Kubo combinatorics for turbulence scaling laws

We present an extension to Kolmogorov–Obukhov refined similarity hypotheses for universal fully-developed turbulence. The extension is applied within Z. She and E. Leveque’s multifractal model of inertial range scaling and its generalizations. Our development has relevance to universal fully developed turbulence, a state we describe explicitly under the additional assumptions of the Kolmogorov–Obukhov similarity hypotheses in terms of the coupling between velocity fluctuations and averaged energy dissipation at all orders. This description is unique and leads to a reparametrization of the She–Leveque model that preserves its original forecasts and is infinitely divisible.