SINGULARITIES IN MULTIFRACTAL TURBULENCE DISSIPATION NETWORKS AND THEIR DEGENERATION

We suggest that large-scale turbulence dissipation is concentrated alo ng caustic networks (that appear due to vortex sheet instability in th ree-dimensional space), leading to an effective fractal dimension D(ef f) = 5/3 of the network backbone (without caustic singularities) and a turbulence intermittency exponent mu = 1/6. If there are singularitie s on these caustic networks then D(eff) < 5/3 and mu > 1/6. It is show n (using the theory of caustic singularities) that the strongest (howe ver, stable on the backbone) singularities lead to D(eff) = 4/3 (an el astic backbone) and to mu = 1/3. Thus, there is a restriction of the n etwork fractal variability: 4/3 < D(eff) < 5/3, and consequently: 1/6 < mu < 1/3. Degeneration of these networks into a system of smooth vor tex filaments: D(eff) = 1, leads to mu = 1/2. After degeneration, the strongest singularities of the dissipation field, epsilon, lose their powerlaw form, while the smoother field 1n epsilon takes it. It is sho wn (using the method of multifractal asymptotics) that the probability distribution of the dissipation changes its form from exponential-lik e to log-normal-like with this degeneration, and that the multifractal asymptote of the field 1n epsilon is related to the multifractal asym ptote of the energy field. Finally, a phenomenon of acceleration of la rge-scale turbulent diffusion of passive scalar by the singularities i s briefly discussed. All results are supported by comparison with expe rimental data obtained by different authors.