Wall scaling laws for a high-Reynolds-number turbulent pipe flow at Re=3008

Abstract

A direct numerical simulation of turbulent pipe flow is performed at Ret = 3008 with a long streamwise domain length (30R) to investigate wall scaling laws in the physical and wavenumber spaces. The power law follows the streamwise mean velocity in the overlap region, y+ = 90-300, evaluated by the power law indicator function. The scale-separated Reynolds shear stress shows that the largescale motions (Λx + > 3000) are more responsible to construct the constant-stress layer than the small-scale motions (Λx + > 3000), and thus it is proposed that the large-scale motions more contribute to the growth of the mean velocity in the overlap region than the small-scale motions. In the premultiplied energy spectra of the streamwise velocity fluctuations, the κx -1 region ssociates with the attached eddies appeared in Λx;/R = 2-5 at y+ =90-300 with the bimodal distribution. Linear growth of small-scale energies to large-scale energies helps to appear the κx -1 region at high Reynolds number.