Refined similarity hypothesis using three-dimensional local averages.

Abstract

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(λ)∼650, on a periodic box of 4096(3) 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)/(rε(r))(1/3), where Δu(r) is the longitudinal velocity increment and ε(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.