We introduce an analytical model that describes the vertical structure of Ekman boundary layer flows coupled to the Monin-Obukhov Similarity Theory (MOST) surface layer representation, which is valid for conventionally neutral (CNBL) and stable (SBL) atmospheric conditions. The model is based on a self-similar profile of horizontal stress for both CNBL and SBL flows that merges the classic 3/2 power law profile with a MOST-consistent stress profile in the surface layer. The velocity profiles are then obtained from the Ekman momentum balance equation. The same stress model is used to derive a new self-consistent Geostrophic Drag Law (GDL). We determine the ABL height (h) using an equilibrium boundary layer height model and parameterize the surface heat flux for quasi-steady SBL flows as a function of a prescribed surface temperature cooling rate. The ABL height and GDL equations can then be solved together to obtain the friction velocity \((u_*)\) and the cross-isobaric angle (\(\alpha _0\)) as a function of known input parameters such as the Geostrophic wind speed and surface roughness \((z_0)\). We show that the model predictions agree well with simulation data from the literature and newly generated Large Eddy Simulations (LES). These results indicate that the proposed model provides an efficient and relatively accurate self-consistent approach for predicting the mean wind velocity distribution in CNBL and SBL flows.

我们引入了一种分析模型，该模型描述了与莫宁-奥布霍夫相似理论（MOST）表层表示耦合的埃克曼边界层流的垂直结构，该模型对于常规中性（CNBL）和稳定（SBL）大气条件有效。该模型基于 CNBL 和 SBL 流的水平应力自相似分布，将经典的 3/2 幂律分布与表层最一致的应力分布相结合。然后从 Ekman 动量平衡方程获得速度分布。相同的应力模型用于推导新的自洽地转阻力定律 (GDL)。我们使用平衡边界层高度模型确定 ABL 高度 ( h )，并将准稳态 SBL 流的表面热通量参数化为指定表面温度冷却速率的函数。然后，ABL 高度和 GDL 方程可以一起求解，以获得摩擦速度\((u_*)\)和交叉等压角 ( \(\alpha _0\) )，作为已知输入参数（例如地转参数）的函数风速和表面粗糙度\((z_0)\)。我们表明，模型预测与文献和新生成的大涡模拟 (LES) 中的模拟数据非常吻合。这些结果表明，所提出的模型为预测 CNBL 和 SBL 流中的平均风速分布提供了一种有效且相对准确的自洽方法。