Direct numerical simulation of turbulent channel flow up to Re τ ≈ 5200

A direct numerical simulation of incompressible channel flow at Reτ = 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 κ = 0.384 ± 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 dependence over a short range in k. Further, consistent with previous experimental observations, when these spectra are multiplied by k (premultiplied spectra), they have a bi-modal structure with local peaks located at wavenumbers on either side of the k range.