The importance of wall-normal Reynolds stress in turbulent rough channel flows

Abstract

In this paper, it is demonstrated by DNS of turbulent rough channels that a proportionality between \documentclass[12pt]{minimal}\begin{document}$\widetilde{u}_2^\prime |_w$\end{document}ũ2′|w (the wall-normal Reynolds stress \documentclass[12pt]{minimal}\begin{document}$\widetilde{u}_2^\prime =\langle u_2^{\prime 2} \rangle ^{1/2}$\end{document}ũ2′=⟨u2′2⟩1/2 at the top of the roughness elements) and the roughness function does exist. This observation confirmed by experiments allows the derivation of a simple expression for the velocity profile in the log-region. This parameterization of rough walls through \documentclass[12pt]{minimal}\begin{document}$\widetilde{u}_2^\prime |_w$\end{document}ũ2′|w is suggested by the direct link between wall structures and \documentclass[12pt]{minimal}\begin{document}$\frac{\partial ^2 \widetilde{u_2^{\prime }}^2}{\partial x^2_{2}}$\end{document}∂2u2′̃2∂x22. Identification of the wall structures, near smooth and different kinds of rough surfaces, demonstrates flow isotropization near rough walls, corroborated by profiles of \documentclass[12pt]{minimal}\begin{document}$\frac{\partial ^2 \widetilde{u_2^{\prime }}^2}{\partial x^2_{2}}$\end{document}∂2u2′̃2∂x22, is depicted by visualizations of ∇2p. The relationship between the roughness function and \documentclass[12pt]{minimal}\begin{document}$\widetilde{u}_2^\prime |_w$\end{document}ũ2′|w allows the derivation of a new kind of Moody diagram, useful in the prediction of friction factors of rough flows at high Reynolds numbers.