A Comprehensive Analysis of the Relation between Intermittency and Dissipation in Non-Homogeneous Turbulent Flows

Abstract

A recent study of various turbulent flows showed that intermittency and dissipation exhibit consistent scaling behavior beyond homogeneous isotropic turbulence (HIT). For turbulent wakes, grid turbulence, and a turbulent jet, the dissipation parameter $C_\varepsilon$ and intermittency parameter $μ$ vary while their product remains constant, independently of the Reynolds number $Re_λ$. Here, we extend this result from centerline hot-wire measurements to non-centerline data, including regions with significant shear. We identify two additional relations: $(γ-1)C_\varepsilon$ remains constant, where $γ$ is the absolute inertial-range spectral slope, and $γ$ varies linearly with the Kolmogorov parameter $C_k$. The main constraint is that the large-scale increment probability density function is Gaussian, indicating random large-scale driving. These relations reduce the varying quantities $C_\varepsilon$, $μ$, $γ$, and $C_k$ to three constants and define a turbulence state that can be characterized by any one of these parameters, independently of shear, flow type, or Reynolds number. We further show that, for a given flow configuration, $C_\varepsilon$ depends on $Re_λ$ and turbulence intensity $TI$. Because the four parameters vary over broad ranges around their nominal HIT values, we interpret this framework as a generalization of HIT to inhomogeneous turbulence. Extensive robustness tests show that the results are insensitive to the specific post-processing method. We also analyze their streamwise and spatial evolution and show that a measured $C_\varepsilon$ can be used to predict $μ$, $γ$, and $C_k$ within quantified uncertainty. The framework thus links key leading-order features of turbulence while recovering established HIT trends.