Singularities in multifractal turbulence dissipation networks and their degeneration

Abstract

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 D eff = 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 D eff < 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 D eff = 4 3 (an elastic backbone) and to μ = 1 3 . Thus, there is a restriction of the network fractal variability: 4 3 < D eff < 5 3 , and consequently: 1 6 < μ < 1 3 . Degeneration of these networks into a system of smooth vortex filaments: D eff = 1, leads to μ = 1 2 . After degeneration, the strongest singularities of the dissipation field, ε, lose their power-law form, while the smoother field In ε 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 ε is related to the multifractal asymptote of the energy field. Finally, a phenomenon of acceleration of large-scale turbulent diffusion of passive scalar by the singularities is briefly discussed. All results are supported by comparison with experimental data obtained by different authors.