The momentum flux-gradient relations derived from field measurements in the urban roughness sublayer in three cities in China

Abstract

Field measurements of the momentum flux and wind velocity gradient were carried out at three urban sites in the cities of Nanjing, Changzhou, and Suzhou, China. The observational data in the urban roughness sublayer are analyzed to derive the momentum flux-gradient relations in terms of framework of the local similarity theory with a least squares fit, and the relations are then compared to the classical similarity relations of Businger et al. (1971). The results show that the momentum flux varies with height; thus, the constant-flux assumption in the Monin-Obukhov Similarity Theory is not met in the urban roughness sublayer. However, the dimensionless wind velocity gradient may be described by the local similarity theory, and the derived flux-gradient relations have the same form as the classical similarity relations do. Under stable conditions, the coefficient βm in the fitted relations increases with height and gradually approaches the value of 4.7 in the classical similarity relations. The trend suggests that the turbulent flow may be described by the classical similarity relations once the height increases and reaches the top of the urban roughness sublayer, and thus, the height of the top of the urban roughness sublayer may be estimated by linear extrapolation of the derived relations in this study. The relation between the critical Richardson number Ric and the coefficient βm is derived as Ric = Prt/βm, where Prt is the turbulent Prandtl number. In the urban roughness sublayer, the value of Ric is larger than 0.2.