Wind-speed profile and roughness sublayer depth modelling in urban boundary layers

We propose a new formulation for the wind-speed profile in the urban boundary layer, which can be viewed as a generalisation of the commonly used logarithmic law. The model is based on the assumption that the role played by the classical aerodynamic roughness length and the displacement height in the logarithmic law is taken by a sole variable, the local length scale, which follows a pattern of exponential decrease with height. Starting from wind-speed profiles collected at Villa Pamphili park, Rome, Italy, an empirical fit is used to determine the model parameters. The results show that the local length scale depends also on the friction velocity and that, with appropriate normalization, it reduces to a family of curves that spreads according to the planar area fraction. Another novel aspect is the estimation of the roughness sub-layer depth, which can be expressed as a function of the friction velocity and morphometric quantities such as the building height and the planar area fraction. It is also found that the rate of growth with height of the Prandtl’s mixing length linked to the new formulation is, just above the canopy, lower than the canonical value 0.41, and approaches the latter value well above the roughness sublayer. The model performance is tested by comparison with laboratory and field data reported in the literature.