Refined similarity hypothesis using three-dimensional local averages

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 Rλ∼650, on a periodic box of 40963 grid points to test the hypotheses using three-dimensional averages. In particular, we study the small-scale properties of the stochastic variable V=Δu(r)/(rεr)1/3, where Δu(r) is the longitudinal velocity increment and εr 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.