Universal scaling laws in fully developed turbulence

The inertial-range scaling laws of fully developed turbulence are described in terms of scalings of a sequence of moment ratios of the energy dissipation field ε_l coarse-grained at inertial-range scale l. These moment ratios ε_l^(p)=〈ε_l^p+1〉/〈ε_l^p〉(p=0, 1, 2,...,) form a hierarchy of structures. The most singular structures ε_l^(∞) are assumed to be filaments, and it is argued that ε_l^(∞)∼l^-2/3. Furthermore, a universal relation between scalings of successive structures is postulated, which leads to a prediction of the entire set of the scaling exponents: 〈ε_l^p〉∼l_p^τ, τ_p=-2/3p+2[1-( 2) / 3 )^p] and 〈δv_l^p〉∼l_p^ζ, ζ_p=p/9+2[1-(2/3)^p/3].