Turbulence without Richardson–Kolmogorov cascade

Abstract

We investigate experimentally wind tunnel turbulence generated by multiscale/fractal grids pertaining to the same class of low-blockage space-filling fractal square grids. These grids are not active but nevertheless produce very much higher turbulence intensities u′/U and Reynolds numbers Reλ than higher blockage regular grids. Our hot wire anemometry confirms the existence of a protracted production region where turbulence intensity grows followed by a decay region where it decreases, as first reported by Hurst and Vassilicos [“Scalings and decay of fractal-generated turbulence,” Phys. Fluids 19, 035103 (2007)]. We introduce the wake-interaction length scale x⋆ and show that the peak of turbulence intensity demarcating these two regions along the centerline is positioned at about 0.5x⋆. The streamwise evolutions on the centerline of the streamwise mean flow and of various statistics of the streamwise fluctuating velocity all scale with x⋆. Mean flow and turbulence intensity profiles are inhomogeneous at streamwise distances from the fractal grid smaller than 0.5x⋆, but appear quite homogeneous beyond 0.5x⋆. The velocity fluctuations are highly non-Gaussian in the production region but approximately Gaussian in the decay region. Our results confirm the finding of Seoud and Vassilicos [“Dissipation and decay of fractal-generated turbulence,” Phys. Fluids 19, 105108 (2007)] that the ratio of the integral length-scale Lu to the Taylor microscale λ remains constant even though the Reynolds number Reλ decreases during turbulence decay in the region beyond 0.5x⋆. As a result, the scaling Lu/λ∼Reλ, which follows from the u′3/Lu scaling of the dissipation rate in boundary-free shear flows and in usual grid-generated turbulence, does not hold here. This extraordinary decoupling is consistent with a noncascading and instead self-preserving single-length scale type of decaying homogeneous turbulence proposed by George and Wang [“The exponential decay of homogeneous turbulence,” Phys. Fluids 21, 025108 (2009)], but we also show that Lu/λ is nevertheless an increasing function of the inlet Reynolds number Re0. Finally, we offer a detailed comparison of the main assumption and consequences of the George and Wang theory against our fractal-generated turbulence data.