  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.
