Abstract Most of the k − e closures for modeling stratified surface layer are derived from the classical similarity functions and might fail in complex terrain due to limitations of the classical similarity functions. Despite the classical similarity functions to limit the flux Richardson number R f , we present new similarity functions estimated from field measurement in full range of R f and propose a k − e model using the new similarity functions to improve predictions of stratified surface layer flows in complex terrain. Measurements show that the classical similarity functions are partially valid in complex terrain and the wind shear under strongly stable conditions is constrained at large R f . According to numerical studies in two areas of complex terrain, models using the classical similarity functions and the new similarity functions both present good predictions of convective airflows in complex terrain. The new similarity functions are shown to significantly improve the k − e model in predicting stably stratified airflows in complex terrain by constraining the wind shear at large R f , while the classical similarity functions without limiting the wind shear lead to significantly misestimating the wind speedup factor under stable conditions. Using the proposed model to predict flows in wind farm could benefit wind resource estimation and wind power forecasting.

中文翻译：

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用于预测复杂地形中分层大气表层流的相似函数和新的 k-ε 闭包

摘要 用于分层地表层建模的 k − e 闭包大多来自经典相似函数，由于经典相似函数的局限性，在复杂地形中可能会失效。尽管使用经典相似函数来限制通量理查森数 R f ，但我们提出了从整个 R f 范围内的现场测量估计的新相似函数，并提出了使用新相似函数的 ak - e 模型，以改进复杂地表层流的预测地形。测量表明，经典相似函数在复杂地形中部分有效，强稳定条件下的风切变被限制在大 R f 。根据两个复杂地形区的数值研究，使用经典相似函数和新相似函数的模型都可以很好地预测复杂地形中的对流气流。新的相似函数通过在大 R f 下限制风切变，显着改善 k − e 模型在复杂地形中预测稳定分层气流，而没有限制风切变的经典相似函数导致对风速加速因子的严重错误估计在稳定的条件下。使用所提出的模型来预测风电场中的流量可以有益于风资源估计和风功率预测。新的相似函数通过在大 R f 下限制风切变，显着改善 k − e 模型在复杂地形中预测稳定分层气流，而没有限制风切变的经典相似函数导致对风速加速因子的严重错误估计在稳定的条件下。使用所提出的模型来预测风电场中的流量可以有益于风资源估计和风功率预测。新的相似函数通过在大 R f 下限制风切变，显着改善 k − e 模型在复杂地形中预测稳定分层气流，而没有限制风切变的经典相似函数导致对风速加速因子的严重错误估计在稳定的条件下。使用所提出的模型来预测风电场中的流量可以有益于风资源估计和风功率预测。