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

TL;DR

This paper presents a direct numerical simulation of turbulent channel flow at a high Reynolds number, revealing key flow characteristics such as logarithmic velocity profiles, scale separation, and spectral features consistent with experimental data.

Contribution

The study provides detailed high-Reynolds-number flow data and confirms the presence of logarithmic regions and spectral behaviors in turbulent channel flow.

Findings

Logarithmic velocity profile with von Karman constant ~0.384

Scale separation between large outer and small inner structures

Spectral analysis shows $k^{-1}$ dependence and bi-modal structure

Abstract

A direct numerical simulation of incompressible channel flow at $Re_\tau$ = 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 Karman constant $\kappa = 0.384 \pm 0.004$. 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 $k$. 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 $k^{-1}$ range.