CHAOS THEORY AND ITS APPLICATIONS TO ATMOSPHERIC BOUNDARY LAYER TURBULENCE RESEARCH
Received date: 1999-07-27
Revised date: 1999-10-13
Online published: 2000-04-01
This paper mainly consists of four sections,its purpose is to give a brief overview of chaos theory and to discuss its applications to the atmospheric boundary layer turbulence in detail.We usually cite the original references and more recent review papers so that interested readers can easily find more detail concerning particular fields of study.Chaos theory and method for characterizing chaos are presented in section 2,including phase space reconstruction method,definition and calculation of fractal dimension and Lyapunov exponents.Applications of chaos theory to the atmospheric boundary layer turulence are discussed in section 3,recent research work of author is introduced:a large amount of observed data obtained by the sonic anemometer from two different field experiments at different places of China is analyzed, which is shown that all time series of atmospheric turbulence fluctuation exhibit chaotic behavior,with strange attractors whose (correlation)dimensions range from 3 to 7,all the maximum Lyapunov exponents are great than zero,as well as,it is first put forward that turbulence kinetic energy derived from turbulence wind speed as a variation is made use of calculating fractal dimension and the maximum lyapnunov exponent to characterize chaos.Finally,some suggestions for further work are given
in section 4.
Key words: Chaos; Correlation dimension; Atmospheric boundary layer; Turbulence.
LI Xin . CHAOS THEORY AND ITS APPLICATIONS TO ATMOSPHERIC BOUNDARY LAYER TURBULENCE RESEARCH[J]. Advances in Earth Science, 2000 , 15(2) : 178 -183 . DOI: 10.11867/j.issn.1001-8166.2000.02.0178
〔1〕Campbell D K. Choas/XAOC:Soviet-American Perspectives on Nonlinear Science〔M〕. The American Institute of Physics,New York:Springer Verlag,1990.500.
〔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.
〔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.
〔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.
〔5〕Hadamard J. Les surfaces a courbures opposees et leurs lignes geodesiques〔J〕. J Math Pures,1898, Appl,4:27~73.
〔6〕Poincare H. Science et Methode.Ernest Flammarion〔M〕.(English translation is Science and Method. Dover Publications,1952.288).Dover:Dover Pub,1908.
〔7〕Lorenz E N. Deterministic nonperiodic flow〔J〕.J Atmos Sci,1963, 20:130.
〔8〕Li T-Y, Yorke J A. Period three implies chaos〔J〕.Am Math Mon,1975,82:985~992.
〔9〕Ruelle D, Takens F.On the nature of turbulence〔J〕.Commun Math Phys,1971,20:167.
〔10〕Ruelle D. Deterministic Chaos: the science and fiction〔J〕.Proc R Soc London, 1990, A 427:241.
〔11〕Hao B-L. Choas〔M〕. River Edge:World Scientific Pub CO,1984.576p.
〔12〕Tsonis A A, Elsner J B. Chaos, strange attractors and weather〔J〕.Bull Amer Meteor Soc,1989,70:14~23.
〔13〕Marek M, Schreiber I. Chaotic Behavior of Deterministic Dissipative Systems〔M〕.Cambridge:Cambridge University Press,1991.365p.
〔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.
〔15〕Berge P Y Pomeau, Vidal C. Order within Chaos〔M〕. New York:John Wiley and Sons Inc,1984.329p.
〔16〕Mandelbrot B B. The Fractal Geometry of Nature〔M〕. San Francisco:Freeman,1983.
〔17〕Falconer K. Fractal Geometery: Mathematical Foundation and Applications〔M〕. New York:Wiley,1990.
〔18〕Grassberger P, Procaccia I. Characterization of strange attrators〔J〕.Phys Rev.Lett, 1983,50:346~349.
〔19〕Eckmann J P, Ruelle D. Ergodic theory of chaos and strange attractors〔J〕. Rev Mod Phys,1985,57:617~656.
〔20〕Guckenheimer J, Holmes P. Nonlinear Oscillations,Dynamical Systems and Bifurcations of Vector Fields〔M〕.New York:Springer-Verlag,1983.453pp.
〔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).
〔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.
〔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.
〔24〕Packard N H. Geometry from a time series〔J〕. Phy Rev Lett,1980, 45: 712.
〔25〕Takens F. Detecting strange attractor in turbulence〔J〕.Le ture Notes in Math,1981, 898: 336.
〔26〕方兆本.走出混沌〔M〕.长沙:湖南教育出版社,1995.71~81.
〔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.
〔28〕Theiler J, Eubank S. Don' t bleach chaotic data〔J〕. Chaos,1993, 3: 771.
〔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.
〔30〕Kantz H. A robust method to estimate the maximal lyapunov exponent of a time series〔J〕. Phys Rev,1994, A185: 77.
〔31〕Farmer J D. Predicting chaotic time series〔J〕. Phys Rev Lett,1987,59:845.
〔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.
〔33〕Ababrbanel H D I. Analysis of Observed Chaotic Data〔M〕.New York: Springer,1996.108~115.
〔34〕Williams G P. Chaos Theory Tamed〔M〕. Great Britain:Taylor &Francis,1997.
〔35〕Froyland J. Introduction to Chaos and Coherence〔M〕. New York: Institute of Physics Publishing, 1992.
〔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.
〔37〕Stanisic M M. The mathematical theory of turbulence〔M〕.Springer: The American Institute of Physics,1985.500pp.
〔38〕Ruelle D. Chance and Chaos〔M〕. Princeton: Princeton University Press,1991.
〔39〕Frisch U. Turbulence〔M〕. Cambridge: Cambridge Uni Press,1995.
〔40〕是勋刚.湍流〔M〕.天津:天津大学出版社,1994.
〔41〕Kantz H, Schreiber T. Nonlinear Time Series Analysis〔M〕.Cambridge: Cambridge Unversity Press,1997.
〔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.
〔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.
〔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.
〔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.
〔46〕Jaramillo P G, Puente C E. Strange attractor in atmosphere boundary-layer turbulence〔J〕. Boundary-Layer Meteorol,1993, 64:175.
〔47〕Rudolfo. W, Peter, Gerard,et al. Search for finite dimensional attractors in atmospheric turbulence〔J〕.Boundary-Layer Meteorology,1995, 73:1~14.
〔48〕Theiler J. Efficient algorithm for estimating the correlation dimension from a set of discrete points〔J〕. Phys Rev,1987,A36:4456.
〔49〕Wolf A,Swift J B, Swinney HL,et al. Determining lyapunov exponents from a time series〔J〕. Physica,1988, 16D(3):285~317.
〔50〕Lorenz E N. Dimension of weather and attractors〔J〕.Nature,1991,353:241~244.
〔51〕Kaimal J C, Finnigan J J. Atmospheric Boundary Layer Flows〔M〕. New York: Oxford Uni Press, 1994.
〔52〕Panofsky H A, Dutton J A. Atmospheric Turbulence〔M〕.New York:John Wiley and Sons,1984.
〔53〕Sorbjan Z. Structure of the atmospheric boundary layer〔M〕.New Jersey: Prentice Hall,1989.
/
〈 |
|
〉 |