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CHAOS, QUANTUMLIKE MECHANICS AND NON-LOCALITY
IN ATMOSPHERIC FLOWS

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A. M. Selvam

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Indian Institute of Tropical Meteorology,
Pune 411 008, India

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Proceedings of the Causality and Locality
in Modern Physics and Astronomy: Open Questions and Possible Solutions
- A Symposium to Honour Jean - Pierre Vigier, York University, Toronto,
Canada, August 25-29, 1997.

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Summary

Atmospheric flows exhibit long-range
spatiotemporal correlations or non-local connections manifested as the
fractal geometry to the global cloud cover pattern concomitant with inverse
powerlaw form for power spectra of temporal fluctuations. Such non-local
connections are ubiquitous to dynamical systems in nature and are recently
identified as signatures of self-organized criticality, a field of study
belonging to the newly emerging science of nonlinear dynamics and chaos.
Mary Selvam (*Can. J. Phys.* 1990: **68**, 831) has proposed a
model, which identifies non-local connections in atmospheric flows as intrinsic
to quantumlike mechanics governing flow dynamics. The model is based on
the concept that spatial integration of enclosed small-scale fluctuations
gives rise to large eddy circulations. The eddy energy spectrum therefore
follows statistical normal distribution, i.e., the additive amplitudes
of eddies, when squared, represent probability densities. Such a result
is observed in microscopic quantum systems such as the electron or the
photon. The model predictions are as follows. (1) The overall flow trajectory
traces a logarithmic spiral with the quasiperiodic *Penrose* tiling
for the internal structure, thereby resulting in non-local connections.
(2) Wave-particle duality is attributed to bimodal (formation and dissipation
respectively) phenomenological form for display of energy in the bi-directional
(updrafts and downdrafts) energy flow intrinsic to eddy circulations, e.g.,
cloud formation and dissipation respectively in updrafts and downdrafts
in atmospheric flows. (3) Atmospheric eddy circulations follow *Kepler*’s
third law of planetary motion. The centrifugal forces representing inertial
mass therefore follow the inverse square law analogous to *Newton*’s
law of gravitation. The model therefore is equivalent to a superstring
model (Kaku, New Scientist 18 Jan.1997, 32) for quantum gravity.
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Model concepts

The model is based on the concept that
spatial integration of enclosed small-scale circulations gives rise to
large eddy circulations. The root mean square (r.m.s) circulation speeds
*W* and *w*_{*} corresponding to radii *R* and *r*
respectively of large and turbulent eddies are related by the equation
(1)
(1)

In the above equation* **n*_{R}
and *n*_{r}
are the respective frequencies. Since *W*^{2} represents the
kinetic energy (K.E) *E*_{R} of large eddy
The constant *H* is proportional
to K. E. (kinetic energy) per cycle/sec of turbulent eddy. *H* is
therefore equivalent to *Planck*’s constant for microscopic quantum
systems. A nested (hierarchical) continuum of progressively increasing
eddy circulations are generated starting from persistent primary small-scale
fluctuations.

Expressing Eq.1 in terms of the
periods *T = 2**pR/W*
and *t = 2**pr/w*_{*}
for a given primary dominant turbulent
eddy of radius *r* and period *t*. The eddy circulations therefore
follow laws analogous to *Kepler*’s third law of planetary motion.
The centrifugal force *F*_{R} of large eddy obtained from
Eq.1 as
*F*_{R}
= *W*^{2}/*R* »*1/R*^{2}
for a given primary dominant turbulent eddy. The hierarchical eddy continuum
generated from a given primary dominant eddy fluctuation has centrifugal
forces which follow the inverse square law form analogous to *Newton*’s
inverse square law for gravitation. The model concepts therefore predict
quantumlike mechanical laws concomitant with inverse square law for centrifugal
forces, which represent eddy inertial masses equivalent to gravitational
masses.