Evidence for Raupach et al.'s mixing-layer analogy in deep homogeneous urban-canopy flows

The mixing-layer analogy is due to Raupach, Finnigan & Brunet (Boundary-Layer Meteorol., vol. 25, 1996, pp. 351-382). In the analogy, the flow in the roughness sublayer of a homogeneous deep vegetation canopy boundary layer is analogous to a plane mixing layer rather than a surface layer. Evidence for the analogy includes the inflected velocity profile, which resembles the velocity profile in a plane mixing layer, and, most notably, the following estimate as a result of the Kelvin-Helmholtz instability: Lambda(x) = 8.1L(s), where Lambda(x) is the spacing of the large-scale eddies, and L-s is the shear length. The mixing-layer analogy has been very successful in vegetation canopy flow research, but has received only limited support in urban-canopy flow research. This work revisits Raupach et al.'s mixing-layer analogy, and we present the evidence for the mixing-layer analogy in urban-canopy flows: the exponential velocity profile in the canopy layer, i.e. (U - U-c)/(U-h - U-c) = exp(z/L-m), and L-m similar to [(U-h/U-c - 1)(U-h/U-c + 3)](-1 ). Here, z is the vertical coordinate, L m is the attenuation length and is a measure of the largest eddy in the canopy layer, Ury is the wind speed at the canopy crest and U c is the velocity in the inactive layer. We conduct direct numerical simulations of various deep homogeneous urban-canopy flows and test the above two scalings. We also discuss why Raupach et al.'s analogy has not seen as many successes in urban-canopy flows as in vegetation canopy flows.