Singularities in multifractal turbulence dissipation networks and their degeneration

We suggest that large-scale turbulence dissipation is concentrated along caustic networks (that appear due to vortex sheet instability in three-dimensional space), leading to an effective fractal dimension Deff = 5/3 of the networl backbone (without caustic singularities) and a turbulence intermittency exponent μ = 1/6. If there are singularities on these caustic networks then Deff < 5/3 and μ > 1/6. It is shown (using the theory of caustic singularities) that the strongest (however, stable on the backbone) singularities lead to Deff = 4/3 (an elastic backbone) and to μ = 1/3. Thus, there is a restriction of the network fractal variability: 4/3 < Deff < 5/3, and consequently: 1/6 < μ < 1/3. Degeneration of these networks into a system of smooth vortex filaments: Deff = 1, leads to μ = 1/2. After degeneration, the strongest singularities of the dissipation field, , lose their power-law form, while the smoother field In takes it. It is shown (using the method of multifractal asymptotics) that the probability distribution of the dissipation changes its form from exponential-like to log-normal-like with this degeneration, and that the multifractal asymptote of the field In is related to the multifractal asymptote of the energy field.