2.3 Turbulent (Chaotic)
Fluctuations and Selfsimilar Structure Formation
Biological auto-organization and pattern formation
have been studied over the past 40 years as non-equilibrium thermodynamic
phenomena (Turing, 1952 Reference ). The
study of the spontaneous, i.e., self-organized formation of structures
in systems far from thermal equilibrium in open systems belongs to the
multidisciplinary field of synergetics (Haken,1989
Reference
). Formation of structure begins by aggregation of molecules in a turbulent
fluid (gas or liquid) medium. Turbulent fluctuations are therefore not
dissipative, but serve to assemble and form coherent structures (Nicolis
and Prigogine, 1977; Prigogine,1980; Prigogine and Stengers, 1988; Insinnia,
1992 Reference ), for example, the formation
of clouds in turbulent atmospheric flows. Traditionally, turbulence is
considered dissipative and disorganized. Yet, coherent (organized) vortex
roll circulations (vortices) are ubiquitous to turbulent fluid flows (Levich,1987;
Frisch and Orszag,1990 Reference ). The
exact physical mechanism for the formation and maintenance of coherent
structures, namely vortices or large eddy circulations in turbulent fluid
flows is not yet identified. The most intense weather systems such as hurricanes
have vividly spiraling cloud formation while the destructive tornado has
spiraling (vortex) air flow in narrow funnel-like protuberances which reach
down to earth and create devastating damage. Recent studies show that clouds
of all sizes (Tessier et al., 1993 Reference
) are selfsimilar in shape which is consistent with commonly visualized
shape of clouds as billows upon billows. Incidentally, it may be mentioned
that cumulus clouds bear a close resemblance to cauliflowers. Meteorological
text books commonly describe the cumulus clouds to have cauliflowerlike
structure. In the midst of turbulence in air flows, clouds retain their
identity in shape and the most astonishing of all is the formation of ice
crystals with exquisitely symmetrical structure. Nature abounds in symmetrical
structures from the macro- to the microscopic scales (Tarasov, 1986 Reference
). Perfect order appears to underlie apparent chaos in turbulent flows.
Turbulence, namely, seemingly random fluctuations of all scales, therefore,
plays a key role in the formation of selfsimilar coherent structures in
the atmosphere. Such a concept is contrary to the traditional view that
turbulence is dissipative, i.e., ordered growth of coherent form is not
possible in turbulent flows. Mary Selvam (1990 Reference
) and Mary Selvam et al. (1992 Reference
) have shown that turbulent fluctuations self-organize to form selfsimilar
structures in fluid flows. Ramified branching networks serve to connect
and assist in the functioning as a unified whole of selfsimilar fractal
objects. A fractal object can be resolved into smaller interconnected
component parts which resemble the whole in shape. The selfsimilar architecture
for fractal objects serve for collection and distribution of information/energy
between the largest and smallest scales. For example, the river system
collects water from tributaries, the lung architecture enables efficiency
of oxygen absorption from air in the alveoli (the smallest branching structure).
Jean (1994 Reference ) has emphasized
the functional importance of ramified structures underlying selfsimilar
fractals
and gives reference to earlier studies which show that such branching structures
can be organized into hierarchies which incorporate the Fibonacci
mathematical sequence.