The shear-stress cospectrum and the horizontal and vertical temperature-flux cospectra in the convective boundary layer (CBL) are predicted using the multi-point Monin–Obukhov similarity (MMO theory). MMO theory was recently proposed and then derived from first principles by Tong and Nguyen (Journal of the Atmospheric Sciences, 2015, Vol. 72, 4337 – 4348) and Tong and Ding (Journal of Fluid Mechanics, 2019, Vol. 864, 640 – 669) to address the issue of the incomplete similarity in the Monin–Obukhov similarity theory. According to MMO theory, the CBL has a two-layer structure: the convective layer (z≫-L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z \gg -L$$\end{document}) and the convective–dynamic layer (z≪-L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z \ll -L$$\end{document}). The former consists of the convective range (k≪-1/L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k \ll -1/L$$\end{document}) and the inertial range (k≫1/z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k \gg 1/z$$\end{document}), while the latter consists of the convective range, the dynamic range (-1/L≪k≪1/z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-1/L \ll k\ll 1/z$$\end{document}), and the inertial range, where z, k, and L are the height from the ground, the horizontal wavenumber, and the Obukhov length, respectively. We use MMO theory to predict the cospectra for the convective range and the dynamic range. They have the same scaling in the convective range for both z≪-L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z \ll -L$$\end{document} and z≫-L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z \gg -L$$\end{document}. The shear-stress cospectrum and the vertical temperature-flux cospectrum have k0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k^0$$\end{document} scaling in both the convective and dynamic ranges. The horizontal temperature-flux cospectrum has k-1/3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k^{-1/3}$$\end{document} and k-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k^{-1}$$\end{document} scaling in the convective and dynamic ranges respectively. The predicted scaling exponents are in general agreement with high-resolution large-eddy-simulation results. However, the horizontal temperature-flux cospectrum is found to change sign from the dynamic range (negative) to the convective range (positive), which is shown to be caused by the temperature–pressure-gradient interaction.

中文翻译：

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对流大气边界层湍流余谱的多点莫宁-奥布霍夫相似度

使用多点 Monin-Obukhov 相似性（MMO 理论）预测对流边界层 (CBL) 中的剪切应力余谱以及水平和垂直温度通量余谱。MMO 理论是最近由 Tong 和 Nguyen（大气科学杂志，2015 年，第 72 卷，第 4337-4348 卷）和通和丁（流体力学杂志，2019 年，第 864 卷，640 669) 来解决 Monin-Obukhov 相似理论中不完全相似的问题。根据MMO理论，CBL有两层结构：动态范围 (-1/L≪k≪1/z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{ mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-1/L \ll k\ll 1/z$$\end{document})，以及惯性范围，其中 z、k 和 L 分别是距地面的高度、水平波数和 Obukhov 长度。我们使用 MMO 理论来预测对流范围和动态范围的余谱。水平温度通量谱有 k-1/3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k^{-1/3}$$\end{document} 和 k-1\documentclass[12pt]{minimal} \ usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ $k^{-1}$$\end{document} 分别在对流和动态范围内缩放。预测的标度指数与高分辨率大涡模拟结果大体一致。然而，