In this paper, we identify a new geometric parameter that governs the turbulent length scale within the urban canopy layer. This parameter is the geometric mean (\(\sqrt[3]{HDX}\)) of the building height (H), width of the road in the streamwise direction (D), and width of the road in the spanwise direction (X). The turbulent length scales in various cities are estimated and nondimensionalised using the proposed parameter. The proposed parameter (\(\sqrt[3]{HDX}\)) corresponds well to the turbulent length scale. It is better than H or D. Additionally, we propose a weighting factor (\({w}_{var}(z)\)) using the local plan area index to achieve good correspondence to the turbulent length scale even when the building height varies. The parameter multiplying \(\sqrt[3]{HDX}\) and \({w}_{var}(z)\) corresponds well to the turbulent length scale in cities with various building heights. Furthermore, the proposed parameter \({w}_{var}(z)\sqrt[3]{HDX}\) is combined with the turbulent length scale of the Mellor–Yamada turbulence model. This combined turbulent length scale can capture the characteristics of the vertical profile of the turbulent length scale better than the conventional method, particularly within the urban canopy layer.

在本文中，我们确定了一个新的几何参数，该参数控制城市冠层内的湍流长度尺度。该参数为建筑物高度(H)、道路流向宽度 (D) 和道路跨度方向宽度 ( X）。使用所提出的参数对各个城市的湍流长度尺度进行了估计和无量纲化。所提出的参数（\(\sqrt[3]{HDX}\) ）与湍流长度尺度很好地对应。它比 H 或 D 更好。此外，我们使用局部规划面积指数提出了一个加权因子（\({w}_{var}(z)\) ），以实现与湍流长度尺度的良好对应，即使建筑物高度各不相同。\(\sqrt[3]{HDX}\)和\({w}_{var}(z)\)相乘的参数很好地对应了不同建筑高度的城市中的湍流长度尺度。此外，所提出的参数\({w}_{var}(z)\sqrt[3]{HDX}\)与 Mellor-Yamada 湍流模型的湍流长度尺度相结合。这种组合的湍流长度尺度可以比传统方法更好地捕捉湍流长度尺度的垂直剖面特征，特别是在城市冠层内。