General Systems Theory Concepts in Atmospheric Flows - Rain Formation in Warm Clouds: General Systems Theory - page 3

Fig. 1.1 Graphic depiction of fractals generated using the Julia set algorithm, the simplest case
for a chaotic attractor. The beautiful complex patterns of fractals generated by simple iterative
computations consists of a hierarchy of self-similar structures, i.e., the large scale is a magnified
version of the small scale

concentration and the mean volume radius (or diameter) of the particulate size spec-
trum. Knowledge of the mean volume radius and total number concentration is suf-
ficient to compute the total particulate size spectrum at any location. In summary,
the model predictions are (i) fractal fluctuations can be resolved into an overall loga-
rithmic spiral trajectory with the quasiperiodic Penrose tiling pattern for the internal
structure. (ii) The probability distribution of fractal space-time fluctuations repre-
sents the power (variance) spectrum for fractal fluctuations and follows universal in-
verse power law form incorporating the golden mean. Such a result that the additive
amplitudes of eddies when squared represent probability distribution is observed in
the subatomic dynamics of quantum systems such as the electron or photon. There-
fore, the irregular or unpredictable fractal fluctuations exhibit quantum-like chaos.
(iii) Atmospheric aerosols are held in suspension by the vertical velocity distribution
(spectrum). The normalized atmospheric aerosol size spectrum is derived in terms of
the universal inverse power law characterizing atmospheric eddy energy spectrum.
The complete theory relating to the formation of warm cumulus clouds and their
responses to the hygroscopic particle seeding are presented. It is shown that warm
rain formation can occur within a time period of 30 min as observed in practice.
Traditional cloud physical concepts for rain development require over an hour for a
full-sized raindrop to form (McGraw and Liu 2003 ). A review of droplet growth in
warm clouds has been given by Devenish et al. ( 2012 ).

1.2 Current Concepts in Meteorological Theory

and Limitations

The nonequilibrium system of atmospheric flows is modeled with assumption of
local thermodynamic equilibrium up to the stratopause at 50 km; molecular motion
of atmospheric component gases is implicitly embodied in the gas constant (Tuck
2010 ). Nonequilibrium systems can be studied numerically, but despite decades