EXPERIMENTAL STUDY OF TURBULENCE AND VERTICAL TEMPERATURE PROFILE

IN THE URBAN BOUNDARY LAYER

Kono, H., Tamura, D. , Iwai, Y., Aoki, T., Watanabe, S., Nishioka, M.*, Ito, Y.**, Adachi, T. ***

University of Hyogo, * Osaka Prefecture University, **Kaijo Sonic Corporation, ***University of Yamanashi

Introduction• Recently, the dispersion of motor vehicle exhaust gas has been

predicted using the new generation models in urban areas (Valkonen et al.,1995, Werferi, 1995).

• The Monin-Obukhov similarity theory has often been used in the models.

• However, the similarity theory cannot be applied within the roughness sublayer. (Rotach, 1993).

• The reason why the similarity theory can not be applied in the roughness sublayer is not known.

• Since the mechanical turbulence generated by buildings is large in the lower part of the urban boundary layer, the turbulence in the roughness sublayer may deviate from the empirical formula at rural smooth sites.

• We studied the turbulence and vertical temperature profile in the lower part of the urban boundary layer by conducting the field observations in Himeji City, carrying out wind tunnel experiments and numerical simulations.

Urban area in Himeji city the site of a microwave-tower, tethered balloon and the

Doppler sodar

Doppler sodar

Meteorological station

72 m tower

N

5km0

tethered balloon

View from the tower looking north

NorthIn the north of the tower is a commercial area with buildings of 10 to 45 m in height.

南

South

In the south and east of the tower is a commercial and residential area with buildings of 7 to30 m in height.

View from the tower looking south

Instruments mounted on the 72 m tower

Sonic Anemometer 54 ｍ

southnorth

T 70m

T 60 m

T 4 0 m

T 18 m

T 4 m

50 Hz, 60 min

46 hours

April to August, 1996

Vertical temperature profileOne year

Thermistor thermometer (Espec RT-30S)

KAIJO SAT-550

Surface temperature

Infrared thermometer MR-40

turbulence

Summer

July 19, 2007　　　　 4： 00～ 11： 00　　　　　　

Measurement of vertical temperature at heights below 300 m

Using tethered balloon

Autumn November 8, 2007

　 5： 00～ 17： 30　　　　

At the park in the center of the city

0

50

100

150

200

250

300

5 7 9 11 13 15 17 19 21 23 25 27

θ (℃)

Z(m

)5 20 6 55： ～ ：

7 35 8 15： ～ ：

8 20 9 00： ～ ：

9 00 10 05： ～ ：

10 55 12 00： ～ ：

12 00 12 50： ～ ：

13 25 14 10： ～ ：

14 15 15 10： ～ ：

15 55 16 55： ～ ：

17 00 17 35： ～ ：

6

78

9

17 12

13

14

0

50

100

150

200

250

300

5 7 9 11 13 15 17 19 21 23 25 27

θ (℃)

Z(m

)5 20 6 55： ～ ：

7 35 8 15： ～ ：

8 20 9 00： ～ ：

9 00 10 05： ～ ：

10 55 12 00： ～ ：

12 00 12 50： ～ ：

13 25 14 10： ～ ：

14 15 15 10： ～ ：

15 55 16 55： ～ ：

17 00 17 35： ～ ：

6

78

9

17 12

13

14

Vertical profile of potential temperature and surface temperature in autumn (8 November, 2007)

RS

Lifted inversion layer

Neutral layer

Vertical profile of potential temperature and surface temperature in summer ( 19 July, 2007)

0

50

100

150

200

250

21 23 25 27 29 31 33θ (℃)

Z(m

)

5:00 6:00～

6:00 7:00～

7:00 8:00～

8:00 9:00～

9:00 10:00～

10:00 11:00～

11:00 12:00～

5

76

8

9

10

11

0

50

100

150

200

250

21 23 25 27 29 31 33θ (℃)

Z(m

)

5:00 6:00～

6:00 7:00～

7:00 8:00～

8:00 9:00～

9:00 10:00～

10:00 11:00～

11:00 12:00～

5

76

8

9

10

11

RS

Lifted inversion layer

unstable

B8 z- d=80m u=2.5m/ s σ w=0.47m/ s σ w/ u=0.19

- 3

- 2

- 1

0

1

2

3

8 383 758 1133 1508 1883

B8 z- d=140m u=3.6m/ s σ w=0.33m/ s σ w/ u=0.09

- 3

- 2

- 1

0

1

2

3

B8 z- d=190m u=2.7m/ s σ w=0.27m/ s σ w/ u=0.10

- 3

- 2

- 1

0

1

2

3

B8 z- d=240m u=2.5m/ s σ w=0.26m/ s σ w/ u=0.10

- 3

- 2

- 1

0

1

2

3w’(m/s)

u・t(m)

B13 z- d=80m u=3.0m/ s σ w=0.71m/ s σ w/ u=0.24

- 3

- 2

- 1

0

1

2

3

9 369 729 1089 1449 1809

B13 z- d=140m u=4.5m/ s σ w=0.47m/ s σ w/ u=0.10

- 3

- 2

- 1

0

1

2

3

B13 z- d=190m u=4.3m/ s σ w=0.62m/ s σ w/ u=0.14

- 3

- 2

- 1

0

1

2

3

B13 z- d=240m u=5.3m/ s σ w=0.82m/ s σ w/ u=0.15

- 3

- 2

- 1

0

1

2

3

u・t(m)

w’(m/s)

(a) 5:00- (b) 11:00-11:00 － 11:10

w' on 19 July (2007) measured by using Doppler sodar in Himeji city

Inversion layer

5:00 －5:15 Convective

turbulence

Neutral layer, RS

1000 m

1000 m

Summary results of turbulence measured at the towerat z = 54 m

Observation period: Apr. 1, June 12 – 15, Aug. 21, 24, 2006, n = 46

50 Hz, 60 min,

Wind directions: southern( SW – ESE)

Observed u*/u at the tower (z = 54m) in Himeji citywind direction: SW - ESE

Businger et al. 1971(rural)

n= 46

Under unstable conditions, turbulence transports momentum less effectively in urban areas than in rural areas.

Panofsky et al. 1977 (rural)

Roth, 2000 (urban)

Observed σw/u* at the tower (z = 54m) in Himeji city

u* mechanical turbulence

σw both mechanical and convective turbulence

u*/σw large mechanical turbulence large

σw/u*

-1-0.8-0.6-0.4-0.200.20.40.60.81

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

(m/s) Neutralw’

u’ (m / s)

-1

0

1

2

-3 -2 -1 0 1 2

(m/s) Unstable

Vectors (u’, w’) observed at the tower

z=54 m

(Kono and Koyaby, 2005)Oct. 21, 9:00 – 9:20

in 1993

Aug. 2, 12 :00 – 12:20

Strong upward convection

R = － 0.4

R = 0

-0.8

-0.4

0.0

0.4

0.8

12 15 18 21 19 21 0 3 6 9 11

ｈｒ

u'w'w'T'

Aug. 2

R

Rw’T’

Ru’w’

Momentum flux, temperature flux, correlation between u’ and w’ and correlation between w’ and T’ measured at the tower (z=54m)

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

11 15 21 19 21 1 3 9 11hr

u'w'(m2/ s2)

w'T'(K m/ s)･

Aug. 2

u’w

’ w

’T’

( m2 / s2 )

( K・m / s )

(Kono and Koyabu, 2005)

－ 0.3 < R(u’w’) < 0 unstable

Rural: - 0.35 < R(u’w’) < -0.2 (Kaimal and Finnigan, 1994)

R(w’T’) = 0.5 unstable (urban & rural)

Oct. 20 – 21, 1993

Urban: － 0.3 < R(u’w’) < 0

unstableRural: - 0.35 < R(u’w’) < -0.2 (Kaimal and Finnigan, 1994)

R(w’T’) = 0.5 unstable (urban & rural)

In urban areas, convective turbulence transports heat but transports momentum less effectively in unstable conditions.

Under unstable conditions, the eddy diffusivity at the lower part of urban boundary layer, is different from that calculated from the empirical formula at smooth sites using the Monin-Obukhov similarity theory.

Test section of the wind tunnel.

Re = 67,000

3m× 0.3 m× 0.3m

1.3 m s-1Wind speed

3m2.5m

Flow straightener

1.8 mm cube

x

z

18 mm cubes, in diamond arrays with 36 mm nearest-neighbour separation

U, -u’w’, σw, σu in the wind tunnel

00.20.40.60.8

11.21.41.61.8

2

- 7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3- u'w'/ u*

2

(z-d)

/δ

(x)

x=67cmx=167cmx=267cmRaupach data

0 1 2 0 1 2

0

5

10

15

20

25

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

U/ U∞

z-d

(cm

)

x=67cmx=167cmx=267cm

0 0.5 1 1.5 0 0.5 1 1.5

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 1 2 3 4 5 6

σ w/ u* (m/ s)

(z-d)

/δ

(x)

x=67cmx=167cmx=267cmRaupach data

0 1 0 1

Raupach, M. R. (1981) Conditional statistics of Reynolds stress in rough-wall and smooth-wall turbulent boundary layers

δ

00.20.40.60.8

11.21.41.61.8

2

0 2 4 6 8 10 12σ u/ u*

(z-d)

/δ

(x)

x=67cmx=167cmx=267cmRaupach data

0 2 0 2

Eddy size λ which has maximum energy in the wind tunnel λ = U / 2 n , d = h = 1.8 cm

RS

IS

Scaled with obstacle size

Scaled with height

LES was used to predict turbulent flow

in the roughness sublayer. • Adaptive research - CFD 2000

• Computational domain: (100 times as large as those in the wind tunnel) streamwise 150 m, span wise 22 m, normal direction 12 m grid spacing 0.33 m. 450×66×26 cells.

• Boundary conditions:　　 The lower boundary: The 1.8 m cubes were placed in diamond

arrays. 　　 The lower boundary and the surface of cubes : the logarithmic

wind profile wall function for a smooth surface　　 The upper and the both side boundary : free slip 　　 The inlet wind speed: 5 m s-1 (uniform)

Side view of calculated vorticity (ωx, ωy)

x

z

ωy

1.5

-1.5

1.5

-1.5

ωx

ω y

ω x

Streamwize vorticity

Spanwise vorticity

At y = 11 m (center)

x

z

View from the topωy, ωx

ωx

ωy

x

z

x

y

y

z

At z / h = 2.5

CONCLUSION In the upper RS, u* / u under unstable conditions, were close to

that under neutral conditions.

These values showed large deviations from the empirical formula presented by Businger et al.(1971) which fitted observations at rural smooth sites.

Therefore, under unstable conditions, turbulence transports momentum less effectively in urban areas than in rural areas.

Ｉ n the RS, the size of eddies having maximum kinetic energy

is scaled with the obstacle size, in the IS, it is proportional to the height. They were shown in the wind tunnel.

LES showed that eddies in the RS were directly generated by

cubes like wakes and they were transported downwind. The eddy structure in the RS is expected to be different from that

in the IS.

Thank you for your attention!

A visualization of the urban boundary layer and U, -u’w’/ u*2,

σw/u*, σu/u* in the wind tunnel. wind

36mm

wind

36mm36mm36mm

0

5

10

15

20

25

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

U/ U∞

z-d

(cm

)

x=67cmx=167cmx=267cm

0 0.5 1 1.5 0 0.5 1 1.5

00.20.40.60.8

11.21.41.61.8

2

0 2 4 6 8 10 12σ u/ u*

(z-d)

/δ

(x)

x=67cmx=167cmx=267cmRaupach data

0 2 0 2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 1 2 3 4 5 6

σ w/ u* (m/ s)

(z-d)

/δ

(x)

x=67cmx=167cmx=267cmRaupach data

0 1 0 10

0.20.40.60.8

11.21.41.61.8

2

- 7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3- u'w'/ u*

2

(z-d)

/δ

(x)

x=67cmx=167cmx=267cmRaupach data

0 1 2 0 1 2

Vertical profile of potential temperature and surface temperature in summer ( 19 July, 2007) and autumn

(8 November, 2007) in an Urban area of Himeji City

(a)Summer

0

50

100

150

200

250

21 23 25 27 29 31 33θ (℃)

Z(m)

5:00 6:00～

6:00 7:00～

7:00 8:00～

8:00 9:00～

9:00 10:00～

10:00 11:00～

11:00 12:00～

5

76

8

9

10

11

0

50

100

150

200

250

21 23 25 27 29 31 33θ (℃)

Z(m)

5:00 6:00～

6:00 7:00～

7:00 8:00～

8:00 9:00～

9:00 10:00～

10:00 11:00～

11:00 12:00～

5

76

8

9

10

11

0

50

100

150

200

250

300

5 7 9 11 13 15 17 19 21 23 25 27

θ (℃)

Z(m

)

5 20 6 55： ～ ：

7 35 8 15： ～ ：

8 20 9 00： ～ ：

9 00 10 05： ～ ：

10 55 12 00： ～ ：

12 00 12 50： ～ ：

13 25 14 10： ～ ：

14 15 15 10： ～ ：

15 55 16 55： ～ ：

17 00 17 35： ～ ：

6

78

9

17 12

13

14

0

50

100

150

200

250

300

5 7 9 11 13 15 17 19 21 23 25 27

θ (℃)

Z(m

)

5 20 6 55： ～ ：

7 35 8 15： ～ ：

8 20 9 00： ～ ：

9 00 10 05： ～ ：

10 55 12 00： ～ ：

12 00 12 50： ～ ：

13 25 14 10： ～ ：

14 15 15 10： ～ ：

15 55 16 55： ～ ：

17 00 17 35： ～ ：

6

78

9

17 12

13

14

(b) Autumn

RSRS

Lifted inversion layer

unstable

Instruments

• Sonic anemometer: KAIJO SAT – 550, 10Hz, 60 min• Temperature: at height 4 m, 18 m, 40 m, 60 m, 70 m• for one year• thermistor thermometer (Espec RT-30S)

• Surface temperature: infrared thermometer Eko Instruments Co. MR-40

• Doppler Sodar: KAIJO KPA200: sampling interval 3 s