Normal and cross-flow Reynolds stresses: differences between confined and semi-confined flows

Understanding turbulent wall-bounded flows remains an elusive goal. Most turbulent phenomena are non-linear, complex and have broad range of scales that are difficult to completely resolve. Progress is made only in minute steps and enlightening models are rare. Herein, we undertake the effort to bundle several experimental and numerical databases to overcome some of these difficulties and to learn more about the kinematics of turbulent wall-bounded flows. The general scope of the present work is to quantify the characteristics of wall-normal and spanwise Reynolds stresses, which might be different for confined (e.g., pipe) and semi-confined (e.g., boundary layer) flows. In particular, the peak position of wall-normal stress and a shoulder in spanwise stress never described in detail before are investigated using select experimental and direct numerical simulation databases available in the open literature. It is found that the positions of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left\langle {v'{^2} } \right\rangle^{ + } $$\end{document}-peak in confined and semi-confined flow differ significantly above δ+ ≈ 600. A similar behavior is found for the position of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left\langle {u'v'} \right\rangle^{ + } $$\end{document}-peak. The upper end of the logarithmic region seems to be closely related to the position of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left\langle {v'{^2} } \right\rangle^{ + } $$\end{document}-peak. The \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left\langle {w'{^2} } \right\rangle^{ + } $$\end{document}-shoulder is found to be twice as far from the wall than the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left\langle {v'{^2} } \right\rangle^{ + } $$\end{document}-peak. It covers a significantly large portion of the typical zero-pressure-gradient turbulent boundary layer.