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 εl coarse-grained at inertial-range scale l. These moment ratios ε(p)l=〈εp+1l〉/〈εpl〉(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: 〈εpl〉∼lτp, τp=-2/3p+2[1-( 2) / 3 )p] and 〈δvpl〉∼lζp, ζp=p/9+2[1-(2/3)p/3].
Zhen-Su She and Emmanuel Leveque
Phys. Rev. Lett. 72, 336 – Published 17 January 1994