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 structures . 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: Fibonacci
Sequence and Selfsimilar Structures ).
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.