*UNIVERSAL QUANTIFICATION FOR
SELF-ORGANIZED CRITICALITY IN ATMOSPHERIC FLOWS *

A.Mary Selvam

Indian Institute of Tropical Meteorology, Pune - 411 008, India

Proceedings(Poster) Conference on Patterns,Nonlinear Dynamics and Stochastic Behaviour in Spatially Extended Complex Systems,October 24-28,1997,Budapest,Hungary

Atmospheric flows exhibit selfsimilar
fluctuations on all scales (space-time) ranging from climate
(kilometers/years) to turbulence (millimeters/seconds) manifested
as the ** fractal **geometry to the global cloud cover
pattern concomitant with inverse power law form for power spectra
of temporal fluctuations. Selfsimilar fluctuations implying
long-range correlations are ubiquitous to dynamical systems in
nature and are identified as signatures of

**MODEL CONCEPTS**

Atmospheric flows is a representative example
of turbulent fluid flows.The model is based on the concept that
spatial integration of enclosed small scale(turbulent eddy)
fluctuations result in organized large eddy circulations. The
eddy energy spectrum therefore follows statistical normal
distribution characteristics according to the** Central Limit
Theorem**. Therefore,the square of the eddy amplitude,i.e.,
variance represents the statistical normal probability density
distribution.Such a result that the additive amplitudes of
eddies,when squared, represent probability densities is observed
in the sub-atomic dynamics of quantum systems such as the
electron or photon. Atmospheric flows therefore follow
quantumlike mechanical laws. The root mean square(r.m.s)
circulation speed

*W*^{2}*=(2/**p**)(r/R)w*^{2}*..........................(1)
*

The square of the eddy amplitude *W*^{2
}represents the kinetic energy ** E** given
as(from Eq.1)

*E=H**n*_{R}*........(2)
*

where *n*_{R}
( proportional to ** 1/R ) **is the frequency of the
large eddy and

The relative phase angle between large and
turbulent eddies is equal to ** r/R** and is directly
proportional to

*R*^{3}*/T*^{2}*=(2/**p**)(r*^{3}*/t*^{2}*)......................(3)
*

Equation(3) is analogous to ** Kepler's
third law of planetary motion**,namely, the square of the
planet's year(period) to the cube of the mean distance from the

**WAVE-PARTICLE DUALITY IN CLOUD FORMATION**

The apparent paradox of wave-particle duality
in microscopic scale quantum systems is however physically
consistent in the context of macroscale atmospheric flows since
the bi-directional energy flow structure of a complete
atmospheric eddy results in the formation of clouds in updrafts
regions and dissipation of clouds in downdrafts regions.The
commonplace occurrence of clouds in a row is a manifestation of
wave-particle duality in the macroscale quantum system of
atmospheric flows. The above-described analogy of quantum-like
mechanics for atmospheric flows is similar to the concept of a
subquantum level of fluctuations whose space- time organization
gives rise to the observed manifestation of subatomic
phenomena,i.e.,quantum systems as order out of chaos
phenomena[G.Grossing,Il Nuovo Cimento 103B(1989) 497].
H.E.Puthoff[Phys.Rev.A.39,2333(1989)] has also put forth the
concept of ** "Gravity as a zero-point fluctuation
force"**( Quantum
fluctuations of empty space).The vacuum zero-point
fluctuation(electromagnetic) energy manifested in the Casimir
effect is analogous to the turbulent scale fluctuations whose
spatial integration results in coherent large eddy structures.