A Universal Relation Between Intermittency and Dissipation in Turbulence

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.