When canopy flows are horizontally averaged to obtain mean profiles, the averaging operation can be defined either as an intrinsic average, normalized by the variable fluid volume, or as a superficial average, normalized by the total volume including solid canopy elements. Properties of spatial averages have been explored extensively in the context of flow through plant canopies, albeit with the assumption that the solid volume fraction is negligible. Without this simplification, properties relevant for non-linear terms apply to intrinsic averages while properties of gradients apply to superficial averages. To avoid inconsistencies and inaccuracies the impact of a non-negligible solid volume fraction should be considered carefully when interpreting mean profiles, when deriving mathematical relations for averaged quantities, and when introducing modelling assumptions for such terms. On this basis, we review the definitions and properties of the method of volume averaging, as developed in the more general context of flow through porous media, and discuss its application to urban canopy flows. We illustrate the properties of intrinsic and superficial averages and their effect on mean profiles with example data from a simulation of flow over constant-height cubes.

中文翻译：

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城市檐篷的体积平均


当冠层流水平平均以获得平均剖面时，平均操作可以定义为通过可变流体体积归一化的内在平均值，或通过包括固体冠层元素的总体积归一化的表面平均值。尽管假设固体体积分数可以忽略不计，但在植物冠层流动的背景下，空间平均值的属性已被广泛探索。如果没有这种简化，与非线性项相关的属性适用于内在平均值，而梯度属性适用于表面平均值。为了避免不一致和不准确，在解释平均分布、推导平均量的数学关系以及引入此类项的建模假设时，应仔细考虑不可忽略的固体体积分数的影响。在此基础上，我们回顾了在多孔介质流的更一般背景下开发的体积平均方法的定义和属性，并讨论了其在城市冠层流中的应用。我们通过恒定高度立方体上的流动模拟的示例数据来说明内在平均和表面平均的属性及其对平均轮廓的影响。