Refined similarity hypothesis using 3D 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 $R_{\lambda }\sim 650$, 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.

References in corpus (2)

• The multifractal nature of turbulent energy dissipation
• Lagrangian Cascade in Three-Dimensional Homogeneous and Isotropic Turbulence

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• Sufficient conditions for local scaling laws for stationary martingale solutions to the 3D Navier-Stokes equations