The general topic of practical modelling of roughness in turbulent flow is discussed. Double averaging is a useful framework, but most models cannot be construed as term-by-term closures to the double averaged equations. Double averaging justifies a drag representation. Drag models are effective for both Reynolds averaged and eddy resolving simulation. Boundary condition models are primarily viable for Reynolds averaged closure. Those models are calibrated with the Hama roughness function for the log-law. But a perplexing observation is that the VonKarman constant depends on roughness height.

中文翻译：

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湍流中粗糙度建模的思考

讨论了湍流中粗糙度实际建模的一般主题。双平均是一个有用的框架，但大多数模型不能解释为双平均方程的逐项闭合。双重平均证明了阻力表示。阻力模型对雷诺平均和涡流解析模拟均有效。边界条件模型主要适用于雷诺平均闭合。这些模型使用对数定律的 Hama 粗糙度函数进行校准。但令人费解的是，冯卡门常数取决于粗糙度高度。