A single-column turbulence model for stratified atmospheric boundary layer (ABL), which solves the transport equations of turbulence probability density function (PDF) using a Lagrangian stochastic modeling (LSM) approach, is proposed in this study. This study adopts previously developed stochastic differential equations (SDEs) for particle velocity and temperature and extends the LSM to simulate inhomogeneous turbulence. The proposed LSM is tested for its ability to fully simulate statistics of inhomogeneous stratified turbulence. In the model, particles evolve by SDEs, and turbulence statistics are calculated by averaging the properties of particles. The model provides a full representation of turbulence PDF and simulates turbulent transport without any modeling assumption. The model performance is evaluated against large-eddy simulation (LES) results in the simulations of convective and stable ABL cases. For the convective ABL, LSM realistically simulates the entrainment process with the temperature and heat flux profiles that closely match with LES. The joint PDF simulated by LSM reproduces a curved and highly skewed shape, and some distinct features, like the asymmetric distribution of vertical velocity and the separation of the PDF in the entrainment zone, are simulated. LSM also reproduces the entrainment enhancement by wind shear in the simulation of sheared convective ABL. The LSM simulation of stable ABL predicts realistic turbulence intensity and mean field profiles, where Gaussian-like PDFs are simulated both in LSM and LES.

本研究提出了分层大气边界层（ABL）的单柱湍流模型，该模型使用拉格朗日随机建模（LSM）方法求解湍流概率密度函数（PDF）的输运方程。本研究采用先前开发的粒子速度和温度随机微分方程 (SDE)，并扩展 LSM 来模拟非均匀湍流。测试了所提出的 LSM 完全模拟非均匀分层湍流统计的能力。在模型中，粒子通过 SDE 演化，并通过平均粒子的属性来计算湍流统计数据。该模型提供了湍流 PDF 的完整表示，并在没有任何建模假设的情况下模拟湍流传输。模型性能根据对流和稳定 ABL 情况模拟中的大涡模拟 (LES) 结果进行评估。对于对流 ABL，LSM 真实地模拟了夹带过程，其温度和热通量分布与 LES 非常匹配。 LSM 模拟的联合 PDF 再现了弯曲且高度倾斜的形状，并且模拟了一些独特的特征，例如垂直速度的不对称分布和夹带区中 PDF 的分离。 LSM 还在剪切对流 ABL 的模拟中再现了风切变的夹带增强作用。稳定 ABL 的 LSM 模拟可预测真实的湍流强度和平均场分布，其中类高斯 PDF 均在 LSM 和 LES 中模拟。