Intermittency of turbulent velocity and scalar fields using three-dimensional local averaging

An efficient approach for extracting three-dimensional 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 θ in the presence of a uniform mean gradient. The Taylor-scale Reynolds number Rλ goes up to 1300, and the Schmidt number Sc up to 512 (albeit at smaller Rλ). The intermittency exponent of the energy dissipation rate is μ≈0.23±0.02, whereas that of enstrophy is slightly larger; trends with Rλ suggest that this will be the case even at extremely large Rλ. The intermittency exponent of the scalar dissipation rate is μθ≈0.35 for Sc=1. These findings are in essential agreement with previously reported results in the literature. We additionally obtain results for high Schmidt numbers and show that μθ decreases monotonically with Sc, either as 1/logSc or a weak power law, suggesting that μθ→0 as Sc→∞, reaffirming recent results on the breakdown of scalar dissipation anomaly in this limit.