Geoscience Reference
In-Depth Information
Chapter 1
General Systems Theory Concepts
in Atmospheric Flows
Abstract
Atmospheric flows, a representative example of turbulent fluid flows,
exhibit long-range spatiotemporal correlations manifested as the fractal geometry to
the global cloud cover pattern concomitant with inverse power law form for spectra
of temporal fluctuations. Such nonlocal connections are ubiquitous to dynamical
systems in nature and are identified as signatures of self-organized criticality. Math-
ematical models for simulation and prediction of dynamical systems are nonlinear
so that analytical solutions are not available. Finite precision computed solutions
are sensitively dependent on initial conditions and give chaotic solutions, identified
as deterministic chaos. Realistic mathematical modeling for simulation and predic-
tion of atmospheric flows requires alternative theoretical concepts and analytical or
error-free numerical computational techniques and therefore comes under the field
of `General Systems research'. General systems theory for atmospheric flows visu-
alizes the hierarchical growth of larger scale eddies from space-time integration of
smaller scale eddies resulting in an atmospheric eddy continuum manifested in the
self-similar fractal fluctuations of meteorological parameters. The model shows that
the observed long-range spatiotemporal correlations are intrinsic to quantum-like
mechanics governing fluid flows. The model concepts are independent of intrinsic
characteristics of the dynamical system such as chemical, physical, electrical, etc.,
and gives scale-free governing equations for fluid flow characteristics.
Keywords
Nonlinear dynamics
·
Chaos
·
Fractals
·
Self-organized criticality
·
General systems theory
1.1
Introduction
Atmospheric flows exhibit self-similar fractal fluctuations generic to dynamical
systems in nature. Self-similarity implies long-range space-time correlations identi-
fied as self-organized criticality (SOC) (Bak et al.
1988
). Yano et al. (
2012
) suggest
that atmospheric convection could be an example of self-organized criticality. At-
mospheric convection and precipitation have been hypothesized to be a real-world
realization of SOC (Peters et al.
2002
,
2010
). The physics of SOC ubiquitous to dy-
namical systems in nature and in finite precision computer realizations of nonlinear
