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 funnellike 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.