# Effects of Unstable Stratification on Ventilation in Hong Kong

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## Abstract

**:**

## 1. Introduction

## 2. Model and Case Description

#### 2.1. LES Model

#### 2.2. Simulation Setup

^{9}and 12 × 10

^{9}grid points had to be used for the neutral and unstable case, respectively. The simulations required between 20 $\mathrm{h}$ and 60 $\mathrm{h}$ of computing time using more than 12,000 cores.

#### 2.3. Inflow Boundary Conditions

#### 2.4. Outflow Boundary Condition

## 3. Results

## 4. Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

^{2}of Kowloon City. Cyclic boundary conditions and neutral stratification were used. As turbulent structures are generally larger in the unstable case than in the neutral case, the latter defined the minimum grid size to be used.

**Figure A1.**Cumulative distribution function of three-dimensional wind velocity V at 4 $\mathrm{m}$ height. Data are averaged over 1 $\mathrm{h}$.

## References

- Xie, X.; Huang, Z.; Wang, J.S. Impact of building configuration on air quality in street canyon. Atmos. Environ.
**2005**, 39, 4519–4530. [Google Scholar] [CrossRef] - Ng, E. Policies and technical guidelines for urban planning of high-density cities—Air ventilation assessment (AVA) of Hong Kong. Build. Environ.
**2009**, 44, 1478–1488. [Google Scholar] [CrossRef] - Ng, E.; Yuan, C.; Chen, L.; Ren, C.; Fung, J.C.H. Improving the wind environment in high-density cities by understanding urban morphology and surface roughness: A study in Hong Kong. Landsc. Urban Plan.
**2011**, 101, 59–74. [Google Scholar] [CrossRef] - Cheng, Y.; Lien, F.; Yee, E.; Sinclair, R. A comparison of large Eddy simulations with a standard k–ϵ Reynolds-averaged Navier–Stokes model for the prediction of a fully developed turbulent flow over a matrix of cubes. J. Wind Eng. Ind. Aerodyn.
**2003**, 91, 1301–1328. [Google Scholar] [CrossRef] - Ashie, Y.; Kono, T. Urban-scale CFD analysis in support of a climate-sensitive design for the Tokyo Bay area. Int. J. Climatol.
**2011**, 31, 174–188. [Google Scholar] [CrossRef] - Tominaga, Y. Visualization of city breathability based on CFD technique: Case study for urban blocks in Niigata City. J. Vis.
**2012**, 15, 269–276. [Google Scholar] [CrossRef] - Yang, L.; Li, Y. City ventilation of Hong Kong at no-wind conditions. Atmos. Environ.
**2009**, 43, 3111–3121. [Google Scholar] [CrossRef] [Green Version] - Yim, S.H.L.; Fung, J.C.H.; Lau, A.K.H.; Kot, S.C. Air ventilation impacts of the “wall effect” resulting from the alignment of high-rise buildings. Atmos. Environ.
**2009**, 43, 4982–4994. [Google Scholar] [CrossRef] - Yuan, C.; Ng, E.; Norford, L.K. Improving air quality in high-density cities by understanding the relationship between air pollutant dispersion and urban morphologies. Build. Environ.
**2014**, 71, 245–258. [Google Scholar] [CrossRef] - Letzel, M.O.; Helmke, C.; Ng, E.; An, X.; Lai, A.; Raasch, S. LES case study on pedestrian level ventilation in two neighbourhoods in Hong Kong. Meteorol. Z.
**2012**, 21, 575–589. [Google Scholar] [CrossRef] - Park, S.B.; Baik, J.J.; Lee, S.H. Impacts of mesoscale wind on turbulent flow and ventilation in a densely built-up urban area. J. Appl. Meteorol. Climatol.
**2015**, 54, 811–824. [Google Scholar] [CrossRef] - Park, S.B.; Baik, J.J. A Large-Eddy Simulation Study of Thermal Effects on Turbulence Coherent Structures in and above a Building Array. J. Appl. Meteorol. Climatol.
**2013**, 52, 1348–1365. [Google Scholar] [CrossRef] - Yang, L.; Li, Y. Thermal conditions and ventilation in an ideal city model of Hong Kong. Energy Build.
**2011**, 43, 1139–1148. [Google Scholar] [CrossRef] - Raasch, S.; Schröter, M. PALM-A large-eddy simulation model performing on massively parallel computers. Meteorol. Z.
**2001**, 10, 363–372. [Google Scholar] [CrossRef] - Maronga, B.; Gryschka, M.; Heinze, R.; Hoffmann, F.; Kanani-Sühring, F.; Keck, M.; Ketelsen, K.; Letzel, M.O.; Sühring, M.; Raasch, S. The Parallelized Large-Eddy Simulation Model (PALM) version 4.0 for atmospheric and oceanic flows: Model formulation, recent developments, and future perspectives. Geosci. Model Dev.
**2015**, 8, 2515–2551. [Google Scholar] [CrossRef] - Lo, K.W.; Ngan, K. Characterising the pollutant ventilation characteristics of street canyons using the tracer age and age spectrum. Atmos. Environ.
**2015**, 122, 611–621. [Google Scholar] [CrossRef] - Park, S.B.; Baik, J.J.; Ryu, Y.H. A Large-Eddy Simulation Study of Bottom-Heating Effects on Scalar Dispersion in and above a Cubical Building Array. J. Appl. Meteorol. Climatol.
**2013**, 52, 1738–1752. [Google Scholar] [CrossRef] - Ronda, R.; Steeneveld, G.; Heusinkveld, B.; Attema, J.; Holtslag, B. Urban fine-scale forecasting reveals weather conditions with unprecedented detail. Bull. Am. Meteorol. Soc.
**2017**. [Google Scholar] [CrossRef] - Lund, T.S.; Wu, X.; Squires, K.D. Generation of Turbulent Inflow Data for Spatially-Developing Boundary Layer Simulations. J. Comput. Phys.
**1998**, 140, 233–258. [Google Scholar] [CrossRef] - Kataoka, H.; Mizuno, M. Numerical flow computation around aeroelastic 3D square cylinder using inflow turbulence. Wind Struct.
**2002**, 5, 379–392. [Google Scholar] [CrossRef] - Orlanski, I. A simple boundary condition for unbounded hyperbolic flows. J. Comput. Phys.
**1976**, 21, 251–269. [Google Scholar] [CrossRef] - Miller, M.J.; Thorpe, A.J. Radiation conditions for the lateral boundaries of limited-area numerical models. Q. J. R. Meteorol. Soc.
**1981**, 107, 615–628. [Google Scholar] [CrossRef] - Gryschka, M.; Fricke, J.; Raasch, S. On the impact of forced roll convection on vertical turbulent transport in cold air outbreaks. J. Geophys. Res. Atmos.
**2014**, 119, 12513–12532. [Google Scholar] [CrossRef] - Atkinson, B.W.; Wu Zhang, J. Mesoscale shallow convection in the atmosphere. Rev. Geophys.
**1996**, 34, 403–431. [Google Scholar] [CrossRef] - Larousse, A.; Martinuzzi, R.; Tropea, C. Flow Around Surface-Mounted, Three-Dimensional Obstacles. In Proceedings of the Turbulent Shear Flows 8: Selected Papers from the Eighth International Symposium on Turbulent Shear Flows, Munich, Germany, 9–11 September 1991; Durst, F., Friedrich, R., Launder, B.E., Schmidt, F.W., Schumann, U., Whitelaw, J.H., Eds.; Springer: Berlin/Heidelberg, Germany, 1993; pp. 127–139. [Google Scholar]
- Hang, J.; Li, Y.; Sandberg, M. Experimental and numerical studies of flows through and within high-rise building arrays and their link to ventilation strategy. J. Wind Eng. Ind. Aerodyn.
**2011**, 99, 1036–1055. [Google Scholar] [CrossRef] - Kim, J.J.; Baik, J.J. A numerical study of the effects of ambient wind direction on flow and dispersion in urban street canyons using the RNG k-e turbulence model. Atmos. Environ.
**2004**, 38, 3039–3048. [Google Scholar] [CrossRef] - Wolf-Grosse, T.; Esau, I.; Reuder, J. Sensitivity of local air quality to the interplay between small- and large-scale circulations: A large-eddy simulation study. Atmos. Chem. Phys.
**2017**, 17, 7261–7276. [Google Scholar] [CrossRef] - Resler, J.; Krč, P.; Belda, M.; Juruš, P.; Benešová, N.; Lopata, J.; Vlček, O.; Damašková, D.; Eben, K.; Derbek, P.; et al. A new urban surface model integrated in the large-eddy simulation model PALM. Geosci. Model Dev. Discuss.
**2017**, 2017, 1–26. [Google Scholar] [CrossRef] - Yaghoobian, N.; Kleissl, J.; Paw, U.K.T. An Improved Three-Dimensional Simulation of the Diurnally Varying Street-Canyon Flow. Bound.-Layer Meteorol.
**2014**, 153, 251–276. [Google Scholar] [CrossRef] - Kuiper, N.H. Tests concerning random points on a circle. Indag. Math.
**1960**, 63, 38–47. [Google Scholar] [CrossRef]

**Figure 1.**Domain setup for the (

**a**) neutral case and (

**b**) unstable case; building height information is depicted in (

**c**). The dashed line marks the recycling area. The gray rectangle marks the city area shown in detail in (

**c**).

**Figure 2.**Instantaneous vertical wind velocity (

**a**) and potential temperature (

**b**) for the unstable case after a simulation time of 6 $\mathrm{h}$ at a height of 100 $\mathrm{m}$. The solid inner rectangle marks the city area.

**Figure 3.**Averaged three-dimensional wind velocity at 2 $\mathrm{m}$ height for the (

**a**) neutral case and (

**b**) unstable case. Buildings are shown in gray.

**Figure 4.**Vertical profile of the wind speed of the mean horizontal wind vector $|{\overrightarrow{v}}_{h}|$ within the recycling area.

**Figure 6.**Normalized velocity ratio ${V}_{r,\mathrm{norm}}$. Values above 1 indicate higher ${V}_{r}$ in the unstable case, while values below 1 indicate higher ${V}_{r}$ in the neutral case.

**Figure 7.**Scatter plot for ${V}_{r}$ and (

**a**) the average building height ${H}_{\mathrm{avg}}$ and (

**b**) the plan area index ${\lambda}_{p}$. Each point represents an average value inside a $100\mathrm{m}\times 100\mathrm{m}$ area within the city. Blue dots represent the neutral case and red crosses represent the unstable case.

**Figure 8.**Time series of wind direction at position $(x,\phantom{\rule{3.33333pt}{0ex}}y)=(2713\mathrm{m},\phantom{\rule{3.33333pt}{0ex}}2671\mathrm{m})$ in the city center. Blue dots represent the neutral case and red crosses represent the unstable case.

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**MDPI and ACS Style**

Gronemeier, T.; Raasch, S.; Ng, E.
Effects of Unstable Stratification on Ventilation in Hong Kong. *Atmosphere* **2017**, *8*, 168.
https://doi.org/10.3390/atmos8090168

**AMA Style**

Gronemeier T, Raasch S, Ng E.
Effects of Unstable Stratification on Ventilation in Hong Kong. *Atmosphere*. 2017; 8(9):168.
https://doi.org/10.3390/atmos8090168

**Chicago/Turabian Style**

Gronemeier, Tobias, Siegfried Raasch, and Edward Ng.
2017. "Effects of Unstable Stratification on Ventilation in Hong Kong" *Atmosphere* 8, no. 9: 168.
https://doi.org/10.3390/atmos8090168