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 ${\mathrm{\epsilon }}_{\mathit{l}}$ coarse-grained at inertial-range scale l. These moment ratios ${\mathrm{\epsilon }}_{\mathit{l}}^{\left(\mathit{p}\right)}$=〈${\mathrm{\epsilon }}_{\mathit{l}}^{\mathit{p}+1\mathrm{}}$〉/〈${\mathrm{\epsilon }}_{\mathit{l}}^{\mathit{p}}$〉(p=0, 1, 2,...,) form a hierarchy of structures. The most singular structures ${\mathrm{\epsilon }}_{\mathit{l}}^{\left(\mathrm{\infty }\right)}$ are assumed to be filaments, and it is argued that ${\mathrm{\epsilon }}_{\mathit{l}}^{\left(\mathrm{\infty }\right)}$∼${\mathit{l}}^{\mathrm{-}2/3}$. Furthermore, a universal relation between scalings of successive structures is postulated, which leads to a prediction of the entire set of the scaling exponents: 〈${\mathrm{\epsilon }}_{\mathit{l}}^{\mathit{p}}$〉∼${\mathit{l}}_{\mathit{p}}^{\mathrm{\tau }}$, ${\mathrm{\tau }}_{\mathit{p}}$=-2/3p+2[1-( 2) / 3 ${)}^{\mathit{p}}$] and 〈δ${\mathit{v}}_{\mathit{l}}^{\mathit{p}}$〉∼${\mathit{l}}_{\mathit{p}}^{\mathrm{\zeta }}$, ${\mathrm{\zeta }}_{\mathit{p}}$=p/9+2[1-(2/3${)}^{\mathit{p}/3\mathrm{}}$].