Networks and multifractal asymptotics in turbulence

Generalized dimensions, D±∞, of turbulent energy dissipation and enstrophy fields are theoretically calculated using effective fractal dimensions of corresponding networks. Good correspondence to laboratory and astrophysical experiments is established for non-singular networks. Results for singular networks are comprised with a multifractal analysis of recent laboratory data and a direct numerical simulation. A relation of the results obtained for turbulent percolation is also briefly discussed.