Dispersive Fluxes Within and Over a Real Urban Canopy: A Large-Eddy Simulation Study

Abstract

Large-eddy simulations (LES) are conducted to study the transport of momentum and passive scalar within and over a real urban canopy in the City of Boston, USA. This urban canopy is characterized by complex building layouts, densities and orientations with high-rise buildings. Special attention is given to the magnitude, variability and structure of dispersive momentum and scalar fluxes and their relative importance to turbulent momentum and scalar fluxes. We first evaluate the LES model by comparing the simulated flow statistics over an urban-like canopy to data reported in previous studies. In simulations over the considered real urban canopy, we observe that the dispersive momentum and scalar fluxes can be important beyond 2–5 times the mean building height, which is a commonly used definition for the urban roughness sublayer height. Above the mean building height where the dispersive fluxes become weakly dependent on the grid spacing, the dispersive momentum flux contributes about 10–15% to the sum of turbulent and dispersive momentum fluxes and does not decrease monotonically with increasing height. The dispersive momentum and scalar fluxes are sensitive to the time and spatial averaging. We further find that the constituents of dispersive fluxes are spatially heterogeneous and enhanced by the presence of high-rise buildings. This work suggests the need to parameterize both turbulent and dispersive fluxes over real urban canopies in mesoscale and large-scale models.

Appendix: Dispersive Flux Fraction and Spatial Fraction for \({\overline{{\varvec{w}}} }^{{{\prime\prime}}}{\overline{{\varvec{s}}} }^{{{\prime\prime}}}\)

For ${\overline{w} }^{{\prime\prime}}{\overline{s} }^{{\prime\prime}}$, the magnitude of dispersive flux fraction decreases with height only for ejection (${F}_{1,{T}_{h}}$) at all thresholds and decreases with increasing thresholds ${T}_{h}$ for all heights, like ${\overline{w} }^{{\prime\prime}}{\overline{u} }^{{\prime\prime}}$ (see Fig. 

Fig. 20

Absolute value of the dispersive flux fraction ${F}_{i,{T}_{h}}$ normalized by $\sum_{i}{|F}_{i,{T}_{h}}|$ for each quadrant ${Q}_{i}$ (Quadrant 1: Outward interaction (O), Quadrant 2: Sweep (S), Quadrant 3: Inward interaction (I), Quadrant 4: Ejection (E)) and for different thresholds ${T}_{h}$ for ${\overline{w} }^{{\prime\prime}}{\overline{s} }^{{\prime\prime}}$. The results at heights $z/H=1, 4, 12$ and 30 are shown

20). At $z/H=1$ and $z/H=4$, only |${F}_{{1,4}}|$ values exceeded 0.25, which is evidence that ejections are the largest structures involved in scalar transport. At $z/H=12$, only |${F}_{{4,4}}|$ values exceed 0.35 and at $z/H=30$, only |${F}_{{4,4}}|$ values exceed 0.2, which shows that the outward interaction has the largest contribution to scalar transport at these two heights. The inward interaction (${S}_{{2,0}}$) occupies the largest horizontal plane for all heights (see Fig. 

Fig. 21

Space fraction ${S}_{i,{T}_{h}}/{S}_{i,0}$ for each quadrant ${Q}_{i}$ (Quadrant 1: Outward interaction (O), Quadrant 2: Sweep (S), Quadrant 3: Inward interaction (I), Quadrant 4: Ejection (E)) and for different thresholds ${T}_{h}$ for ${\overline{w} }^{{\prime\prime}}{\overline{s} }^{{\prime\prime}}$. The results at heights ${z}/{H}=1, 4, 12$ and 30 are shown

21). In summary, ejections and outward interactions are the dominant structure within the urban canopy and inertial sublayer, respectively, for ${\overline{w} }^{{\prime\prime}}{\overline{s} }^{{\prime\prime}}$.