Abstract
In this paper, the attractors of turbulent flows in phase space are reconstructed by the time delay technique using observed data of atmospheric boundary-layer turbulence, which include high resolution temperature, humidity andthree-dimensional wind speed measurements in Gansu province and Beijing, China. The correlation dimensions and largest Lyapunov exponents have been computed. The results indicate that all the largest Lyapunov exponents in different conditions of time, site and atmospheric stability are greater than zero. This means that the atmospheric boundary-layer turbulence system is really chaotic and has appropriate low-dimensional strange attractors whose dimension numbers range from 3 to 7 and vary with different variables (dynamical variables or non-dynamical variables) and atmospheric stability. Turbulent kinetic energy is first applied to reconstruct the attractor of turbulence, and is found to be feasible.
Similar content being viewed by others
References
Abarbanel, H. D. I. andKennel, M. B.: 1993, ‘Local False Nearest Neighbors and Dynamical Dimensions from Observed Chaotic Data’ Phys. Rev. E 47, 3057-3068.
Grassberger, P. andProcaccia, I.: 1983, ‘Measuring the Strangeness of Strange Attractors’ Physica D 9, 189-208.
Hu, F.: 1995, Turbulence, Intermittency and Atmospheric Boundary-Layer, Chinese Academic Press, Beijing, 288 pp. (in Chinese).
Hu, F.,Li, X.,Chen, H., andLiu, G.: 1999, ‘Turbulence Characteristics in the Rough Urban Canopy Layer’ Clim. Environ. Res. 4, 252-258 (in Chinese).
Jaramillo, G. P. andPuente, C. E.: 1993, ‘Strange Attractors in Atmosphere Boundary-Layer Turbulence’ Boundary-Layer Meteorol. 64, 175-197.
Kantz, H. andSchreiber, T.: 1997, Nonlinear Time Series Analysis, Cambridge University Press, Cambridge, 304 pp.
Li, X.: 1998, Study on the Chaotic Characteristics of Atmospheric Boundary-Layer Turbulence, Ph.D. Dissertation, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 140 pp. (in Chinese).
Lorenz, E. N.: 1963, ‘Deterministic Nonperiodic Flow’ J. Atmos. Sci. 20, 130-141.
Lorenz, E. N.: 1991, ‘Dimension of Weather and Climatic Attractors’ Nature 353, 241-244.
Moon, F. C.: 1992, Chaotic and Fractal Dynamics: An Introduction for Applied Scientists and Engineers, John Wiley & Sons, New York, 528 pp.
Packard, N. H.,Crutchfield, J. P.,Farmer, J. D., andShaw, R. S.: 1980, ‘Geometry for a Time Series’ Phys. Rev. Lett. 45, 712-716.
Qiao, J.: 1996, The Fine Structure of Turbulence in Unstable Atmospheric Surface Layer, Ph.D. Dissertation, Beijing University, Beijing, 100 pp. (in Chinese).
Takens, F.: 1981, ‘Detecting Strange Attractors in Turbulence’ in D. A. Rand andL. S. Young (eds.), Lecture Notes in Mathematics, Vol. 898, Springer, New York, pp. 366-381.
Theiler, J.: 1987, ‘Efficient Algorithm for Estimating the Correlation Dimension from a Set of Discrete Points’ Phys. Rev. A 36, 4456-4462.
Tsonis, A. A. andElsner, J. B.: 1989, ‘Chaos, Strange Attractors andWeather’ Bull. Amer.Meteorol. Soc. 70, 14-23.
Williams, G. P.: 1997, Chaos Theory Tamed, Taylor & Francis, London, 499 pp.
Wolf, A.,Swift, J. B.,Swinney, H. L., andVastano, J. A.: 1985, ‘Determining Lyapunov Exponents from a Time Series’ Physica D 16, 285-317.
Yang, P.,Liu, J., andYang, S.: 1990, ‘The Chaotic Attractors in the Lower Atmosphere’ Chinese J. Atmos. Sci. 14, 335-341 (in Chinese).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Xin, L., Fei, H. & Gang, L. Characteristics Of Chaotic Attractors In Atmospheric Boundary-Layer Turbulence. Boundary-Layer Meteorology 99, 335–345 (2001). https://doi.org/10.1023/A:1018940512240
Issue Date:
DOI: https://doi.org/10.1023/A:1018940512240