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Boundary-Layer Meteorology manuscript No.(will be inserted by the editor)

Flow and pollutant transport in urban street canyons of different aspect ratios

with ground heating

Xian-Xiang Li · Rex E. Britter · Leslie K. Norford · Tieh

Yong Koh · Dara Entekhabi

Received: September 8, 2010

Abstract A validated large-eddy simulation model was employed to study the effect of the aspect ratio and

ground heating on the flow and pollutant dispersion in urban street canyons. Three ground heating intensities

(neutral, weak and strong) were imposed in the street canyons of aspect ratio 1, 2, and 0.5. The detailed

patterns of flow, turbulence, temperature and pollutant transport were analysed and compared. Of all the cases

simulated, significant changes of flow and scalar patterns were caused by ground heating in the street canyon

of aspect ratio 2 and 0.5, while only the street canyon of aspect ratio 0.5 showed change in flow regime (from

wake interference flow to skimming flow). Ground heating generated strong mixing of heat and pollutant, but

the normalised temperature inside street canyons was spatially uniform and somewhat insensitive to the aspect

ratio and heating intensity. The quadrant analysis of pollutant flux showed that sweeps dominated in most of

the regions within the street canyon, while ejections dominated in the wake of the line source and above the

street canyon. The ground heating was shown to enhance ejections at the leeward roof-level corner.

X-X Li

CENSAM, Singapore-MIT Alliance for Research and Technology, S16-05-08, 3 Science Drive 2, Singapore 117543

E-mail: [email protected]

R.E. Britter

Department of Urban Studies and Planning, Massachusetts Institute of Technology, Cambridge, MA, USA

L.K. Norford

Department of Architecture, Massachusetts Institute of Technology, Cambridge, MA, USA

T-Y Koh

School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371

D. Entekhabi

Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

2 Xian-Xiang Li et al.

Keywords Aspect ratio · Ground heating · Large-eddy simulation · Pollutant dispersion · Urban street

canyon · Unstable stratification

1 Introduction1

With rapid urbanization and city expansion, the sustainable development of the urban environment is now2

facing many challenges, such as urban heat island effect, deteriorating air quality and severe securities con-3

cerns (Fernando et al., 2001; Britter and Hanna, 2003; Belcher, 2005). As the typical element of the urban area,4

the street canyon exhibits a distinct climate where microscale meteorological processes dominate (Oke, 1988).5

These unique microscale meteorological processes affect not only the local air quality but also the comfort of6

city inhabitants (Bottema, 1993). Therefore, many research efforts have been devoted to the characteristics of7

airflow and pollutant dispersion in urban street canyons during the past few decades (Ahmad et al., 2005; Li8

et al., 2006; Vardoulakis et al., 2003).9

Located within the roughness sublayer (RSL), the flow in urban street canyon has a strong dependence on10

the local urban morphology. The flow field inside an urban street canyon is mainly determined by the aspect11

ratio (AR) defined as building-height-to-street-width ratio (h/b, where h is the building height and b the street12

width; see Fig. 1). The flow inside street canyons can be classified into different flow regimes according to the AR,13

i.e. isolated roughness flow (IRF), wake interference flow (WIF) and skimming flow (SF) regimes (Oke, 1988).14

It was shown that within the SF regime, different ARs resulted in different number of primary recirculations in15

urban street canyons (Li et al., 2008, 2009). Another factor, the thermal effect (due to solar radiation, release of16

stored heat, and anthropogenic heat), also has a profound impact on the flow field, and therefore, the pollutant17

dispersion in street canyons, as demonstrated by many previous studies (Nakamura and Oke, 1988; Ca et al.,18

1995; Sini et al., 1996; Uehara et al., 2000; Kim and Baik, 2001; Xie et al., 2006).19

With the development of computer hardware and algorithms, the computational fluid dynamics (CFD)20

technique has become a popular and powerful tool in urban street canyon research due to its efficiency and21

relatively low cost (Li et al., 2006). Of the many CFD models, Reynolds-averaged Navier-Stokes equations22

(RANS) models have provided many insights into the characteristics of the airflow and dispersion in urban23

street canyons during the past two decades. Recently, large-eddy simulation (LES) has become popular in24

street-canyon studies mainly owing to its power of handling transient and unsteady turbulent processes (e.g.,25

Liu and Barth, 2002; Cui et al., 2004; Liu et al., 2004, 2005; Cai et al., 2008; Letzel et al., 2008; Li et al., 2008).26

LES of urban street canyons of different AR with ground heating 3

The LES model developed by Li et al. (2010) was validated against wind-tunnel data and then was applied27

to study the flow and dispersion inside the urban street canyon of AR 1 with ground heating. With different28

ground heating intensities, the flow, turbulence and pollutant dispersion exhibited some characteristics that29

were not present under isothermal conditions. They demonstrated that LES could be an ideal tool to study the30

thermal effects in street canyons.31

In this paper, the LES model developed in Li et al. (2010) is employed to study the effect of AR and ground32

heating on the flow and pollutant dispersion in urban street canyons. The objective is to investigate how the33

change of urban geometry will affect the flow pattern and pollutant transport when ground heating is present.34

2 Numerical model and boundary conditions35

2.1 Numerical model36

The LES code (Li et al., 2010) developed for incompressible turbulent flow based on a one-equation subgrid-scale37

(SGS) model is employed in this study. The thermal buoyancy forces are, using the Boussinesq approximation,38

taken into account in both the dimensionless Navier-Stokes equations and the transport equation for SGS39

turbulent kinetic energy (TKE). The reference length scale H (the building height of the street canyon of40

AR 1), the reference velocity scale U (free-stream velocity) and the reference temperature θa (the ambient41

temperature) are used to make the governing equations dimensionless.42

The details of the numerical model can be found elsewhere (Li et al., 2008; Li, 2008; Li et al., 2010) and will43

not be repeated here.44

2.2 Computational domain and boundary conditions45

Figure 1 depicts the schematic computational domain used in the current study, which represents a typical46

street canyon in an idealised manner. The spanwise-homogeneous computational domain consists of a street47

canyon of height h at the bottom and a free shear layer of height h above the building. The width of the street48

is b and the length is L.49

The background atmospheric flow is simulated in the form of a pressure-driven free stream in the free shear50

layer only. The approaching wind flow is perpendicular to the street axis, which results in a free-stream wind51

speed U in the streamwise direction. The air flow boundary conditions are set to be periodic in the streamwise52


and spanwise directions. No-slip conditions are set at all rigid walls. At the top of the domain, a shear-free53

boundary condition is assumed.54

A line source with emission rate Q is located on the ground with a distance xs (= b/2 in this study) from55

the leeward building. At the inlet, the temperature is set to θa and the pollutant concentration is set to zero56

(free of pollutant). At the outlet, the convective boundary conditions (Li et al., 2008) are prescribed for both57

the temperature and pollutant to make sure that they are convected outside the domain and will not enter58

into the domain again from the inlet. The air temperature at the top is set to ambient temperature θa and the59

ground level (bottom) maintains a constant temperature θf = θa +∆θ (ground heating). The temperatures at60

the rigid walls can either be set to a fixed value (ambient temperature θa) or adiabatic (no heat flux at walls);61

We take the former situation in the present study.62

2.3 Simulation conditions63

In this study, three street canyons of different AR, i.e., 0.5 (h = H, b = 2H), 1.0 (h = b = H) and 2.064

(h = 2H, b = H) are considered. For each aspect ratio, three scenarios of ground heating (no heating, weak65

heating and strong heating) will be investigated. Table 1 summarizes the conditions for all the cases studied, in66

which the Richardson number is defined as67

Ri = − gh

U2

∆θ

θa, (1)

where g is the gravitational acceleration.68

3 Flow and turbulence fields69

3.1 Mean flow70

Figures 2-4 show the mean flow quantities of the street canyons under different ground heating conditions. The71

streamfunction plot for the street canyon of AR 1 (not shown here) exhibits a roughly symmetric pattern with72

corner vorticies and an impinging streamline on the windward wall near the canyon roof (Li et al., 2010). The73

streamfunctions increase in magnitude with increasing ground heating intensities. For the deep street canyons74

of AR 2 with no buoyancy forcing there are two large counter rotating vortices one above the other with75

again three small corner vortices and an impinging streamline (figs. 2a, 3d, and 4d). The upper vortex is larger,76

stronger and obviously driving the vortex below. With weak heating at the ground of the street canyon there is a77


marked change in the vortices (Figs. 2b, 3e, and 4e). The bottom vortex becomes a little larger but considerably78

stronger. The buoyancy injected at the ground has obviously strengthened the adjacent vortex which appears79

to be assisting in driving the upper vortex. With even greater heating there is only one dominant vortex with80

its centre approximately 1/3 the way up the street canyon (Figs. 2c, 3f, and 4f). It is very interesting to notice81

that the direction of rotation of this dominant vortex is that of the previous upper vortex and not that of the82

lower vortex that appeared to be increasing in strength with increased buoyancy injected from the ground. It83

seems that there must be a fairly catastrophic change of the flow pattern at some critical condition. As can84

be seen in Figure 2c. there are also three corner vortices and one of these, near the upper leeward wall, is of85

considerable size. It is also of interest to note the somewhat complicated route that the buoyancy takes to get86

from the ground to the canyon roof. The direction of the flow at the canyon ground changes with larger injected87

buoyancy as does the flow near the side walls of the canyon that transports heat to the street canyon roof.88

For the case of a wide street canyon of AR 0.5 with no ground heating, Figures 3g and 4g show again two89

vortices but are aligned side by side. The downstream vortex is by far the larger and has the same sense of90

rotation as that in the street canyon of AR 1. The upstream one is smaller but still filling about 1/4 of the91

canyon and rotating in the opposite direction. Provision of a weak ground heating alters the flow drastically92

by changing the flow structure to a single dominant vortex with three small corner vortices and an impinging93

streamline near the windward roof. The great change in the streamline is undoubtedly due to the existing vortex94

sweeping the buoyant fluid back to the leeward wall where it rises, reinforcing the clockwise rotation and this is95

similar to the reinforcement seen in Figures 3b-c and 4b-c for the street canyon of AR 1. A strong ground heating96

produces an even stronger and more symmetric vortex, which extends even higher above the roof level. This is97

in line with what Xie et al. (2007) calculated with a k − ε model. Kim and Baik (2001), however, reported two98

counter-rotating vortices in a street canyon of AR 0.6 with ∆θ = 10 − 16 K. It is evident that when buoyancy99

forces are introduced, the flow regime in the street canyon of AR 0.5 changes from WIF to SF, although the SF100

regime here is somewhat different from the classical definition (e.g., in Oke, 1988) in that the vortex extends101

above the street canyon to strongly disturb the free-stream flow, which does not happen in the street canyons102

of AR 1 and 2.103

In all cases the buoyancy introduced at the ground of the street canyon acts to increase the strength of the104

velocity field within the canyon in addition to changing the flow structure markedly in some situations. This is105

clearly seen in Figures 4. In the street canyon of AR 1, the vertical velocity is more organized on the windward106

side, the region where the free-stream fluid is first entrained into the canyon. It becomes less organized and more107


diffusive as it moves around the street canyon. However, with increasing buoyancy at the ground the updraft108

on the leeward side becomes more organized and comparable to the downdraft on the windward side (Fig. 4).109

In the street canyon of AR 2 this is even more marked, particularly with strong heating (Figs. 3f and 4f). The110

buoyant upflow and ingested downflow are very strong. Based on the principle of mass conservation, there must111

be a general equality of upflow and downflow, but their strengths have been equally affected by the buoyancy112

forces.113

Similar observations can be made for the street canyon of AR 0.5 but they are even more striking (Figs. 3g-114

i and 4g-i). As the ground heating is intensified, the streamwise velocities inside the street canyon increase115

markedly and, somewhat surprisingly, the streamline pattern becomes strongly symmetric. For the vertical116

velocities, the symmetry is not quite as apparent but it is still unusual. Additionally, with strong heating the117

peak vertical velocities are about half the free-stream velocity while the peak streamwise velocities are about118

the same as the free-stream velocity.119

3.2 Momentum flux120

The momentum fluxes at the top of the street canyon represent the mixing between the free-stream flow and121

the flow inside the street canyon. They reflect mass, momentum, sensible and latent heat and the various air122

pollutants to or from the canyon and they are important in many urban studies. In Figure 5a-c for the street123

canyon of AR 1, the momentum flux into the street canyon (or the exchange velocity at the canyon roof level)124

increases by a factor of about 4 as the buoyancy is increased. It is also important to note that the momentum125

fluxes are very small within the street canyon when compared with those at the roof level. Much the same is126

seen in the results for AR 2 (Fig. 5d-f). A slightly surprising observation is that with strong heating (Fig. 5f),127

there is an organized pattern of Reynolds stresses within the canyon of considerable magnitude. This is likely128

to be just an outcome of the strong organized flow in the canyon in this case.129

The case of AR 2 has the lowest momentum flux and the case of AR 0.5 has the highest. It is apparent130

that the lower aspect ratio allows for greater instability and mixing at the interface. For all aspect ratios131

the introduction of ground heating produces greater mixing across the canyon top as evidenced by the larger132

momentum fluxes.133


4 Scalar fields134

4.1 Temperature135

4.1.1 Mean temperature136

In the street canyon of AR 1 (Fig. 6a-b), it is clear that most of the street canyon is well mixed (or that137

while the non-dimensional temperature (< θ > −θa)/∆θ varies from 0 to 1.0, most of the canyon is bounded138

by temperatures that are only a factor of the temperature difference between the ground and the ambient139

temperature, with a typical value of 0.10). This small magnitude reflects that the exchange process across the140

canyon top is relatively strong compared with the surface heat transfer at the ground of the street canyon.141

Additionally the thermal plume above the street canyon unsurprisingly extends higher into the free stream for142

the case with strong heating (Fig. 6b).143

For the case of AR 2 (Fig. 6c-d) the effect of increased ground heating is more complicated in that the two-144

vortex structure is transformed into a single-vortex structure. However, for both heating cases the mixing as145

defined above is much the same. With the strong ground heating, in accordance with the dramatic flow pattern146

change, the leeward corner becomes hotter than the windward corner (Fig. 6d), contrary to the situation when147

only weak heating is present (Fig. 6c).148

Much the same mixing of heat is observed in the street canyon of aspect ratio 0.5 (Fig. 6e-f). So the mixing149

of heat within the street canyon is strong and somewhat insensitive to the AR (0.5 to 2) and heating intensity,150

which varies between small (down to zero) and quite strong (with a Richardson number Ri up to -2.9). The151

numerical studies by Solazzo and Britter (2007) suggested that the flow and turbulence developed within the152

street canyon produced a temperature distribution essentially spatially uniform (apart from a relatively thin153

near-wall thermal boundary layer). In their cases with all the canyon facets heated (different from our ground-154

heated cases), they concluded that the non-dimensional in-canyon temperature was proportional to the AR. For155

AR = 1, the in-canyon temperature was 0.11, which is very close to the results in our study.156

4.1.2 Heat flux157

The turbulent transfer of heat within and across the street canyon is crucial for the in-canyon temperature158

distribution. The non-dimensional vertical heat flux < w′′θ′′ > /(U∆θ) are shown in Figure 7. In the street159

canyon of AR 1 (Fig. 7a-b), there are local maxima at the leeward roof level, leeward and windward ground160


corners. It is clearly seen that some heat is circulating inside the street canyon at the core region, while substantial161

heat exchange occurs at the roof level. With strong ground heating (Fig. 7b), the heat exchange at the roof level162

is stronger, which explains the lower non-dimensional in-canyon temperature in the previous section (Fig. 6b).163

In the street canyon of AR 2 (Fig. 7c-d), the magnitude of heat fluxes is smaller compared with that in the164

street canyon of AR 1 and AR 0.5, presumably due to the higher AR and lower momentum flux observed in165

the previous section. Local maxima occur at the interface between vortices under both weak and strong heating166

conditions, suggesting large heat transfer there via turbulence. Different from the cases of AR 1 and 0.5, the167

local maxima at the roof level are much lower than those at vortex interfaces and near the ground. Therefore,168

more heat is accumulated and recirculated within the street canyon (Fig. 7d).169

The distribution of heat flux in the street canyon of AR 0.5 (Fig. 7e-f is much similar to that in the street170

canyon of AR 1, while the magnitude in the case of AR 0.5 is slightly larger than that in AR 1.171

4.2 Pollutant transport172

4.2.1 Mean pollutant distribution173

As shown in Figure 8, the general levels of non-dimensional pollutant concentrations < c > UHL/Q vary quite174

considerably with changing aspect ratio and heating intensity at the ground level. At the core region within the175

street canyons (where the pollutant distribution is quite uniform), the pollutant concentration changes from 45,176

20 to 12.5 for AR = 1, from 70, 55 to 20 for AR = 2, and from 10, 7.5 to 3.5 for AR = 0.5, with the ground177

heating from neutral, weak to strong, respectively. Table 2 summarizes the pollutant ratio residing inside the178

street canyons for each case. The street canyon of AR 0.5 is most effective in pollutant removal, and strong179

ground heating also plays an important role in this.180

For the street canyon of AR 2, when there is no heating or the ground heating is weak (Fig. 8d, e), the181

pollutant distribution exhibits two layers, roughly corresponding to the two layers in their streamlines. At the182

interface of these two layers, pollutant transport is solely through turbulent and molecular diffusion, which183

is ineffective compared with that by advection, resulting in the high accumulation of pollutants at the lower184

street canyon and high pollutant retention inside the street canyon (Table 2). With the dramatic change of flow185

pattern when strong ground heating is present (Fig. 8f), the pollutant transport inside the street canyon by186

advection is much more effective and the pollutant retention reduces from 97.0% to 92.7%, in sharp contrast to187

the reduction from 97.8% to 97.0% by weak ground heating.188


It is worth noting the difference between the temperature and pollutant, although they are both treated189

as scalars (one active and one passive) and governed by equations of the same form. The main reasons for190

their different distribution patterns are twofold. On one hand, the source sizes are obviously different: the191

temperature has an area source occupying the whole street floor, while the pollutant source is a line source192

situated in the middle of the street floor. Smaller sources are known to produce more detail in the concentration193

field (Fackrell and Robins, 1982). On the other hand, the boundary conditions for each scalar are different, as194

outlined in Section 2.2. Physically, there are heat transfer at solid walls, which are impermeable for pollutants.195

Mathematically, with the eddy-diffusivity assumption adopted in modeling the SGS heat (pollutant) fluxes, the196

governing equations are essentially elliptic. In addition, the temperature is fixed at most boundaries, therefore197

the temperature distribution must be basically fixed and independent of the heating intensity (Li et al., 2010).198

In contrast, the boundary conditions for the pollutant are mostly no-flux and hence the pollutant distribution199

is rather sensitive to the aspect ratio and heating intensity.200

4.2.2 Pollutant flux201

To further examine how the buoyancy force enhances pollutant transport, the vertical pollutant fluxes < w′′c′′ >202

(HL/Q) for each case are depicted in Figure 9 for comparison.203

In the street canyon of AR 1 (Fig. 9a-c), the ground heating weakens the pollutant flux along the windward204

wall and instead, strengthens the pollutant flux at the roof level, in the wake of the line source and along the205

leeward wall. This may suggest that more pollutants are removed from the street canyon (through the roof-level206

leeward corner) while less are entrained inside (through the roof-level windward corner).207

In the street canyon of AR 2 (Fig. 9d-f), the pollutant flux is strengthened by weak ground heating in the208

wake of the line source and at the interface of two primary vortices. At the roof level, only a small magnitude209

of flux increment can be found. This is in line with the negligible increment in pollutant removal by the weak210

ground heating, as noted in the previous section. With strong ground heating (Fig. 9f), the pollutant flux pattern211

somewhat resembles that in the street canyon of AR 1 (Fig. 9c). High pollutant flux is observed near the ground212

leeward corner and the roof level.213

For the street canyon of AR 0.5 (Fig. 9g-i), the intensified pollutant flux by increasing ground heating does214

not cover the roof level as the case for the other two ARs described above. Instead, the contour of pollutant215

flux also extends above the roof level, which indicates the substantial pollutant exchange does not occur at the216


roof level in this case. Hence, along the roof level, turbulence is not the sole mechanism for pollutant removal217

when ground heating is introduced.218

4.2.3 Quadrant analysis219

To quantify the number and contribution of each quadrant to the pollutant flux < w′′c′′ > (Fig. 10; note220

that the definition of each quadrant for pollutant flux is different from that for Reynolds stress), the quadrant221

analysis technique (Wallace et al., 1972) is adopted. Q2 and Q4 events are generally rare and contribute little to222

the pollutant flux. The more significant events are Q1 (ejections) which transport high-pollutant air upwards,223

and Q3 events (sweeps) which transport low-pollutant air downwards. The relative frequency of occurrence of224

ejections and sweeps and their contributions to < w′′c′′ > are indicators of the pollutant transport mechanism.225

Figure 11 shows the ratio of contribution to < w′′c′′ > by ejections to that by sweeps, S1/S3, in the street226

canyon of AR 1, where Si is the contribution from the i-th quadrant (i = 1, 2, 3, 4). It is evident that within the227

street canyon, sweeps dominate at most locations (although their frequencies of occurrence are comparable),228

except in the wake of the line source where ejections occur about twice more often than sweeps. With increasing229

ground heating intensity, the area where sweeps dominate increases. At the roof level, the ejections and sweeps230

occur and contribute equally when there is no ground heating. However, when the ground heating is introduced,231

the contribution of ejections outweighs that of sweeps near the leeward roof-level corner, where the flow inside232

the street canyon is coupled with the free-stream flow (Li et al., 2010).233

Above the roof level, the frequency of occurrence of ejections is higher than that of sweeps, but the contribu-234

tion of ejections is much smaller. This feature is true for all the ground heating intensities and is insensitive to235

stability conditions, which is consistent with the measurement of urban RSL turbulence (Christen et al., 2007).236

Another important quantity is the ratio of (unorganized) counter flux contributions (from Q2 and Q4) to237

(organized) contributions (from Q1 and Q3) in the direction of the average pollutant flux, that is Exuberance238

defined as239

Ex =S2 + S4

S1 + S3. (2)

Ex can be regarded as an indicator for the efficiency of the transfer. Figure 12 contrasts Ex in the street canyon240

of AR 1 with different ground heating intensity. Near the line source, the transfer is the least efficient, while241

in the wake of the line source, the transfer is quite efficient. At the roof level with a small shift to the leeward242

corner, Ex reaches its maximum. This maximum increases significantly from -0.1 to -0.05 with the increasing243


heating intensity. It is interesting to note that the ground heating increases the transfer efficiency in the wake244

of the line source, but decreases dramatically the efficiency near the line source.245

5 Conclusion246

It has been demonstrated that ground heating introduced in the street canyon strengthens the vortex motion.247

Of all the cases simulated, significant changes of flow and scalar patterns have been caused by ground heating248

in the street canyons of AR 2 and 0.5, while only the street canyon of AR 0.5 shows a change in flow regime249

(from wake interference flow to skimming flow). Strong ground heating in the street canyon of AR 2 can change250

the two-vortex structure into a one-vortex structure due essentially to the reinforced lower vortex. Strangely,251

the strong ground heating leads to a more symmetric vortex structure in the street canyons of AR 1 and 0.5.252

Stronger ground heating produces greater mixing between the flow in the street canyon and that above, as253

reflected by larger momentum fluxes across the roof level of the street canyon.254

The mixing of heat in the street canyons of different ARs is observed to be strong. The normalised tempera-255

ture inside the street canyon is spatially uniform and somewhat insensitive to the aspect ratio and the intensity256

of ground heating.257

Generally, ground heating greatly facilitates pollutant removal for the street canyons at different ARs. For258

the street canyon of AR 0.5, when ground heating is introduced, the roof level is no longer the place where the259

pollutant removal occurs, and turbulence is not the sole mechanism for pollutant removal.260

The quadrant analysis of pollutant flux shows that sweeps dominate in most of the regions within the street261

canyon, while ejections dominate in the wake of the line source and above the street canyon. The ground heating262

is shown to enhance ejections at the leeward roof-level corner.263

It is of much importance to study the turbulence structure in the urban roughness sublayer, especially264

near the roof level, where the exchange processes of momentum and scalar (temperature and pollutant) mainly265

occur. By checking the relative relations between ejections and sweeps of Reynolds stress in the vicinity of the266

roughness, Coceal et al. (2007) claimed that there is some similarity between the urban RSL, the RSL over267

vegetation, and the mixing layer. The current study may provide some more evidence for this similarity with268

the quadrant analysis of pollutant flux. More analysis based on the results obtained from the current study can269

be done to validate and establish this mixing-layer analogy for urban RSL as Raupach et al. (1996) has done270

for vegetation canopies.271


Acknowledgment272

This project was funded by Singapore National Research Foundation (NRF) through the Singapore-MIT Alliance273

for Research and Technology (SMART) Center for Environmental Sensing and Modeling (CENSAM).274

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Table 1: Richardson numbers Ri and aspect ratios h/b for each case.

AR Richardson number Ri

h/b Weak heating Strong heating

0.5 −0.9 −2.9

1.0 −0.6 −2.4

2.0 −0.5 −2.0

Table 2: Ratio of pollutants inside the street canyon of different AR with different ground heating intensity.

HHHHHH

HHAR

HeatingNeutral Weak Strong

0.5 90.7% 80.5% 72.5%

1 93.6% 89.3% 83.6%

2 97.8% 97.0% 92.7%


U

u db

building

Leeward Windward

buildingh

h = h f

Inlet

b

xs

Outlet

z

x

b

f

θa

Street canyon

Line source

Freestream flow

θ = θ + a ∆ θ

Fig. 1: Schematic diagram of computational domain for the flow and pollutant transport in a street canyon with

ground heating.


(a)

-0.03

-0.02

0 0

0.001

0.005

0.01

-0.04

-0.01-0.001

00

x/H

z/H

-0.50

0.51

1.50

0.5 1

1.5 2

2.5

(b)

-0.03

-0.02-0.01

0

0.001

0.001

0.005

0.01

0.02

0.025

-0.035

-0.010

-0.00100

x/H

z/H

-0.50

0.51

1.50

0.5 1

1.5 2

2.5

(c)

0.005 0

-0.02

-0.08

-0.06

0

-0.04

00

x/H

z/H

-0.50

0.51

1.50

0.5 1

1.5 2

2.5

Fig.

2:Spatial

distributionof

thedim

ensionlessstream

functionψ

.in

thestreet

canyonof

AR

2.(a)

Neutral;

(b)w

eakheating;

(c)strong

heating.D

ashedlines

indicatenegative

values(clockw

iserotating).


(a)

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

(b)

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

(c)

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

0.70.60.50.40.30.20.10

-0.1-0.2-0.3-0.4-0.5

u/U

(d)

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

(e)

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

(f)

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

0.50.40.30.20.10.0750.050.0250

-0.1-0.2

u/U

(g)

x/H

z/H

-1 0 1 2 30

0.5

1

1.5

2

(h)

x/H

z/H

-1 0 1 2 30

0.5

1

1.5

2

(i)

x/H

z/H

-1 0 1 2 30

0.5

1

1.5

2

0.90.70.50.30.10

-0.1-0.3-0.5-0.7-0.9

u/U

Fig. 3: Flow patterns and normalised streamwise velocities < u > /U in the street canyon of AR 1 with (a)

neutral, (b) weak, and (c) strong heating; in the street canyon of AR 2 with (d) neutral, (e) weak, and (f) strong

heating; in the street canyon of AR 0.5 with (g) neutral, (h) weak, and (i) strong heating.


(a)

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

(b)

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

(c)

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

0.50.40.30.20.10

-0.1-0.2-0.3-0.4-0.5-0.6

w/U

(d)

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

(e)

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

(f)

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

0.250.20.150.10.050

-0.05-0.1-0.15-0.2-0.25

w/U

(g)

x/H

z/H

-1 0 1 2 30

0.5

1

1.5

2

(h)

x/H

z/H

-1 0 1 2 30

0.5

1

1.5

2

(i)

x/H

z/H

-1 0 1 2 30

0.5

1

1.5

2

0.40.30.20.10

-0.1-0.2-0.3-0.4-0.5-0.6

w/U

Fig. 4: Flow patterns and normalised vertical velocities < w > /U in the street canyon of AR 1 with (a) neutral,

(b) weak, and (c) strong heating; in the street canyon of AR 2 with (d) neutral, (e) weak, and (f) strong heating;

in the street canyon of AR 0.5 with (g) neutral, (h) weak, and (i) strong heating.


(a)

-0.004-0.006-0.002 -0.002

00

0

0.002

0

0

0

0

-0.007

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

(b)

-0.005

-0.01-0.015

-0.005-0.005

00

0

0

0.002

0.002

0.002

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

(c)

-0.01

-0.015

-0.02-0.025-0.03

-0.01

-0.01-0.005

0.005

0

00

0.005

0.0050.005

0.010

-0.005

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

(d)

-0.003

-0.002

-0.004

-0.002

0.001

0

0

0

0

-0.002

0

0

0 0

0

-0.001

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

(e)

-0.004-0.003

-0.005-0.002

-0.002

0.0010

0.001

0

0

-0.001

0

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

(f)

-0.0125-0.01

-0.0075-0.0025

-0.005

0

0.0025

0.005

0.00250

0

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

(g)

0

-0.005

0

0

0

0

-0.014

0

0

-0.01

x/H

z/H

-1 0 1 2 30

0.5

1

1.5

2

(h)

-0.01

-0.02

-0.010

0

0

00

x/H

z/H

-1 0 1 2 30

0.5

1

1.5

2

(i)

-0.01-0.02

-0.03

-0.01 -0.01

-0.020

0

0.010.01

0

-0.035

x/H

z/H

-1 0 1 2 30

0.5

1

1.5

2

Fig. 5: Normalised Reynolds stress < u′′w′′ > /U2 in the street canyon of AR 1 with (a) neutral, (b) weak, and

(c) strong heating; in the street canyon of AR 2 with (d) neutral, (e) weak, and (f) strong heating. Solid lines

represent positive value while dashed lines represent negative value.


(a)

0.01

0.05

0.10.15

0.2

0.250.3

0.125

0.025

0.0750.05

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

(b)

0.010.025

0.050.025

0.075

0.10.125

0.15

0.175

0.2

0.250.3

0.09

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

(c)

0.025

0.15

0.01

0.05

0.075

0.125

0.1

0.175

0.2

0.25

0.3

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

(d)

0.010.025

0.05

0.075

0.1

0.125

0.15

0.175

0.2

0.225

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

(e)

0.01

0.075

0.15

0.45

0.2

0.3

0.35

0.025

0.25

0.025

0.05

0.1

0.125

x/H

z/H

-1 -0.5 0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

(f)

0.010.025

0.05

0.075

0.10.1250.15

0.2

0.25

0.3

0.025

x/H

z/H

-1 -0.5 0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

Fig. 6: Normalised mean temperature (< θ > −θa)/∆θ in the street canyon of AR 1 with (a) weak and (b)

strong heating; in the street canyon of AR 2 with (c) weak and (d) strong heating; in the street canyon of AR

0.5 with (e) weak and (f) strong heating.


(a)

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

(b)

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

0.0180.0160.0140.0120.010.0080.0060.0040.0020

(c)

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

(d)

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

0.010.0090.0080.0070.0060.0050.0040.0030.0020.0010

(e)

x/H

z/H

-1 0 1 2 30

0.5

1

1.5

2

(f)

x/H

z/H

-1 0 1 2 30

0.5

1

1.5

2

0.020.0180.0160.0140.0120.010.0080.0060.0040.0020

-0.002

Fig. 7: Normalised heat flux < w′′θ′′ > /(U∆θ) in the street canyon of AR 1 with (a) weak and (b) strong

heating; in the street canyon of AR 2 with (c) weak and (d) strong heating; in the street canyon of AR 0.5 with

(e) weak and (f) strong heating.


(a)

12.5

5

15

20

40

50

60

10080

18030

30

10

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

(b)

12.5

5

10

15

20

2530

4050

12.5

100

7.5

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

(c)

10

1 2.5

5

15

12.5

20

25

3050

100

7.5

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

(d)

2.5

20

5

1

60

10

4050

90 10080

200

150

300 250

30

70

80

65

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

(e)

2.5

20

5

1

50

10

30

40

6070 80

100

90

20090

55

55

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

(f)

5

10

2.5

40

7.5

1

15

70

30 15

20

25

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

(g)

1

57.5

10

2.5

25

10050

10

x/H

z/H

-1 0 1 2 30

0.5

1

1.5

2

(h)

1

2.5

57.510

25 50

15

20

x/H

z/H

-1 0 1 2 30

0.5

1

1.5

2

(i)

1

2

2.5345

7.5

1050

2.5

x/H

z/H

-1 0 1 2 30

0.5

1

1.5

2

Fig. 8: Normalised pollutant concentration < c > UHL/Q in the street canyon of AR 1 with (a) neutral, (b)

weak, and (c) strong heating; in the street canyon of AR 2 with (d) neutral, (e) weak, and (f) strong heating;

in the street canyon of AR 0.5 with (g) neutral, (h) weak, and (i) strong heating.


(a)

0.25

0.75

1.25

1 0.750.5

0.25

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

(b)

0.5

1

1.5

1 0.75

0.5

0.25

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

(c)

0.75

1.52

1 0.750.5

0.25

1.25

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

(d)

0.250.50.751

0

0

0

0.25 0.5

0.75 1.25

0

0.250.5

1

0 0

0

0

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

(e)

0.250.5

0.751

0

0 0.250.50.75

12

0.75

1

2.5

1.5

0 0

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

(f)

0.25

0.50.751

0

0.25

0.5 0.25

1

1.52.5

0.75

0

1.25

0.15

0.15

x/H

z/H

-0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

(g)

0 0.25

0.5 0

0

0 0

0

00 0.25

-0.25

-0.750.5

x/H

z/H

-1 0 1 2 30

0.5

1

1.5

2

(h)

0 0.25

0.5 0

0

0.25

00.5

0.75

0

0

x/H

z/H

-1 0 1 2 30

0.5

1

1.5

2

(i)

0

0.25

0.75

0

0.25

00.5

0.75

0

0

0.5

1

x/H

z/H

-1 0 1 2 30

0.5

1

1.5

2

Fig. 9: Normalised pollutant fluxes < w′′c′′ > (HL/Q) in the street canyon of AR 1 with (a) neutral, (b) weak,

and (c) strong heating; in the street canyon of AR 2 with (d) neutral, (e) weak, and (f) strong heating; in the

street canyon of AR 0.5 with (g) neutral, (h) weak, and (i) strong heating.


c''

w''

Q1: Ejections

c'' > 0, w'' > 0

Q2: Outward interactions

c'' < 0, w'' > 0

Q3: Sweeps

c'' < 0, w'' < 0

Q4: Inward interactions

c'' > 0, w'' < 0

Fig. 10: Schematic diagram of quadrant analysis for < w′′c′′ >.


(a)

1 1.5

0.5

2

1.5

10.

51

33.

5

1.5 1

1.5

1.5

0.5

0.5

1

1.5

11.

5

0.51

2.5

1.5

x/H

z/H

-0.5

00.

51

1.5

0

0.51

1.5

(b)

1

2

0.5

1

1.5

0.5

1

1

1

11

1

2

2.5

1.5

2

3.5

3

0.5

0.5

0.5

1

1 1.5

1.5

x/H

z/H

-0.5

00.

51

1.5

0

0.51

1.5

(c)

1

2

0.5

2.5

1

1.5

0.5

1

1

11

1

1

2.5

1.5

1.51.5

2

3.5

3

0.5

0.5

0.5 1

1 1.5

1 x/H

z/H

-0.5

00.

51

1.5

0

0.51

1.5

Fig

.11

:R

atio

ofco

ntri

buti

onto<w

′′c′

′>

byej

ecti

ons

toth

atby

swee

ps,S

1/S

3,

inth

est

reet

cany

onof

AR

1.(a

)N

eutr

al;

(b)

wea

k;(c

)st

rong

heat

ing.


(a)

-1 -1.5

-1

-1-1.5

-0.5

-1

-1.5

-1

-0.5-0.25

-0.5

-0.25

-2

-0.25-0.5

-2-0.25

-1

-0.1

-0.5

-0.5

-0.25

-0.1

-1

x/H

z/H

-0.50

0.51

1.50

0.5 1

1.5

(b)

-1.5

-1 -0.5

-0.5

-1-1.5

-0.25

-2

-0.1

-0.5

-0.5

-0.25

-0.5

-0.1

-0.1

-2

-0.25

-0.25

-0.25

-0.05-1

-0.05

-0.1

x/Hz/H

-0.50

0.51

1.50

0.5 1

1.5

(c)

-1.5

-1 -0.5

-0.5

-1-1.5

-0.25

-2

-0.1

-0.5

-0.25

-0.25

-0.5

-0.05

-0.1

-2

-0.25

-0.1

-0.1

-0.05-1

x/H

z/H

-0.50

0.51

1.50

0.5 1

1.5

Fig.

12:E

xuberanceof<w

′′c ′′>

inthe

streetcanyon

ofA

R1.

(a)N

eutral;(b)

weak;

(c)strong

heating.