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*4. Cell Dynamical System Model for Fluid Flows*

In summary (Mary Selvam,1990,1993a,b,1994,1997;Mary Selvam et al.,1992, 1996;Mary Selvam,Joshi and Vijayakumar,1994;Mary Selvam,Pethkar and Kulkarni,1995;Mary Selvam and Radhamani,1994,1995;Mary Selvam and Joshi 1995 References ), spatial integration of enclosed turbulent fluctuations give rise to large eddy circulations in fluid flows. Therefore, starting with turbulence scale fluctuations, progressively larger scale eddy fluctuations can be generated by integrating circulation structures at different scale ranges. Such a concept envisages only the magnitude (intensity) of the fluctuations and is independent of the properties of the medium in which the fluctuations are generated. Also, selfsimilar space-time growth structure is implicit to hierarchical growth process, i.e. the large scale structure is the envelope of enclosed small scale structure . Successively larger scale structures form a hierarchical network and function as a unified whole.

Such a concept, leads as a natural consequence, to the result that the successive values of the radii and the root mean square (r.m.s.) eddy circulation speed follow the Fibonacci mathematical series(see Section 2.4). The overall envelope of the large eddy traces a logarithmic spiral with the quasiperiodic Penrose tiling pattern for the internal structure (Figure 6 Fivefold and Spiral Symmetry Associated with Fibonacci Sequence). Atmospheric circulation structure therefore consists of a nested continuum of vortex roll circulations (vortices within vortices) with a two-way ordered energy flow between the larger and smaller scales. Such a concept is in agreement with the observed long-range spatiotemporal correlations in atmospheric flow patterns.

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