A computational steady Reynolds-averaged Navier–Stokes model is developed for a neutrally-stratified unidirectional flow in the atmospheric boundary layer (ABL) over generic two-dimensional cosine-shaped hills. Simulations are performed for a hill of a constant height and three different hill slopes. The hill surface is treated as smooth and aerodynamically rough. Atmospheric-boundary-layer inflow profiles for computations of the flow over a hill are generated from the precursor two-dimensional simulations with applied Neumann boundary conditions and an additional body force (wind-source term) introduced into the momentum equation, which value varies with increasing height. This body force ensures the appropriate momentum transport along an empty computational domain and its physical meaning is put in perspective regarding the realistic twisted ABL. The results obtained using the standard constants of the standard k − ε turbulence model are compared to the results obtained using several sets of modified constants of this same turbulence model, to evaluate the influence of the inactive turbulence. The results generally indicate good agreement with the characteristics of strong flow over hills. While the modified turbulence constants yield better results for the ABL flow over flat terrain, the flow characteristics over a hill are more accurate when the standard constants of the standard k − ε turbulence model are used.

中文翻译：

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通用山上的大气边界层：单向体力驱动流的计算模型

为大气边界层 (ABL) 中一般二维余弦形山丘上的中性分层单向流开发了计算稳定雷诺平均 Navier-Stokes 模型。对恒定高度的山丘和三个不同的山坡进行模拟。山丘表面被处理为光滑且空气动力学粗糙。用于计算山上流动的大气边界层流入剖面是从前驱二维模拟生成的，其中应用了诺依曼边界条件和引入动量方程的附加体力（风源项），该值随增加高度。这种体力确保沿着空的计算域进行适当的动量传输，并且其物理意义在现实扭曲的 ABL 中得到了体现。将使用标准 k - ε 湍流模型的标准常数获得的结果与使用同一湍流模型的几组修正常数获得的结果进行比较，以评估非活动湍流的影响。结果普遍表明与强流过山丘的特征吻合良好。虽然修正的湍流常数对平坦地形上的 ABL 流产生更好的结果，但当使用标准 k - ε 湍流模型的标准常数时，山上的流特征更准确。将使用标准 k - ε 湍流模型的标准常数获得的结果与使用同一湍流模型的几组修正常数获得的结果进行比较，以评估非活动湍流的影响。结果普遍表明与强流过山丘的特征吻合良好。虽然修正的湍流常数对平坦地形上的 ABL 流产生更好的结果，但当使用标准 k - ε 湍流模型的标准常数时，山上的流特征更准确。将使用标准 k - ε 湍流模型的标准常数获得的结果与使用同一湍流模型的几组修正常数获得的结果进行比较，以评估非活动湍流的影响。结果普遍表明与强流过山丘的特征吻合良好。虽然修正的湍流常数对平坦地形上的 ABL 流产生更好的结果，但当使用标准 k - ε 湍流模型的标准常数时，山上的流特征更准确。