CHAOS, QUANTUMLIKE MECHANICS AND NON-LOCALITY IN ATMOSPHERIC FLOWS

A. M. Selvam

Indian Institute of Tropical Meteorology, Pune 411 008, India

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.

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.

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 W² 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 = 2pR/W and t = 2pr/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 = W²/R »1/R² 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.