  The refined similarity hypotheses of Kolmogorov, regarded as an important
ingredient of intermittent turbulence, has been tested in the past using
one-dimensional data and plausible surrogates of energy dissipation. We employ
data from direct numerical simulations, at the microscale Reynolds number
$R_\lambda \sim 650$, on a periodic box of $4096^3$ grid points to test the
hypotheses using 3D averages. In particular, we study the small-scale
properties of the stochastic variable $V = \Delta u(r)/(r \epsilon_r)^{1/3}$,
where $\Delta u(r)$ is the longitudinal velocity increment and $\epsilon_r$ is
the dissipation rate averaged over a three-dimensional volume of linear size
$r$. We show that $V$ is universal in the inertial subrange. In the dissipation
range, the statistics of $V$ are shown to depend solely on a local Reynolds
number.
