Refined similarity hypothesis using 3D local averages

TL;DR

This paper tests Kolmogorov's refined similarity hypotheses in 3D turbulence data from high-resolution simulations, revealing universality in the inertial range and local Reynolds number dependence in the dissipation range.

Contribution

The study employs 3D averages from direct numerical simulations to validate the refined similarity hypotheses, providing new insights into turbulence intermittency.

Findings

V is universal in the inertial subrange

V's statistics depend on local Reynolds number in the dissipation range

High-resolution 3D data supports refined similarity hypotheses

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 $R_\lambda \sim 650$, 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.