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Published online by Cambridge University Press: 10 June 2015
A direct numerical simulation of incompressible channel flow at a friction Reynolds number ($\mathit{Re}_{{\it\tau}}$) of 5186 has been performed, and the flow exhibits a number of the characteristics of high-Reynolds-number wall-bounded turbulent flows. For example, a region where the mean velocity has a logarithmic variation is observed, with von Kármán constant
${\it\kappa}=0.384\pm 0.004$. There is also a logarithmic dependence of the variance of the spanwise velocity component, though not the streamwise component. A distinct separation of scales exists between the large outer-layer structures and small inner-layer structures. At intermediate distances from the wall, the one-dimensional spectrum of the streamwise velocity fluctuation in both the streamwise and spanwise directions exhibits
$k^{-1}$ dependence over a short range in wavenumber
$(k)$. Further, consistent with previous experimental observations, when these spectra are multiplied by
$k$ (premultiplied spectra), they have a bimodal structure with local peaks located at wavenumbers on either side of the
$k^{-1}$ range.