Investigation of a Geometric Parameter Corresponding to the Turbulent Length Scale Within an Urban Canopy Layer

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 ( HDX 3 ) 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 ( HDX 3 ) 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 HDX 3 and w var ( z ) corresponds well to the turbulent length scale in cities with various building heights. Furthermore, the proposed parameter w var ( z ) HDX 3 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.