Reynolds number effects in rib-roughened turbulent channel flow

A study involving the direct numerical simulation (DNS) of turbulent rough channel flow at Reynolds number Reτ=180\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Re}_{\tau }=180$$\end{document} is undertaken, to investigate the effects of Reynolds number variation on the various statistical quantities and the near-wall dynamical structures. The definition of Reynolds number predominantly considered in this study, Reτ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Re}_{\tau }$$\end{document}, is based on the wall friction velocity uτ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u_{\tau }$$\end{document} and the half-height of the channel h. The channel walls are roughened by square ribs elongated along the span of the channel. The ribs are arranged at a constant pitch width and in a manner such that the crests face the ones on the opposite wall, i.e., the roughness on the channel is symmetric about the channel centerline. The results obtained from the current DNS are compared with those from two DNSs at a higher Reynolds number of 400, one of them with roughness height k+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k^+$$\end{document} comparable to that in the current DNS and the other with a higher value of k+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k^+$$\end{document}. The mean streamline patterns are contrasting in the presence or absence of the secondary vortex; the effects on the location of a seemingly persistent saddle point are also observed. Variation of the skin friction coefficient over a pitch width has apparently lent support to the observations. A measure of the roughness function is presented. The near-wall structures in terms of the contours of the fluctuating velocity reveal finer scale structures at the higher Reynolds number, when the value of k+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k^+$$\end{document} is also high.