6. Results and Discussions
The important results of this study (Figures 7 - 10 and Tables1 - 3 ) are discussed in the following.
A majority of spectra follow closely (not exactly) the universal inverse power-law form of the statistical normal distribution (Figures 7 -9) consistent with model predictions( Section 4 ) listed below.
(a) Quantumlike mechanics for atmospheric flows,since the variance or square of the eddy amplitude represents the probability density, a feature exhibited by microscopic quantum systems such as the electron or photon(( Section 4.1 ).
(b) Atmospheric flow dynamics as given by Equation 3 implies universal spectrum for fluctuations and also laws analogous to Kepler's third law for planetary motion(Equation 4). Observed universal spectra therefore imply indirectly that atmospheric flows may follow Kepler's third law of planetary motion.
(c) Universal quantification for self-organized criticality or long-range correlations in the interannual variability of atmospheric flows. Long-range correlations are non-local connections, an inherent feature of quantum systems (Maddox, 1988b;Dewdney et.al.,1988 References).
(d) Multifractal structure for atmospheric temporal fluctuations, i.e. the fluctuations are scaling with the scale factor being different for different time scale ranges.The multifractal structure for temporal fluctuations is quantified terms of the unique statistical normal distribution.
(e) A majority of phase spectra are the same as the variance spectra (Figures 7 - 10) indicating that increments in wavelength and phase are related (( Section 4.2, item d ), i.e. a manifestation of 'Berry's phase' inherent to quantum systems (Berry ,1988;Maddox ,1988b; Kepler et al. 1991;Kepler,1992 References).
(f) A majority of spectra exhibit dominant periodicities (Table 3) close to model predicted(Equation 5 and Section 5) for quasicrystalline structure in atmospheric flows (Figures 5 & 6 Fivefold and Spiral Symmetry Associated with Fibonacci Sequence). Model predicted dominant periodicities closely correspond to those reported for many other meteorological parameters (Burroughs,1992;Terray,1995 References). The periodicities 3.6 and 5.8 years may correspond to the low and high frequency components of ENSO(El Nino - Southern Oscillation) cycle(Philander,1990 References).Quasibiennial and quasi-triennial oscillations in some atmospheric parameters have been reported(Kane,1996).Mukerjee(Mukerjee ,1995 References) has reported formation of quasicrystalline patterns in fluid substrates.