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A direct numerical simulation of incompressible channel flow at $Re_\tau$ =5186 has been performed, and the flow exhibits a number of the characteristicsof high Reynolds number wall-bounded turbulent flows. For example, a regionwhere the mean velocity has a logarithmic variation is observed, with vonKarman constant $\kappa = 0.384 \pm 0.004$. There is also a logarithmicdependence of the variance of the spanwise velocity component, though not thestreamwise component. A distinct separation of scales exists between the largeouter-layer structures and small inner-layer structures. At intermediatedistances from the wall, the one-dimensional spectrum of the streamwisevelocity fluctuation in both the streamwise and spanwise directions exhibits$k^{-1}$ dependence over a short range in $k$. Further, consistent withprevious experimental observations, when these spectra are multiplied by $k$(premultiplied spectra), they have a bi-modal structure with local peakslocated at wavenumbers on either side of the $k^{-1}$ range.

Direct numerical simulation of turbulent channel flow up to $Re_\tau \approx 5200$