General Systems Theory Concepts in Atmospheric Flows - Rain Formation in Warm Clouds: General Systems Theory - page 5

and Hallett 1997 , 1998 ) have applied the systems approach to study cloud droplet
size distributions.
Townsend ( 1956 ) had visualized large eddies as envelopes enclosing turbulent
(smaller scale) eddies. General systems theory for atmospheric flows (Selvam 1990 ,
2005 , 2012a , b , 2013 ; Selvam and Fadnavis 1998 ) visualizes the hierarchical growth
of larger scale eddies from space-time integration of smaller scale eddies resulting
in an atmospheric eddy continuum manifested in the self-similar fractal fluctuations
of meteorological parameters. The basic thermodynamical parameters such as pres-
sure, temperature, etc., are given by the same classical statistical physical formulae
(kinetic theory of gases) for each component eddy (volume) of the atmospheric
eddy continuum. It may be shown that the Boltzmann distribution for molecular
energies also represents the eddy energy distribution in the atmospheric eddy con-
tinuum (Selvam 2011 ). In the following, general systems theory model concepts for
atmospheric flows are summarized with model predictions for atmospheric flows
and cloud growth parameters. Model predictions are compared with observations.
The atmospheric boundary layer (ABL), the layer extending up to about 10 km
above the surface of the earth plays an important role in the formation of weather
systems. It is important to identify and quantify the physical processes in the ABL
for realistic simulation of weather systems of all scales.
The ABL is often organized into helical secondary circulations which are often
referred to as vortex roll or large eddies (Brown 1980 ). It is not known how these
vortex rolls are sustained without decay by the turbulence around them. The author
(Selvam 1990 , 2007 ) has shown that the production of buoyant energy by the mi-
croscale fractional condensation (MFC) in turbulent eddies is responsible for the
sustenance and growth of large eddies. Earlier Eady ( 1950 ) has emphasized the
importance of large-scale turbulence in the maintenance of the general circulation
of the atmosphere.
The nondeterministic model described below incorporates the physics of the
growth of macroscale coherent structures from microscopic domain fluctuations
in atmospheric flows (Selvam 1990 , 2007 , 2013 ). In summary, the mean flow at
the planetary ABL possesses an inherent upward momentum flux of frictional ori-
gin at the planetary surface. This turbulence-scale upward momentum flux is pro-
gressively amplified by the exponential decrease of the atmospheric density with
height coupled with the buoyant energy supply by microscale fractional condensation
on hygroscopic nuclei, even in an unsaturated environment (Pruppacher and Klett
1997 ). The mean large-scale upward momentum flux generates helical vortex-roll
(or large eddy) circulations in the planetary ABL and is manifested as cloud rows and
(or) streets, and mesoscale cloud clusters (MCC) in the global cloud cover pattern.
A conceptual model (Selvam and Fadnavis 1998 , Selvam 1990 , 2005 , 2007 , 2009 ,
2011 , 2012a , b , 2013 ) of large and turbulent eddies in the planetary ABL is shown in
Figs. 1.2 and 1.3 . The mean airflow at the planetary surface carries the signature of
the fine scale features of the planetary surface topography as turbulent fluctuations
with a net upward momentum flux. This persistent upward momentum flux of sur-
face frictional origin generates large-eddy (or vortex-roll) circulations, which carry
upward the turbulent eddies as internal circulations. Progressive upward growth of a