Intermittency of turbulent velocity and scalar fields using 3D local averaging

TL;DR

This paper introduces an efficient method for analyzing 3D local averages in turbulence simulations to study intermittency, revealing how scalar dissipation intermittency decreases with increasing Schmidt number, impacting turbulence modeling.

Contribution

It proposes a novel approach for extracting 3D local averages in spherical subdomains and applies it to analyze intermittency in turbulence, extending understanding at high Reynolds and Schmidt numbers.

Findings

Intermittency exponent of energy dissipation is approximately 0.23.

Intermittency exponent of scalar dissipation decreases with increasing Schmidt number.

Scalar dissipation intermittency tends to zero as Schmidt number approaches infinity.

Abstract

An efficient approach for extracting 3D local averages in spherical subdomains is proposed and applied to study the intermittency of small-scale velocity and scalar fields in direct numerical simulations of isotropic turbulence. We focus on the inertial-range scaling exponents of locally averaged energy dissipation rate, enstrophy and scalar dissipation rate corresponding to the mixing of a passive scalar $\theta$ in the presence of a uniform mean gradient. The Taylor-scale Reynolds number $R_\lambda$ goes up to $1300$, and the Schmidt number $Sc$ up to $512$ (albeit at smaller $R_\lambda$). The intermittency exponent of the energy dissipation rate is $\mu \approx 0.23$, whereas that of enstrophy is slightly larger; trends with $R_\lambda$ suggest that this will be the case even at extremely large $R_\lambda$. The intermittency exponent of the scalar dissipation rate is $\mu_\theta \approx 0.35$ for $Sc=1$. These findings are in essential agreement with previously reported results in the literature. We further show that $\mu_\theta$ decreases monotonically with increasing $Sc$, either as $1/\log Sc$ or a weak power law, suggesting that $\mu_\theta \to 0$ as $Sc \to \infty$, reaffirming recent results on the breakdown of scalar dissipation anomaly in this limit.