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

Refined similarity hypothesis using 3D local averages