  We present an extension to Kolmogorov's refined similarity hypothesis 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 modification rectifies an apparent gap between the
implicit continuum of length scales in Obukhov's conception of a turbulent
energy cascade, and scaling law models derived from Kolmogorov's refined
similarity hypothesis that lack infinite divisibility. The development has
relevance to universal fully developed turbulence, a state we describe
explicitly 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.
