Townsend (1956) has investigated the structure and dynamics of large eddy formations in turbulent shear flows and has shown that large eddies of appreciable intensity form as a chance configuration of the turbulent motion as illustrated in the following example. Consider a large eddy of radius

(1)

The above equation can
be applied directly to derive the r.m.s. circulation speed Therefore, considering turbulence scale yardsticks for length and time, large eddy growth occurs in discrete unit length steps during unit intervals of time and is analogous to 'cellular automata' (Hayot, 1987) computational technique where microscopic domain processes simulate successfully the macroscale flows with simple no scale (scale invariant) analytic equations. The above concept of deterministic chaos is also a 'randomly exact' method of determination of macroscale flow characteristics which is conceived of as a space-time integrated mean of all inherent non-trivial microscopic domain dynamical processes and is therefore scale invariant.

The physics of deterministic chaos therefore enables to identify turbulence as topology dependent and intrinsic to boundary layer flows, the temperature inversion and wind shear being manifestations of large eddy growth from turbulent energy generation processes. This concept is in direct contrast to the conventional view that inversion layers act as atmospheric lids suppressing convective activity and that boundary layer turbulence, e.g. Clear Air Turbulence (CAT) is generated by wind shear in inversion layers, the index of such shear produced turbulence being measured by the Richardson number (Holton, 1979).

(2)

where (3)

(4)

The sun is the main source
of energy which drives the ABL circulations and therefore periodicities
in the weather patterns may finally be related to solar energy input cycles
as shown in the following (1) 40-50 day oscillations in the atmospheric
general circulation and also the ENSO (~5 years) phenomena may result from
the diurnal cycle of solar radiation (1dayx40~40-50 days and 1dayx40x40~
5years) (2) the QBO may result from the semi-diurnal pressure oscillation
(12 hoursx40x40~2 years) (3) the 22 year oscillation in weather patterns
may result from the 5 minute oscillations of the sun's atmosphere (5minsx40A continuous periodogram analysis of high resolution surface pressure values may be used to determine the amplitude and phase of these semi-permanent atmospheric cycles at different locations. Eddy energy enhancement at any scale, for e.g. the CO

The deterministic chaos model envisages the ABL flow to consist of a web of closed logarithmic spiral circulations anchored to the earth's surface as a unified whole single extended object and having visible manifestation in cloud formation in the troposphere. The atmospheric circulation pattern consisting of dominant eddies at decadic scale range intervals is analogous to (1) the superstrings of a 10-dimensional (

The fractal dimension

The particles in the region of chaos follow laws analogous to Kepler's third law of planetary motion as shown in the following. The periods

The rising large eddy gets progressively diluted by vertical mixing due to turbulent eddy fluctuations and a fraction

and may be written as

where

The physical concept of large eddy growth by the period doubling process enables to derive the universal constants

From Eq.(1) the function

(5)

(6)

Therefore or from
Eqs.(5) and (6). The above equation relating the universal constants is
a statement of the law of conservation of energy, i.e. the period doubling
growth process generates a threefold increase in the spin angular momentum
of the resulting large eddy and propagates outward as the total large eddy
energy flux in the medium. In an earlier section (Section 7) it was shown
that the spin angular momentum of the resulting large eddy accounts for
the observed value of three for the moment coefficient of kurtosis of the
normal distribution. The property of inertia enables propagation of turbulence
scale perturbation in the medium by release of the latent energy potential
of the medium. An illustrative example is the buoyant energy generation
by water vapour condensation in the updraft regions in the ABL.
The universal Feigenbaum's constants

Since large eddy growth involves increase in radius simultaneous with angular displacement from origin, the trajectory of airflow associated with the large eddies will follow a logarithmic spiral pattern both in the horizontal and vertical. The complete eddy circulation consisting of the ascent and the return descent airflow therefore occurs in the form of logarithmic spiral vortices. The full continuum of atmospheric eddies exist as a unified whole in the form of vortices within vortices as displayed in the extreme cases of the tornado funnel and the dust devil. Large eddy growth is initiated at a single point location and growth occurs in a spiral wave form analogous to the self-organized Belousov-Zabotinsky (Ananthakrishnan, 1986) reaction in chemical systems. In the following, quantitative relations are derived for cloud parameters as simple analytic equations from considerations of the microscopic scale dynamics. The angular rotation and the associated incremental radial growth per second at any location (

The deterministic chaos model enables universal no scale (scale invariant) quantification of the steady state cloud dynamical, microphysical and electrical processes (Mary Selvam and Murty, 1985) as listed in the following. (1) The ratio of the actual cloud liquid water content (