Evaluation of the outer-layer scaling in a developing urban boundary layer using lattice Boltzmann method

Boundary layer thickness is the representative length scale in the outer layer, which is the upper part of the turbulent boundary layer including the logarithmic layer. Meanwhile it is considered not to be a relevant parameter to describe the inner-layer flow characteristics in conventional similarity laws, i.e. Monin-Obukhov similarity. The top-down mechanism (Hunt and Carlotti, 2001) explains the sustaining process of the entire turbulent boundary layer with the primal importance of an impingement of the outer-layer turbulence, which has a outer-layer length scale, under modification by local mean wind shear and the blocking effect on the ground. In addition, Marusic et al. (2010) indicated that the super-structures, which follow the outer-layer scaling, are controlling the smaller eddies within the inner layer. These studies indicate the importance of the turbulence structures of the outer-layer scale to consider the mechanism to sustain the boundary layer turbulence. The main focus of this study is to examine the validity of the outer-layer scaling for the vertical distributions of turbulent statistics in the entire part of the boundary layer, and also for the vertical variation of the characteristic size of coherent structure of turbulence. This is examined in a developing boundary layer over a realistic urban geometry, which is reproduced by a numerical simulation of the lattice Boltzmann method (LBM) with implemented large eddy simulation (LES) model. The use of a developing boundary layer allowed testing the outer-layer scaling under various sizes of the boundary layer thickness. The use of LBM with massively parallel GPU computing in our super computing system, TSUBAME2.5, accomplished a huge size of computational domain, which is 20 km by 5 km by 1 km in streamwise, spanwise and vertical directions respectively, and the spatial resolution of 2 m in all directions. A realistic building geometry in a coastal area of Tokyo is explicitly resolved in this simulation. This large domain size with large roughness composed of buildings caused about 500 m of boundary layer thickness at 18 km downstream from the inlet. This overcomes the threshold of d>40~50H (H is the height of roughness) proposed by Jimenez (2004) to separate enough the inner- and outer-layer length scale and reproduce the logarithmic layer. It resulted that outer-layer scaling works well above 0.6d where the flow is similar irrespective of the surface types. Meanwhile, the lower layer depends on the local roughness properties. Concerning the structural characteristics, we observed that there are maximum size of eddies which follow the outer-layer scaling and penetrate entire boundary layer. The size is almost constant above 0.6d, and becomes thinner with decreasing height below 0.6d in which local mean wind shear modify the size of structures. These results support the validity of the top-down mechanism in a neutral urban boundary layer. A comparison with the Doppler lidar observation in an atmospheric surface layer over same building geometry is also conducted.