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 devel-oped 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.(c) 2022 Elsevier B.V. All rights reserved.