Log-stable law of energy dissipation as a framework of turbulence intermittency

TL;DR

This paper introduces a new framework for turbulence intermittency based on a stable distribution of the logarithm of energy dissipation, extending Kolmogorov's classical theory to better describe small-scale turbulence fluctuations.

Contribution

It proposes a one-parameter, stable distribution-based model for turbulence intermittency, extending Kolmogorov's 1941 theory to incorporate small-scale fluctuations.

Findings

Derived scaling laws for dissipation rate and velocity differences.

Model aligns with theoretical constraints and observed data.

Provides insight into physics determining the model parameter.

Abstract

To describe the small-scale intermittency of turbulence, a self-similarity is assumed for the probability density function of a logarithm of the rate of energy dissipation smoothed over a length scale among those in the inertial range. The result is an extension of Kolmogorov's classical theory in 1941, i.e., a one-parameter framework where the logarithm obeys some stable distribution. Scaling laws are obtained for the dissipation rate and for the two-point velocity difference. They are consistent with theoretical constraints and with the observed scaling laws. Also discussed is the physics that determines the value of the parameter.