Liu Luoqin, Gadde Srinidhi N, Stevens Richard J A M
Physics of Fluids Group, Max Planck Center Twente for Complex Fluid Dynamics, University of Twente, 7500 AE Enschede, Netherlands.
Phys Rev Lett. 2021 Mar 12;126(10):104502. doi: 10.1103/PhysRevLett.126.104502.
Conventionally neutral atmospheric boundary layers (CNBLs), which are characterized with zero surface potential temperature flux and capped by an inversion of potential temperature, are frequently encountered in nature. Therefore, predicting the wind speed profiles of CNBLs is relevant for weather forecasting, climate modeling, and wind energy applications. However, previous attempts to predict the velocity profiles in CNBLs have had limited success due to the complicated interplay between buoyancy, shear, and Coriolis effects. Here, we utilize ideas from the classical Monin-Obukhov similarity theory in combination with a local scaling hypothesis to derive an analytic expression for the stability correction function ψ=-c_{ψ}(z/L)^{1/2}, where c_{ψ}=4.2 is an empirical constant, z is the height above ground, and L is the local Obukhov length based on potential temperature flux at that height, for CNBLs. An analytic expression for this flux is also derived using dimensional analysis and a perturbation method approach. We find that the derived profile agrees excellently with the velocity profile in the entire boundary layer obtained from high-fidelity large eddy simulations of typical CNBLs.
传统中性大气边界层（CNBLs）在自然界中经常出现，其特征是地表位温通量为零，并被位温逆温层所覆盖。因此，预测CNBLs的风速剖面对于天气预报、气候建模和风能应用具有重要意义。然而，由于浮力、切变和科里奥利力效应之间复杂的相互作用，以往预测CNBLs中速度剖面的尝试取得的成功有限。在此，我们利用经典的莫宁-奥布霍夫相似理论的思想，并结合局部尺度假设，推导出了稳定性校正函数ψ = -c_ψ(z/L)^(1/2)的解析表达式，其中c_ψ = 4.2是一个经验常数，z是离地面的高度，L是基于该高度位温通量的局部奥布霍夫长度，适用于CNBLs。还使用量纲分析和微扰方法推导出了该通量的解析表达式。我们发现，推导得到的剖面与通过典型CNBLs的高保真大涡模拟获得的整个边界层中的速度剖面非常吻合。
