International E-publication: Publish Projects, Dissertation, Theses, Books, Souvenir, Conference Proceeding with ISBN.  International E-Bulletin: Information/News regarding: Academics and Research

An overview of the nonlinear chaos theory in the atmospheric systems

    ,

Author Affiliations

  • 1Department of Physics, D.N. College, Murshidabad, West Bengal-742201, India
  • 2J.D. Birla Institute, Departments of Sciences and Commerce, 11 Lower Rawdon Street, Kolkata-700020, India

Res. J. Recent Sci., Volume 7, Issue (3), Pages 51-52, March,2 (2018)

Abstract

The nonlinear behaviour of the dynamical atmospheric systems may be properly studied by the chaos theory. The atmospheric flows exhibit fractal fluctuations in space and time. Due to nonlinear complexity, the actual physical mechanism of the atmospheric system is yet to be clearly understood. Thus a comprehensive study of the atmospheric instability in the light of nonlinear chaos theory is highly needed. An overview of the developments of the chaos theory in understanding the atmospheric systems is done in this paper. Proper estimation of the nonlinear chaos theory in meteorology may be significant and helpful for accurate prediction of atmospheric instability.

References

  1. Poincare H. (1890)., Sur le problème des trois corps et les équations de la dynamique., Acta Mathematica, 13(1), 5(7).
  2. Shaffee A. and Shaffee S. (1987)., Implications of the spatial finiteness of mesoscale meteorological fields., Phys. Rev. A, 35, 892.
  3. Yang P. (1991)., On the chaotic behaviour and predictability of the real atmosphere., Adv. Atmos. Sci., 8(4), 407-420.
  4. Lorentz E.N. (1991)., Dimension of weather and climate attractors., Nature, 353, 241-244.
  5. Li T.Y. and Yorke J.A. (1975)., Period three implies chaos., Am. Math. Mon., 82(10), 985-992.
  6. Cohen E.G.D. (1997)., Lectures given at thr International Meeting “Boltzmann’s legacy- 150 years after his birth”., Academia Nazionaledei Lincei, 25-28 May, 1994.
  7. West B.J. (2004)., Comments on the renormalization group, scaling and measures of complexity., Chaos, Solitons and fractals, 20, 33-44.
  8. Selvam A.M. (2009)., Fractal fluctuations and statistical normal distribution., Fractals, 17(3), 333-349.
  9. Selvam A.M. and Fadnavis S. (1998)., Signatures of a universal spectrum for atmospheric interannual variability in some disparate climatic regimes., Meteorology and Atmospheric Physics, 66(1-2), 87-112.
  10. Tesla Timeline (2012) (http://www.teslauniverse.com/ nikola-tesla-timeline-1856-birth-of-tesla, goto-1861). Tesla Universe.16 August 2012, undefined
  11. Hadamard J. (1898)., Les surfaces à courbures opposées et leurs lignes géodesique., J. Math. Pures Appl., 4, 27-73.
  12. Nash J.E. and Sutcliffe J.V. (1970)., River flow forecasting through conceptual models. Part I—A discussion of principles., J. Hydrol., 10(3), 282-290.
  13. Lorenz E.N. (1963)., Deterministic Nonperiodic Flow., J. Atmos. Sci., 20, 130-141.
  14. Lorenz E.N. (1965)., A Study of the Predictability of a 28-Variable Atmospheric Model., Tellus, 17(3), 321-333.
  15. Mandelbrot B.B. (1977)., Fractals., from, chance and dimension, Freeman Publishers, San Francisco.
  16. Mandelbrot B.B. (1983)., The Fractal Geometry of Nature., W.H. Freeman publication.
  17. Rulle D. and Takens F. (1971)., On the nature of turbulence., Commun. Math. Phys., 20(3), 167-192.
  18. Rulle R. (1990)., Deterministic chaos: The Science and the Friction., Proc. Roy. Soc. London., 427A, 241-248.
  19. Boeing G. (2016)., Visual Analysis of Nonlinear Dynamical Systems: Chaos, Fractals, Self-Similarity and the Limits of Prediction., Systems, 4(4), 37. doi:10.3390/systems4040037
  20. Poincare H. (1908)., Science of Method., Dover publication, New York, 288.
  21. Li W. (2010)., A bibliography on 1/f noice., http://www.nslij-genetics.org/wli/1fnoise, 5/01/2017
  22. Milotti E. (2001)., 1/f noise, a pedagogical review., invited talk to E-GLEA-2, Buenos Aires, Sept. 10-14, 2001
  23. Takens F. (1981)., Detecting Strange Attractors in Turbulence., Dynamical Systems and Turbulence, Lecture Notes in Mathematics, 898, Springer-Verlag, New York, 366-381.
  24. Zeng X., Pielke R.A. and Eykholt R. (1993)., Chaos theory and its applications to the atmosphere., Bulletin of the American Meteorological Society, 74(4), 631-644.