Sogachev Andrey

Wind Energy Division, Risø National Laboratory for Sustainable Energy , DTU, Building 118, Box 49, DK-4000, Roskilde, Denmark, anso@risoe.dtu.dk

SCADIS (scalar distribution) model: overview

(Sogachev et al., 2002, 2004; Sogachev and Panferov, 2006; Sogachev et al., 2008, Sogachev 2009)

Basic equations:

momentum, heat,moisture,scalars (CO2, SO2, O3), turbulent kinetic energy (E)

One-and-a-half-order turbulence closurebased on equations of E and ε (dissipation rate) : ( E-l, E-ε.)

E-ω closure based on ω (ε/E) equation

Terrain-following coordinate system

Horizontal and vertical resolutions (depending on a specific problem)

SCADIS model: domain

q(t),T(t), C(t), V(t), U(t)

Clouds ( t )

T ( soil ), q ( soil ), FCO2

( soil ), V = 0 , U = 0

Q0

( t),

l o w e r b o u n d a r y c o n d i t i o n s

3 - 5 km

1 - 10 km

Upper boundary conditions

(Sogachev et al., 2002, 2004; Sogachev and Panferov, 2006; Sogachev et al., 2008, Sogachev 2009)

SCADIS model: physical processes in the model grid-cell

FCO2

E R H

G

y

f

x

f

¶

¶

¶

¶,

10 - 100 m

advection

yf

xf

¶¶

¶¶ ,

(Sogachev et al., 2002, 2004; Sogachev and Panferov, 2006; Sogachev et al., 2008, Sogachev 2009)

Turbulence model: governing equations

.0¶¶

i

i

xU

0

12 j ii ij ijk j k

j i j

u uU U PU Ut x x x

¶¶ ¶ ¶

¶ ¶ ¶ ¶

¶¶

¶¶

i

j

j

iijji x

UxUKEuu

32

¶¶

¶

¶¶

¶¶

¶

EiEij

j PxEK

xxEU

tE

j

ijiE x

UuuP¶¶

iiuuE 21

lEC

2343

EL PC

Eu 21

22 24

1 3 2 3Lu u u u u

iii uUU with

1 2jj i i

KU C P Ct x x x E

¶ ¶ ¶ ¶ ¶ ¶ ¶ ¶

( , , )K f C E

( , , )l f C E

, ,El with

2

1 22 1

kC C C

Accounting for plant drag and buoyancy: the traditional way

' 'vv

gB w

0

12 j ii ij ijk j k

ji

j i

u uU U PU Ux x x

St

¶¶ ¶ ¶

¶ ¶ ¶ ¶

( Raupach and Shaw, 1982 )( ) ,i d iS c A z U U

?

j i

di

pjE

E E K EU P Bt x x x

S S

¶ ¶ ¶ ¶ ¶ ¶ ¶ ¶

*1 3 52 4 p dj

j i i

KU P C Bt x x

C C S C SE

Cx E

¶ ¶ ¶ ¶ ¶ ¶ ¶ ¶

1 2*1 1 max( ) /C C C C l l

( Apsley and Castro, 1997)

max 0.00027 g Cl U f (Blackadar, 1962)

Modelling of Askervein flow

Askervein Hill topographic map (brawn isolines) and dimensionless speed-up, ΔS estimated by SCADIS at z = 10 m above the ground (colored field). Figure 1 also shows the reference site (RS) (with ΔS = 0 ), the 210o wind direction in our simulations and the lines A, AA and B along which the measurements were made. Background of Figure 1 is taken from Castro et al., 2003.

Modelling of Askervein flow

Dimensionless speed-up, ΔS at z = 10 m above the ground along lines A (a) and AA (b). During measurements along line AA two different sets of instruments were used.

(a) (b)

Uncertainties: buoyancy

3 EB C BE

(Baumert and Peters, 2000)

?j Ej i E i

E E K EU Pt x x x

¶ ¶ ¶

¶ ¶ ¶ ¶ ¶

2ECK ES

ECK

2

1 2 ?j Ej i i

KU C P Ct x x x E

¶ ¶ ¶

¶ ¶ ¶ ¶ ¶

1

2

0 CCPE

( Ayotte et al., 1999 )

(Sogachev and Panferov., 2006)

Uncertainties: dissipation

Accounting for plant drag and buoyancy: the revised way

' 'vv

gB w

0

12 j ii ij ijk j k

ji

j i

u uU U PU Ux x x

St

¶¶ ¶ ¶

¶ ¶ ¶ ¶

( Raupach and Shaw, 1982 )( ) ,i d iS c A z U U

1 2*1 1 max( ) /C C C C l l ( Apsley and Castro, 1997) max 0.00027 g Cl U f

0dpS

jj i E i

S

E E K EU P Bt x x x

¶ ¶ ¶ ¶ ¶ ¶ ¶ ¶

*1 2 1 2

*dj

j i i

KU P C C Bt x x x E E

C C S

¶ ¶ ¶ ¶ ¶ ¶ ¶ ¶

*15 2C CC *

13 2C CC 4 0C

1/ 212 ( )dd C cS A z U E (Sogachev and Panferov, 2006 )

(Blackadar, 1962)

(Sogachev 2009 )

dpS S (Seginer et al., 1976)

Accounting for plant drag and buoyancy: the revised way

... ?E Pt

¶

¶

... ? ? ?E Pt

¶

¶

*1 2? ?... P

t EC C

¶

¶

2*1

*21 ?

... PCt E

CC

C

E

¶

¶

2

2

1

2*

1

*

1

...

( )B d

P CCt E

C B a a SE

C

¶

¶

Treatment of the plant drag

a)

0 6 12

z / h

0

5

10

c)

0 3 6

b)

-1.0 -0.5 0.0

d)

| U | / u*

0 3 6

z / h

0

1

2e)

< u'w' > / u*2

-1.0 -0.5 0.0

f)

E / u*2

0 3 6

(after Sogachev and Panferov, 2006)

◄Furry hill wind-tunnel experiment(Finnigan and Brunet, 1995)

▲The Pine forest canopy (Katul and Chang, 1999)

►The Elora corn canopy (Wilson et al., 1982; Wilson, 1988)

a)

A h0 2 4

z / h

0

1

2

3

d)

< u'w' > / u*2

-1.0 -0.5 0.0

z / h

0

1

c)

E / u*2

0 3 6

b)

U / u*

0 4 8

e)

U / u*

0 2

f)

E / u*2

0 2 4

b)

|U| / u*

0 3 60.0

0.5

1.0

1.5

c)

< u'w' > / u*2

-1.0 -0.5 0.0

z / h

0.0

0.5

1.0

1.5d)

E / u*2

0 3 60.0

0.5

1.0

1.5

a)

A h0 10 20

z / h

0.0

0.5

1.0

1.5

Treatment of the plant drag

(Sogachev and

Panferov, 2006)

4

2

6

x / h-10 0 10 20 30

z / h

0.0

0.5

1.0

1.5

2.0

2.5

3.0

1.00.5

1.5

1.0

0.5

x / h-10 0 10 20 30

10

5

x / h-10 0 10 20 30

U ( m s-1 ) l ( m ) E ( m2 s-2 )

a) E-l model

4

2

6

x / h-10 0 10 20 30

z / h

0.0

0.5

1.0

1.5

2.0

2.5

3.0

510

x / h-10 0 10 20 30

1.0

1.00.5

1.0

0.5

0.5

x / h-10 0 10 20 30

U ( m s-1 ) l ( m ) E ( m2 s-2 )

b) E- model

SCADIS reproduces the experimental variation in length scales

The basic requirement of K-theory – that the length scale of the mixing process be substantially smaller than that of the inhomogeneity in the mean scalar or momentum gradient (Corrsin 1974) – is not violated for disturbed flow and for slow spatial variation of cdA (Finnigan and Belcher, 2004).

Verification: low-roughness surface

Converse Prandtl number

1 4

1.35 /(1. 1.35Ri) for Ri 0

1.35 (1 15Ri ) for Ri 0

(Businger et al. 1971, Sogachev et al. 2002)

Wind speed ( m s-1 )Fig. 1 (a) ABL wind evolution and (b) surface characteristics: u* and Monin-Obukhov length, L, during fair weather over low-roughness land derived by E-ω model.

Uncertainties: Turbulent Prandtl number, Pr versus Ri

21Pr ( )z

UP B K Ri Bz

¶ ¶

211 Pr ( )z Ri RUP B K

zi¶ ¶

Verification: low-roughness surface

(Paulson, 1970)

0*

0

( ) ln zu z zU zz L L

22ln 1 / 2 ln 1 / 2

2arctan / 2 0

5 0

X X

zz XLL

z zL L

1 4

where 1 15 zXL

Fig. 2 (a) Wind evolutions and (b) wind profiles for different hours in the atmospheric surface layer during fair weather over low-roughness land derived by E-ω and analytical models.

Verification: forested surface

(Laakso et al., 2007)

Uncertainties: buoyancy inside canopy

Uncertainties: buoyancy inside canopy

1/ 212 ( )dd cS A z U EC (Sogachev and Panferov, 2006 )

? 12 (Ri)const C f 1 2 1 212 12 (Ri)C const C f

Uncertainties: buoyancy inside canopy

Uncertainties: buoyancy inside canopyH =16 m, LAI = 1.38

(Christen and Novak, 2008)

ABL evolution

Energy budget above canopy layer

Ri in ABL

Low-level jet

Low-level jet effects on wind energy related variables

Summary

Much work remains to be done…