Journal of Statistical Physics, Vol. 36, Nos. 5/6, 1984, p. 649-663.
We present a qualitative overview of our work on the issue of fractal structures
in turbulence. We explain why fully developed turbulence is not space filling
and describe how its fractal dimension can be estimated theoretically. The
implications of the fractal nature of turbulence on transport processes like
turbulent diffusion and on fluctuations in passive scalars are discussed. The
latter affect wave propagation in turbulent media and these effects are examined.
In addition we consider clouds in the atmosphere which are claimed to have
fractal perimeters (or surfaces) and outline the physical reasons for this
phenomenon. The fractal dimension of clouds is tied to the theory of turbulent
diffusion and is computed theoretically. Indications of the road ahead are given.