*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.