Direct assessment of Kolmogorov's first refined similarity hypothesis

Abstract

Using volumetric velocity data from a turbulent laboratory water flow and numerical simulations of homogeneous, isotropic turbulence, we present a direct experimental and numerical assessment of Kolmogorov's first refined similarity hypothesis based on three-dimensional measurements of the local energy dissipation rate ${\epsilon }_r$ measured at dissipative scales $r$. We focus on the properties of the stochastic variables $V_L=\Delta u(r)/(r{\epsilon }_r{)}^{1/3}$ and $V_T=\Delta v(r)/(r{\epsilon }_r{)}^{1/3}$, where $\Delta u(r)$ and $\Delta v(r)$ are longitudinal and transverse velocity increments. Over one order of magnitude of scales $r$ within the dissipative range, the distributions of $V_L$ and $V_T$ from both experiment and simulation collapse when parameterised by a suitably defined local Reynolds number, providing the first conclusive experimental evidence in support of the first refined similarity hypothesis and its universality.

arXiv commentAs published in PRFluids, 5 pages, 2 figures

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