Multi-Point Monin–Obukhov Similarity of Turbulence Cospectra in the Convective Atmospheric Boundary Layer

Abstract

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 ($z \gg -L$) and the convective–dynamic layer ($z \ll -L$). The former consists of the convective range ($k \ll -1/L$) and the inertial range ($k \gg 1/z$), while the latter consists of the convective range, the dynamic range ($-1/L \ll k\ll 1/z$), 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 $z \ll -L$ and $z \gg -L$. The shear-stress cospectrum and the vertical temperature-flux cospectrum have $k^0$ scaling in both the convective and dynamic ranges. The horizontal temperature-flux cospectrum has $k^{-1/3}$ and $k^{-1}$ 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.