Turbulence without Richardson-Kolmogorov cascade

Nicolas Mazellier; Christos Vassilicos

doi:10.1063/1.3453708

paper

Turbulence without Richardson-Kolmogorov cascade

arXiv:0911.0841 · doi:10.1063/1.3453708

Abstract

We present an experimental investigation of intense turbulence generated by a class of low-blockage space-filling fractal square grids. We confirm the existence of a protacted production region followed by a decaying region, as first reported by Hurst & Vassilicos (Physics of Fluids, 2007). We show that the centerline streamwise variation of most of the statistical properties of the turbulent flow can be scaled by a wake interaction length-scale $x_{*}$ . We also confirm the finding of Seoud and Vassilicos (Physics of Fluids, 2007) that the ratio of the integral length-scale $L_{u}$ to the Taylor micro-scale $λ$ remains constant in the decaying region whereas the Reynolds number $R e_{λ}$ strongly decreases. As a result the scaling $L_{u} / λ \sim R e_{λ}$ which follows from the $u^{' 3} / L_{u}$ scaling of the dissipation rate in boundary-free shear flows and in usual grid-generated turbulence does not hold here. However, we show that the ratio $L_{u} / λ$ is an increasing function of the inlet Reynolds number $R e_{0}$ . This extraordinary decoupling is consistent with a self-preserving single length-scale decaying homogeneous turbulence proposed by George & Wang (Physics of Fluids, 2009) with which our results are compared.

37 pages, 25 figures, submitted to Physics of Fluids, revised version (shortened introduction and conclusion)

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