cites 2005, novosibirsk modeling and simulation of global structure of urban boundary layer...

CITES 2005, Novosibirsk

Modeling and Simulation of Global Structure of Urban Boundary Layer

Kurbatskiy A. F.Institute of Theoretical and Applied Mechanics of

SB RAS, Novosibirsk, Russia


O U T L I N E:

Motivation

Introduction

Urban Boundary Layer

Improved Model for the Turbulent ABL

Urban Heat Island in a Calm and Stably Stratified Environment

Impact of UHI on the Global Structure of the ABL

Impact of the UHI and the UCL on the ABL Structure

Conclusions


Motivation

The aim of lecture consists in a statement of the improved turbulence model for the urban boundary layer and results of its verification in the simple 2D cases.


Introduction

●Complexity of simulation of urban air quality problems consists in the necessary of resolution the variety spatial-temporal scales over which the phenomena proceed.

●The two most important scales include: an 'urban' scale of a few tens kilometers (a

typical scale of city) where large amounts of contaminants are emitted, and

a 'меsо' scale of a few hundreds of kilometers where secondary contaminants are formed and dispersed.


Introduction● In order to compute the mean and turbulent

transport and the chemical transformations of pollutants, several meteorological variables, such as wind, turbulent fluxes, temperature etc., it is necessary to known as more as possible precisely.

These meteorological variables can be calculated by an improved model for the turbulent ABL.

● The two most important effects of the urbanized surface have an influence on the air flow structure:

Differential heating of the urbanized surfaces which can generate the so-called urban heat island effect.

Drag due to buildings.


The development of ABL over flat terrain

The development of ABL over flat terrain

The potential temperature θ and wind velocity U are shown forthe convective and stable boundary layers.


Urban Boundary Layer


Improved Turbulence Model for the ABL


12 ;i

i ijk j kj i

ij

DU Pg U

Dt x x

,jj

D

Dt xh

ij i jτ < u u > is th e Reynolds stress

i ih < u θ > is the heat f lux

.

GOVERNING EQUATIONS FOR TURBULENT PBL


Turbulence equations

ijijijjiijijij ПhhPDDt

D

k

ijk

k

jikij x

U

x

UP

kk

iji

jj

iij pux3

2

x

pu

x

puП

ijk

j

k

iij 3

2x

u

x

u2

ii g

kijkji

kij pu

3

2uuu

xD

,Пxx

UhD

Dt

Dhi

2i

jij

j

ij

hi

i

,x

pП

ii

jij

hi uu

xD

i jReynolds stress, u u ij

i iHeat flux, h u θ


An updated expressions for the pressure-velocity Пij (= Пij

(1)+ Пij(2)+ Пij

(3)) and the pressure-temperature

Пiθ (= Пiθ(1)+ Пiθ

(2)+ Пiθ(3)) correlations

Mellor-Yamada model (1982, Mellor, 1973):

Пij(1)=Cτ-1bij

Пij(2)~-ESij most of rapid terms are neglected

Пij(3)=0 no buoyancy effects are included

Пiθ(1)=C1θhi, Пiθ

(2)=0, Пiθ(3)=C3θβ<θ2>,

(E=1/2<uiui> is TKE; Sij=(Ui,j+ Uj,i)/2)


An updated expressions for the pressure-velocity Пij (= Пij

(1)+ Пij(2)+ Пij

(3)) and the pressure-temperature Пiθ (= Пiθ

(1)+ Пiθ(2)+ Пiθ

(3)) correlationsLaunder’s model (1975)

Present model (2001)

Пij(1)= C1τ-1bij

Пij(2) =-4/3C2ESij - C2(Zij+Σij)

Пij(3) = C3Bij

Пiθ(1) = C1θ τ

-1hi , Пiθ

(2) =-C2θhjUi,j , Пiθ

(3) = C3θβi<θ2>

Σij=bikSij+Sikbkj-2/3δijbkmSmk;

The model constants of Пij are

C1, C2, C3, C1θ, C2θ= C3θ

Zeman and Lumley model (1979)

Canuto et al. model (2002) Пij

(1)= C1τ-1bij

Пij(2)=-4/5ESij - α1Σij- α2Zij

Пij(3) =(1-β5)Bij

Пiθ(1) = C1θ τ

-1hi , Пiθ

(2) =-3/4α3(Sij+5/3Rij) hj , Пiθ

(3) =γ1βi<θ2>

Zij=Rikbkj-bikRkj; Bij=βihj+ βjhi- 2/3δijβkhk


Level-3 Algebraic Models for Reynolds Stress and Scalar Fluxes

ij3ijij2ij1ij BSEb

ijijijijijijij ПBSE3

40Db

Dt

D

,Пxx

Uh0D

Dt

Dhi

2i

jij

j

ij

hi

i

2

3i4j

ijijjij gx

E3

2bhA

Coupled algebraic system equations for and jiuu :uh ii


Level-3 Fully Explicit Algebraic Models for

Reynolds Stress and Scalar Fluxes : 2D case

, ,M

U Vuw vw K

z z

H cw Kz

M MK E S

H HK E S

2 22 6 5

1 21 ( )

3c M HG s G gD

2

HG N 2

MG S2N g

z

2 22 U V

Sz z

HHM62H5

2H4HM3H2M1 G)GGdGd(GdGGdGdGd1D

E

E/gGs1

ssGssGs1s

D

1S

2H6

54H32H10M

6

1

1 2 11

3H HS s GD c


Three-parametric turbulence model

:uu)2/1(E,)TKE(energykineticTurbulent ii

2Temperature var iance , :

,hx

UD

2

1

Dt

DEii

j

iijii

,E

DDt

D 2

,x

Uh

E2h

x

Ub

j

iij3i

i2

j

iij10

jj ux/D E3/2uub ijjiij

,2x

h2DDt

D

ii

2

2

2jx/

2ii ux/D

i

2

Eiii x

EEc

xD

2

1

i

2

aia x

aEc

xD

2,a

,2

2

ER

E2R

2

TKE dissipation,


Air Circulation above an Urban Heat Island

in a Calm and Stably Stratified Environment


Air Circulation above an Urban Heat Island


Thermal circulation above an urban heat island

Experiment

of Lu et al. (JAM.1997.V.36)

Computation by three-parametric

turbulence model

(Kurbatskii A.

JAM. 2001. V.40)


(A. F. Kurbatskiy, J. Appl. Meteor. 2001. V. 40. №10)

26.5 26.5

27

27.5

28

28

28

28

.5

28.5

28

.5

29

29

29

29

29 29

29.5

29.5

29.5

29.5

30

30

30

30.530.5

3131

31.531.5

3232

32.532.5

30

33 33

28.5

32.5

32

27.5

27

2626

28

r / D

Z/Z

i

-1.5 -1 -0.5 0 0.5 1 1.50

0.5

1

1.5


Dispersion of passive tracer above UHI in a Calm and Stably Stratified Environment

0.2

0

0.05

0.2

0

0.150.15

0.15 0.150.100.10

0.05

r / D

Z/Z

i

-1.5 -1 -0.5 0 0.5 1 1.5

0.5

1

1.5


Impact of a Urban Heat Island on

the Global Structure of the ABL


2D case: Computational domain

wind

0

5Z , km

45 55 120 X, km

urban heat island

Synoptic flow


1.0

2.0

X, km

Z,k

m

40 60

0.5

1

1.5

2

2.5

0

UG=1 m/sat 1200 LST

Vertical section of horizontal wind speed (UG=1ms-1)

Vertical section of potential temperature and horizontal wind speed

UG=3 ms-1

UG=5 ms-1

( a ) ( b )

( c )

0.8

1.8

1.8

1.8

2.3

2.3

2.3 2.3

2.8

2.8

2.8

2.8

2.8

3.0

3.0

3.0

3.0

3.0

3.0

3.3

2.8

3.8

3.3

2.3

3.3

X (km)

Z(k

m)

20 40 60 80 100 120

0.5

1

1.5

2

2.5UG=3ms-1

3.5

3.5

3.5

3.5

4.0

4.0

4.0

4.0

4.0

4.5

4.55

.0

5.05.0

5.5

6.06.0

6.5

7.07.0

7.57.5

8.08.0

8.58.5

4.5

4.5

6.5

5.5

3.5

X (km)

Z(k

m)

20 40 60 80 100 120

0.5

1

1.5

2

2.5UG=3ms-1

3.5

3.0 3.0

3.0

3.0

3.5

3.5

3.5

3.5

4.0

4.0

4.5

4.5

4.5

4.5

5.0

5.05.0

5.55.5

6.06.06.56.5

7.07.07.0

7.57.58.08.0

8.58.5

4.0

4.0

4.5

3.5

3.54.0

X (km)

Z(k

m)

20 40 60 80 100 120

0.5

1

1.5

2

2.5UG=5ms-1

1.82.1 2.12.4 2.42.7

2.73.0

3.0

3.3

3.3

3.3

3.6 3.6

3.63.9

3.9

3.9

3.94.2

4.2

4.24.5

4. 5

4.5

4.54.8

4.8

4.8

4.8

5.1

5.1

5.4

X (km)

Z(k

m)

20 40 60 80 100 120

0.5

1

1.5

2

2.5UG=5ms-1


Velocity vectors and isotachs of vertical speed at 12:00 LST

-0.1-0

.2

0.21. 0

0.50.7

-0.1

X ,km

Z,k

m

40 50 60

0.5

1

1.5

2

0

UG=3 ms-1


Vertical section of potential temperature and horizontal wind speed

UG=3 ms-1

UG=5 ms-1

( a ) ( b )

( c )

0.8

1.8

1.8

1.8

2.3

2.3

2.3 2.3

2.8

2.8

2.8

2.8

2.8

3.0

3.0

3.0

3.0

3.0

3.0

3.3

2.8

3.8

3.3

2.3

3.3

X (km)

Z(k

m)

20 40 60 80 100 120

0.5

1

1.5

2

2.5UG=3ms-1

3.5

3.5

3.5

3.5

4.0

4.0

4.0

4.0

4.0

4.5

4.55

.0

5.05.0

5.5

6.06.0

6.5

7.07.0

7.57.5

8.08.0

8.58.5

4.5

4.5

6.5

5.5

3.5

X (km)

Z(k

m)

20 40 60 80 100 120

0.5

1

1.5

2

2.5UG=3ms-1

3.5

3.0 3.0

3.0

3.0

3.5

3.5

3.5

3.5

4.0

4.0

4.5

4.5

4.5

4.5

5.0

5.05.0

5.55.5

6.06.06.56.5

7.07.07.0

7.57.58.08.0

8.58.5

4.0

4.0

4.5

3.5

3.54.0

X (km)

Z(k

m)

20 40 60 80 100 120

0.5

1

1.5

2

2.5UG=5ms-1

1.82.1 2.12.4 2.42.7

2.73.0

3.0

3.3

3.3

3.3

3.6 3.6

3.63.9

3.9

3.9

3.94.2

4.2

4.24.5

4. 5

4.5

4.54.8

4.8

4.8

4.8

5.1

5.1

5.4

X (km)

Z(k

m)

20 40 60 80 100 120

0.5

1

1.5

2

2.5UG=5ms-1


Height of boundary layer

X (km)

Z(k

m)

20 40 60 80 100 120

0.5

1

1.5

2

2.5

32

1

0

1-UG =1m/sec

2-UG=3 m/sec

3-UG=5 m/sec

Height of boundary layerat 1200 LST

city


Height of boundary layer

3.5

3.5 4.0

4.0

4.0

4.0

4.5

5.05.0

5.55.5

6.06.0

6.56.5

7.07.0

7.57.5

8.08.0

8.58.58.5

3.5

4.0

4.5

X (km)

z(k

m)

20 40 60 80 100 120

0.5

1

1.5

2

2.5

0

No longitudinal diffusion of heat

5.5

6.0

6.5

7.0

7.5

8.0

8.5

4.0

4.0

5.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

8.0

8.5

3.5

3.5

4.0

4.5

5.0

4.5

4.5

3.5

X (km)

Z(k

m)

20 40 60 80 100 120

0.5

1

1.5

2

2.5

0

With longitudinal diffusion of heat

wzz

Wx

Ut

x

<u


Impact of the UHI and the UCL on the Mesoscale Flow


Typical Flat Urban Modeling Domain


Parameterization of Urban Roughness

wind

The concept of incorporation of urbancanopy model

( b )

wind

( a )

Scheme of the numerical grid in the urbanarea by Kondo et al. (1998)

Scheme of the numerical grid in the urbanarea by Martilli (2002)


Governing Equations for UBL

2D case:0,x zU W

1,t x z zxU UU WU fwP Vu

uD

,t x zzV UV WV fUwv vD

0

21,t x z z z

W UW WW wP g

.t x z x zuU W w θD


Turbulent fluxes

H c

∂Θ= +

∂K

zw θ -

M

∂U ∂V=- ,

∂z ∂zKuw , vw

M MK =E S H HK =E S

2 22 6 5

1 21 ( )

3 M HG s G gD

c is the countergradient term

2

20 1 2 3 4 5 6

11 1 ( )M H H HS s s G s s G s s s G g

D E

61

1 2 11

3H HS s GD c

2,HG N 2

,MG S

2 ,N gz

2 2

2 U VS

z z

2 21 2 3 4 5 61 M H M H H H M H HD d G d G d G G d G d G d G G G

1 2 3 1 2, ( 1,...,6) ( , , , , )i id s i arethe functionsof c c c c c

/E


Three-parametric turbulence model

,,2μ E i i ii ii jj i+ (c /σ )(E /ε)E, , = Uu u u tE, ED

22( / )( / ) , , ˆ

E i ic EE tε, εD

0 1 2 3

2( )i iij

i ii

jj j

bu u

U E U

x x

2 2( / )( / ) , , 2 , 2 ,E i i iiE uc 2tθ ,

( , , , ) .iA U E are the extra terms in urban areas AD


Parameterization of Effects of Urban Surfaces on the Airflow

[Raupach et al.(1991), Raupach (1992), Vu et al.(2002), Martilli (2002)]

The extra terms DA in the Governing Equations are:

DU = turbulent momentum flux (roofs and canyon floors) +

drag (vertical walls)

Dθ = turbulent fluxes of sensible heat from roofs and the canyon floor +

the temperature fluxes from the walls

DE = increasing of conversion of mean kinetic energy into the TKE

[ by as, for example, Raupach and Shaw (1982)]

a ‘second’ dissipation linked with the scale

of turbulence L=L(z) induced by the presence

of the buildings

pε 0.ˆ ( 7)c 1/2

ε pε

ED c

Lε


Results of Simulation


Vertical section of potential temperature and horizontal wind speed at 1200 LST

UG=3 ms-1

UG=5 ms-1

3.0

3.5

3.53.5

4.0

4.0

4.54.55.0

5.55.5

6.06.0

6.56.5

7.07.0

7.57.58.08.0

8.58.5

4.03.5

4.5

4.0

3.5

6.5

X, KM

Z,K

M

20 40 60 80 100 120

0.5

1

1.5

2

2.5a)

0

3.0

3.0

3.5

4.0

4.0

4.0

4.5

4.54.5

5.05.05.55.5

6.06.06.56.5

7.07.0

7.57.57.5

8.08.0

8.58.5

3.5 3.53.0

3.0

5.0

6.5

6.0

8.5

4.0

4.0

3.0

3.5

5.0

3.5

X, KM

Z,K

M

20 40 60 80 100 120

0.5

1

1.5

2

2.5

0

c)

2.5

2.5

2.5

2.5

3.0

3.03

.0

3.0

3.0

3.0

3.5

3.5

3.5

3.5

4.0

3.0

2.01.5

2.0

3.0

2.5

4.0X,KM

Z,K

M

20 40 60 80 100 120

0.5

1

1.5

2

2.5

0

b)

2.0 2.5

3.03.54.0

4.5

4.5

4.5

4.5

4.5

5.0

5.0 5.0

5.0

5.0

5.0

5.0

5.0

5.5

6.0

X,KM

Z,K

M

20 40 60 80 100 120

0.5

1

1.5

2

2.5

0

d)


Vector field of horizontal wind speed and isotachs of vertical velocity for 12:00 LST

0.2

0.2

0.6

0.8 -0

.2

-0.2

-0.3

X , KM

Z,K

M

40 50 60

0.5

1

1.5

2

2.5

UG=3ms-1


Vector field of horizontal wind speed and isotachs for vertical velocity for 12:00 LST

-0.1

0

0.1

0

-0.07

0.1

5

0.1

3

-0.0

7

X, KM

Z,K

M

40 50 60

0.5

1

1.5

2

2.5

UG=5ms-1


Vertical section of potential temperature and horizontal wind speed at 1200 LST

UG=3 ms-1

UG=5 ms-1

3.0

3.5

3.53.5

4.0

4.0

4.54.55.0

5.55.5

6.06.0

6.56.5

7.07.0

7.57.58.08.0

8.58.5

4.03.5

4.5

4.0

3.5

6.5

X, KM

Z,K

M

20 40 60 80 100 120

0.5

1

1.5

2

2.5a)

0

3.0

3.0

3.5

4.0

4.0

4.0

4.5

4.54.5

5.05.05.55.5

6.06.06.56.5

7.07.0

7.57.57.5

8.08.0

8.58.5

3.5 3.53.0

3.0

5.0

6.5

6.0

8.5

4.0

4.0

3.0

3.5

5.0

3.5

X, KM

Z,K

M

20 40 60 80 100 120

0.5

1

1.5

2

2.5

0

c)

2.5

2.5

2.5

2.5

3.0

3.03

.0

3.0

3.0

3.0

3.5

3.5

3.5

3.5

4.0

3.0

2.01.5

2.0

3.0

2.5

4.0X,KM

Z,K

M

20 40 60 80 100 120

0.5

1

1.5

2

2.5

0

b)

2.0 2.5

3.03.54.0

4.5

4.5

4.5

4.5

4.5

5.0

5.0 5.0

5.0

5.0

5.0

5.0

5.0

5.5

6.0

X,KM

Z,K

M

20 40 60 80 100 120

0.5

1

1.5

2

2.5

0

d)


Vertical section of potential temperature and horizontal wind speed(3 ms-1) for simulation at 1200 LST

Present computation

Computation

of Martilli

(JAM,2002,V.41,1

247-1266)

3.0

3.5

3.53.5

4.0

4.0

4.54.55.0

5.55.5

6.06.0

6.56.5

7.07.0

7.57.58.08.0

8.58.5

4.03.5

4.5

4.0

3.5

6.5

20 40 60 80 100 120

0.5

1

1.5

2

2.5a)

0

Z , km

km

2.5

2.5

2.5

2.5

3.0

3.03

.0

3.0

3.0

3.0

3.5

3.5

3.5

3.5

4.0

3.0

2.01.5

2.0

3.0

2.5

20 40 60 80 100 120

0.5

1

1.5

2

2.5

0

b)

Z , km

km


Vertical section of potential temperature and

horizontal wind speed

UG=3 ms-1

UG=3 ms-1

2.5

2.5

2. 5

2.5

3.0

3. 0

3.0

3.0

3.0

3.0

3.5

3.5

3.5

3.5

3.5

3.5

4.0

4.0

3.0

1.5

2.54

.0

X, KM

Z,K

M

20 40 60 80 100 120

0.5

1

1.5

2

2.5

0

b)

1.3

1.3

1.3

1.8

1.8

1.8

2.3

2.3

2.3

2.8

2.8

2.8

2.8

2.8

2.8

3.3

3.3

3.3

3.33

.33

.33

.3

3.8

3.84.3

1.32.3

X,KM

Z,K

M

20 40 60 80 100 120

0.1

0.2

0.3

0.4

0.5

0

d)

4.04.5

5.0

5.0

5.55.55.0

4.5

3.5 3.54

.0

3.54.0

3.5

4.5

6.0 6.0

6.5 6.5

7.0 7.0

7.5 7.5

8.0 8.0

8.58.5

4.0

X, KM

Z,K

M

20 40 60 80 100 120

0.5

1

1.5

2

2.5

0

a)

12:00 LST

5.0

5.0

4.54.5

4.0 4.03.53.5

4.5

4.0

4.5

X, KM

Z,K

M

20 40 60 80 100 120

0.1

0.2

0.3

0.4

0.5

0

c)

24:00 LST


Temperature field above the city

3.0 3.03.54.0

4.5

4.5

4.5

5.0

4.0

4.3

3.8

4.34.3

3.8

4.8

4.8

4.8

4.5

3.5

4.03.8

X, km

Z,k

m

20 40 60 80 100 120

0.1

0.2

0.3

0.4

0.5

0

UG=3ms-1 24:00 LST

Temperature field avove the city


The Vertical Temperature Profiles

Temperature, 0K

Z,k

m

2 3 4 5 6 70

0.1

0.2

0.3

1200 LST

2400LST1200LST

2400LST

blue lines are at the city centerred lines are out the city


Vertical section of potential temperature and

horizontal wind speed

UG=3 ms-1

UG=3 ms-1

2.5

2.5

2. 5

2.5

3.0

3. 0

3.0

3.0

3.0

3.0

3.5

3.5

3.5

3.5

3.5

3.5

4.0

4.0

3.0

1.5

2.54

.0

X, KM

Z,K

M

20 40 60 80 100 120

0.5

1

1.5

2

2.5

0

b)

1.3

1.3

1.3

1.8

1.8

1.8

2.3

2.3

2.3

2.8

2.8

2.8

2.8

2.8

2.8

3.3

3.3

3.3

3.33

.33

.33

.3

3.8

3.84.3

1.32.3

X,KM

Z,K

M

20 40 60 80 100 120

0.1

0.2

0.3

0.4

0.5

0

d)

4.04.5

5.0

5.0

5.55.55.0

4.5

3.5 3.54

.0

3.54.0

3.5

4.5

6.0 6.0

6.5 6.5

7.0 7.0

7.5 7.5

8.0 8.0

8.58.5

4.0

X, KM

Z,K

M

20 40 60 80 100 120

0.5

1

1.5

2

2.5

0

a)

12:00 LST

5.0

5.0

4.54.5

4.0 4.03.53.5

4.5

4.0

4.5

X, KM

Z,K

M

20 40 60 80 100 120

0.1

0.2

0.3

0.4

0.5

0

c)

24:00 LST


Vertical profiles of ‘local’ friction velocity

u* / u*max

Z/Z

H

-1 0 1 2 30

1

2

3

4

5

6

7

1 2

Rotach M.

Oikawa and Meng

Feigenwinter C.

UG=3 ms-1

UG=5 ms-1

Real scale data

Computation

1/ 42 2

*u uw vw


Verticals profiles of ratio u*/U

u* / U

Z/Z

H

0 0.05 0.1 0.15 0.2 0.25 0.3 0.350

1

2

3

4

5

6

7

1 2

Real scale datafrom Roth (2000)

Computation:UG=3ms

-1

UG=5ms-1


Vertical profiles of TKE in the centre city

+ ++

++

E / (u* max)2

Z/Z

H

0 1 2 3 4 5 6 7 80

1

2

3

4

5

+

1

4

2

3

UG=3ms-1

UG=5ms-1

Rotach(1993)

Oikawa, Meng(1995)

Feigenwinter (1999)

Louka et al.(2000)

Computation:1,3 - at 1200 LST2,4 - at 2400 LST

Observations data:


Turbulent kinetic energy, 2 -2m s

0.39

0.39

0.39

1.16 1.16

1.16

1.16

1.16

1.931.93

1.93

1.93

1.93

1.93

2.7

1

2.71

2.71

2.71

3.48

3.48

3.4

8

4.2

5

4.25

4.25

5.03

5.03

5.03

5.80

X, km

Z,k

m

20 40 60 80 100 120

0.5

1

1.5

2

2.5

UG=3ms-1

12:00 LST


0.2

0.2

0.6

0.8 -0

.2

-0.2

-0. 3

X , KM

Z,K

M

40 50 60 70 80 90 100

0.5

1

1.5

2

2.5

UG=3ms-1


CONCLUSIONS■ Using the updated expressions for the pressure-velocity

and pressure-temperature correlations, we have derived an improved turbulence model to describe the Urban Boundary Layer.

■ In simple 2D case are investigated the modifications in global structure of the ABL caused by the Urban Heat Island and the Urban Canopy Layer.

■ The comparison between computed results and field observational data on various integrated turbulent characteristics reveals that the improved model can simulate the turbulent transport processes within and above the building canopy with satisfactory accuracy.

cites 2005, novosibirsk modeling and simulation of global structure of urban boundary layer...

Documents

present model

lumley model

model constants of ij

urban scale

ij1 ij2 ij3

bij ij2

pressurevelocity ij

pressuretemperature