Kubo Combinatorics for Turbulence Scaling Laws

TL;DR

This paper extends Kolmogorov's similarity hypothesis within a multifractal framework to better model turbulence, ensuring infinite divisibility and aligning with the energy cascade concept.

Contribution

It introduces a modified turbulence scaling law that bridges the gap between continuum cascade models and multifractal theories, preserving predictive accuracy.

Findings

Reparametrized She-Leveque model maintains original forecasts.

Ensures infinite divisibility in turbulence scaling laws.

Provides a unified description of energy dissipation and velocity fluctuations.

Abstract

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.