Self-organization and fractal dynamics in turbulence

Results of analysis of the field of helicity, obtained in three different turbulent laboratory flows (grid-flow, boundary layer and jet) and a simple helical fracton model has been used in order to provide a quantitative explanation of anomalous turbulent diffusion in the troposphere and in the ocean. It is shown that Kolmogorov turbulence is critical in respect to the localization effects of subregions with large helicity (helical fractons) and it breaks up into helical fractons under the condition D_f≤2, where D_f=2d/d_w is the so called fracton dimension (D is the fractal dimension of the turbulent fractal and D_w is the dimension of random walks on this fractal). For strictly Kolmogorov turbulence D₁=2. We study the internal structure of helical fractons and demonstrate that they are characterized by D_f= 4 3. Finally, we look at the influence of helical fractons on diffusion of a passive scalar in turbulence. It is shown that their influence is manifested in the scaling law for the turbulent diffusivity in the form K≈l ^{8 7} in both three-dimensional and quasi-two-dimensional situations. This (anomalous) law is in a very good agreement with a large number of experimental data of different authors in the troposphere and in the upper ocean.