Turbulence without Richardson-Kolmogorov cascade

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 $\lambda$ remains constant in the decaying region whereas the Reynolds number $Re_\lambda$ strongly decreases. As a result the scaling $L_{u}/\lambda \sim Re_{\lambda}$ 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 $L_u/\lambda$ is an increasing function of the inlet Reynolds number $Re_0$. 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.