parameterization of atmospheric stratification and issues in connection with canopy flow
DESCRIPTION
Parameterization of atmospheric stratification and issues in connection with canopy flow. Sogachev Andrey. Wind Energy Division, Risø National Laboratory for Sustainable Energy , DTU, Building 118, Box 49, DK-4000, Roskilde, Denmark, [email protected] . - PowerPoint PPT PresentationTRANSCRIPT
Sogachev Andrey
Wind Energy Division, Risø National Laboratory for Sustainable Energy , DTU, Building 118, Box 49, DK-4000, Roskilde, Denmark, [email protected]
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…