A Universal Relation Between Intermittency and Dissipation in Turbulence

TL;DR

This paper uncovers a universal inverse relationship between the intermittency factor and the dissipation constant in various turbulent flows, providing a new empirical link across scales.

Contribution

It establishes a novel empirical relation between intermittency and dissipation in turbulence, validated across diverse flow types using extensive experimental data.

Findings

Intermittency factor $$ is inversely proportional to dissipation constant $C_$.

The relation holds across wakes, grid turbulence, and jets.

Provides a unified view of turbulence scaling laws.

Abstract

Fundamental quantities of turbulent flows, such as the dissipation constant $C_\varepsilon$ and the intermittency factor $\mu$, are examined in relation to each other for a broader class of non-ideal turbulent flows. In the context of the energy cascade, it is known that $C_\varepsilon$ reflects its basic overall properties, while $\mu$ quantifies the intermittency that emerges throughout the cascade. Using an extensive hot-wire dataset of turbulent wakes, grid-generated turbulence, and an axisymmetric jet, we individually analyze these quantities as one-dimensional surrogates of the energy cascade, considering only data that exhibit consistent scaling behavior. We find that $\mu$ is inversely proportional to $C_\varepsilon$, offering a new empirical principle that bridges the gap between large and small scales in arbitrary turbulent flows.