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 and nevertheless produce very much higher turbulence intensities u ′ /U and Reynolds numbers Re λ 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 & Vassilicos [15]. We introduce the wake-interaction length-scale x * and show that the peak of turbulence intensity demarcating these two regions along the centreline is positioned at about 0.5x * . The streamwise evolutions on the centreline 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 & Vassilicos [31] that the ratio of the integral length-scale L u to the Taylor microscale λ remains constant even though the Reynolds number Re λ decreases during turbulence decay in the region beyond 0.5x * . As a result the scaling L u /λ ∼ Re 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. This extraordinary decoupling is consistent with a non-cascading and instead self-preserving single-length scale type of decaying homogeneous turbulence proposed by George & Wang [12], but we also show that L u /λ is nevertheless an increasing function of the inlet Reynolds number Re 0 . Finally, we offer a detailed comparison of the main assumption and consequences of the George & Wang theory against our fractal-generated turbulence data.

The structure of turbulent flames in fractal- and regular-grid-generated turbulence

“…These observations are similar to those obtained in previous wind tunnel experiments [3][4][5] for much larger grids.…”

“…N-1 denotes the overall number of iterations. Other references such as [3] or [4] use slightly different approximations of Eq. 1 for calculating the blockage ratio and vary in the degree of accuracy obtained.…”

“…The existence of the distinct turbulence production region of fractal grids can be explained by their fractal, or multi-scale, geometry [4]. In the case of fractal grids, various length scales are excited at the same time, producing wakes of different widths as shown schematically in Fig.…”

“…Vassilicos et al [3][4][5][6] proposed fractal grids as a new type of low blockage turbulence generators with a number of potential applications [7][8][9][10][11][12][13][14]. Fractal grids consist of structures with multiple length scales rather than one length scale.…”

On the Formation Mechanisms of Artificially Generated High Reynolds Number Turbulent Boundary Layers

“…In these conditions, the incoming freestream turbulence level is 0.05%; the same wind tunnel has been broadly documented before e.g. Mazellier and Vassilicos (2010) or Valente and Vassilicos (2014).…”