Nonlinear Dynamics and Chaos: Applications in Atmospheric Sciences

Abstract

Atmospheric flows, an example of turbulent fluid flows, exhibit fractal fluctuations of all space-time scales ranging from turbulence scale of mmsec to climate scales of thousands of kilometers -years and may be visualized as a nested continuum of weather cycles or periodicities, the smaller cycles existing as intrinsic fine structure of the larger cycles. The power spectra of fractal fluctuations exhibit inverse power law form signifying long -range correlations identified as self -organized criticality and are ubiquitous to dynamical systems in nature and is manifested as sensitive dependence on initial condition or 'deterministic chaos' in finite precision computer realizations of nonlinear mathematical models of real world dynamical systems such as atmospheric flows. Though the selfsimilar nature of atmospheric flows have been widely documented and discussed during the last three to four decades, the exact physical mechanism is not yet identified. There now exists an urgent need to develop and incorporate basic physical concepts of nonlinear dynamics and chaos into classical meteorological theory for more realistic simulation and prediction of weather and climate. A review of nonlinear dynamics and chaos in meteorology and atmospheric physics is summarized in this paper. Dynamical systems and fractal space-time fluctuationsDynamical systems in nature, i.e., systems that change with time, such as fluid flows, heartbeat patterns, spread of infectious diseases, etc., exhibit nonlinear (unpredictable) fluctuations. Conventional mathematical and statistical theories deal only with linear systems and the exact quantification and description of nonlinear fluctuations was not possible till the identification in the 1970s by Mandelbrot 6,12 , of the universal symmetry of self-similarity, i.e., fractal geometry underlying the seemingly irregular fluctuations in space and time 13,14 . Fractals, as the name implies, describe non-Euclidean objects generic to nature such as tree

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