| This study has developed techniques for analyzing the scale-by-scale decrease in anisotropy with increasingly smaller length scales in turbulent flows, and applied these to study the effect of the mean shear rate S* on the approach to isotropy in homogeneous uniformly-sheared turbulent flow. Data used for this study is from direct numerical simulations (DNS) of homogeneous, uniformly-sheared turbulence for mean shear rates 0 ≤ S* ≤ 4.5 are provided by Schumacher (2004). Anisotropy metrics are here for the first time computed separately for the velocity fluctuations associated with each scale k in Fourier or wavelet decompositions of the global velocity fields. Results are presented for the Reynolds stress anisotropy norms |bij(k)| and |B2D(kx, kz), normalized velocity derivative moments of ∂u/∂ y, and multifractal scale-similarity norms L 1(r). To deal with the apparent anisotropy, this study has used synthetically-generated realizations of isotropic white-noise fields to characterize the local isotropy level present at each wavenumber, and has used a spatial windowing technique to maintain the number of effectively independent structures in the sample constant at all scales. Results for the | bij(k)| norm for all four S* cases show an increasing level of anisotropy at the high wavenumbers, regardless of the level of statistical uncertainty in the scale-by-scale anisotropy assessment, with the corresponding scale-by-scale anisotropy metrics based on wavelet decompositions showing largely similar features as do those from Fourier decompositions. At lower wavenumbers, the anisotropy results for the four shear rates rapidly converge to match the minimum statistical uncertainty determined by corresponding values for guaranteed-isotropic white-noise data having the same sample size. Overall, there is no clear evidence of any shear rate dependence in the anisotropy metrics considered herein. The |B2D(k x,kz)| maps show the anisotropy aligned with the directions of the spatial grid, regardless of shear rate S*. This observed anisotropy may be the result of a numerically-induced effect similar to that shown by Kumar to result from conventional finite-differencing methods, or may be associated with the construction of velocity fields on the grid in the spatial domain from the Fourier modes in the pseudospectral code. |
