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:Λx = 8.1Ls, whereΛx is the spacing of the large-scale eddies, and Ls 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-Uc)/(Uh-Uc) = exp(z/Lm), and Lm ∼ [(Uh/Uc-1)(Uh/Uc + 3)]-1. Here, z is the vertical coordinate, Lm is the attenuation length and is a measure of the largest eddy in the canopy layer, Uh is the wind speed at the canopy crest and Uc 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.