Direct numerical simulation of turbulent channel flow up to

TLDR

A direct numerical simulation of incompressible channel flow at Reτ = 5186 was performed to study high‑Reynolds‑number wall‑bounded turbulence. The simulation revealed a logarithmic mean‑velocity region with κ = 0.384 ± 0.004, logarithmic variance of spanwise velocity, clear scale separation between outer and inner layers, a k⁻¹ spectral range for streamwise velocity fluctuations, and bimodal premultiplied spectra with peaks flanking the k⁻¹ range.

Abstract

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.