunov exponents from a time series〔J〕. Physica,1988, 16D(3):285~317.
[21]  〔50〕Lorenz E N. Dimension of weather and attractors〔J〕.Nature,1991,353:241~244.
[22]  〔1〕Campbell D K. Choas/XAOC:Soviet-American Perspectives on Nonlinear Science〔M〕. The American Institute of Physics,New York:Springer Verlag,1990.500.
[23]  〔2〕郝柏林.分叉混沌、奇怪吸引子、湍流及其它〔J〕.物理学进展,1983,3(3):329~416.
[24]  〔3〕黄永念.分叉、分形、混沌和湍流之间的关系〔A〕.见:中国科学院力学研究所编.现代流体力学进展〔C〕.北京:科学出版社,1991.7~15.
[25]  〔4〕胡非.湍流、间歇性与大气边界层〔M〕.北京:科学出版社,1995.12~17.
[26]  〔5〕Hadamard J. Les surfaces a courbures opposees et leurs lignes geodesiques〔J〕. J Math Pures,1898, Appl,4:27~73.
[27]  〔6〕Poincare H. Science et Methode.Ernest Flammarion〔M〕.(English translation is Science and Method. Dover Publications,1952.288).Dover:Dover Pub,1908.
[28]  〔7〕Lorenz E N. Deterministic nonperiodic flow〔J〕.J Atmos Sci,1963, 20:130.
[29]  〔8〕Li T-Y, Yorke J A. Period three implies chaos〔J〕.Am Math Mon,1975,82:985~992.
[30]  〔9〕Ruelle D, Takens F.On the nature of turbulence〔J〕.Commun Math Phys,1971,20:167.
[31]  〔10〕Ruelle D. Deterministic Chaos: the science and fiction〔J〕.Proc R Soc London, 1990, A 427:241.
[32]  〔11〕Hao B-L. Choas〔M〕. River Edge:World Scientific Pub CO,1984.576p.
[33]  〔12〕Tsonis A A, Elsner J B. Chaos, strange attractors and weather〔J〕.Bull Amer Meteor Soc,1989,70:14~23.
[34]  〔13〕Marek M, Schreiber I. Chaotic Behavior of Deterministic Dissipative Systems〔M〕.Cambridge:Cambridge University Press,1991.365p.
[35]  〔14〕Zeng X, Pielke R A, Eykholt R. Choas theory and its applications to the atmosphere〔J〕. Bulletin of the American Meteorological Society, 1993,74(4): 631~644.
[36]  〔34〕Williams G P. Chaos Theory Tamed〔M〕. Great Britain:Taylor &Francis,1997.
[37]  〔35〕Froyland J. Introduction to Chaos and Coherence〔M〕. New York: Institute of Physics Publishing, 1992.
[38]  〔36〕Buzug T, Pfister G. Optimal delay time and embedding dimension for delay-time coordinates by analysis of the global static and local dynamical behavivour of strange attractors〔J〕. Phys Rev,1991, A 45:7 073.
[39]  〔37〕Stanisic M M. The mathematical theory of turbulence〔M〕.Springer: The American Institute of Physics,1985.500pp.
[40]  〔38〕Ruelle D. Chance and Chaos〔M〕. Princeton: Princeton University Press,1991.
[41]  〔39〕Frisch U. Turbulence〔M〕. Cambridge: Cambridge Uni Press,1995.
[42]  〔40〕是勋刚.湍流〔M〕.天津:天津大学出版社,1994.
[43]  〔41〕Kantz H, Schreiber T. Nonlinear Time Series Analysis〔M〕.Cambridge: Cambridge Unversity Press,1997.
[44]  〔42〕杨培才,刘锦丽,杨硕文.低层大气运动的混沌吸引子〔J〕.大气科学,1990,14(3): 335~341.
[45]  〔43〕郭光.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.
[46]  〔44〕林振山.非线性力学与大气科学〔M〕.南京:南京大学出版社,1993.
[47]  〔45〕高志球,王介民.HEIFE绿洲和沙漠地区大气边界层湍流混沌特性研究〔J〕.高原气象,1998,17(4):398~402.
[48]  〔46〕Jaramillo P G, Puente C E. Strange attractor in atmosphere boundary-layer turbulence〔J〕. Boundary-Layer Meteorol,1993, 64:175.
[49]  〔47〕Rudolfo. W, Peter, Gerard,et al. Search for finite dimensional attractors in atmospheric turbulence〔J〕.Boundary-Layer Meteorology,1995, 73:1~14.
[50]  〔48〕Theiler J. Efficient algorithm for estimating the correlation dimension from a set of discrete points〔J〕. Phys Rev,1987,A36:4456.
[51]  〔51〕Kaimal J C, Finnigan J J. Atmospheric Boundary Layer Flows〔M〕. New York: Oxford Uni Press, 1994.
[52]  〔52〕Panofsky H A, Dutton J A. Atmospheric Turbulence〔M〕.New York:John Wiley and Sons,1984.
[53]  〔53〕Sorbjan Z. Structure of the atmospheric boundary layer〔M〕.New Jersey: Prentice Hall,1989.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133