large eddy simulation of stable boundary layers with a prognostic subgrid tke equation
DESCRIPTION
Large Eddy Simulation of Stable Boundary Layers with a prognostic subgrid TKE equation. Stephan R. de Roode and Vincent Perrin Clouds, Climate and Air Quality, Dept. of Applied Sciences , Delft University of Technology, Delft, Netherlands. 8 th Annual Meeting of the EMS, Amsterdam, 2008. - PowerPoint PPT PresentationTRANSCRIPT
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Large Eddy Simulation of Stable Boundary Layers with a prognostic subgrid TKE equation
8th Annual Meeting of the EMS, Amsterdam, 2008
Stephan R. de Roode and Vincent Perrin
Clouds, Climate and Air Quality, Dept. of Applied Sciences,
Delft University of Technology, Delft, Netherlands
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ContentsProblem/question- Dutch LES model: Stable boundary layer simulation dominated by subgrid contributions
Strategy- Analysis of subgrid prognostic TKE model
LES results- subgrid vs resolved- similarity relations- high resolution results
Conclusions
8th Annual Meeting of the EMS, Amsterdam, 2008
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Prognostic subgrid TKE equation (Deardorff 1980)
subgrid fluxes ,
eddy diffusivity
length scale
subgrid TKE
€
u j" ψ" = −Kh∂ψ∂x j
€
u i"u j" = −Km∂u j
∂x i
+ ∂u i
∂x j
⎛
⎝ ⎜
⎞
⎠ ⎟
€
Km,h = cm,hλe1/2
€
λ =min Δ,cne1/2
NBV
⎛ ⎝ ⎜
⎞ ⎠ ⎟
€
∂e∂t
+u j∂e∂x j
= gθ0
w"θv" −u i"u j"∂u i
∂x j
−∂u j" e+ p"/ρ( )
∂x j
−ε
8th Annual Meeting of the EMS, Amsterdam, 2008
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GABLS SBL intercomparison case
Neutral layer becomes stable due to a prescribed surface cooling (-0.25 K/h)
Original set up according to Beare et al. (2003): x=y=z=6.25 m
Length scale correction turned off: λ==(x y z)1/3
ch=cm(ch,1+ch,2,λ) = cm(ch,1+ch,2)
cm=0.12, ch,1=1, ch,2=2
8th Annual Meeting of the EMS, Amsterdam, 2008
LES results: Examples taken from the 5th hour
Turbulent fluxes dominated by subgrid contribution
0
50
100
150
200
264 264.5 265 265.5 266
height (m)
potential temperature (K)
0 2 4 6 8 100
50
100
150
200
U
V
(m/s)
height (m)
-0.006 -0.004 -0.002 0 0.0020
50
100
150
200
subgridresolvedtotal
w'θ' (mKs)
height (m)
-0.02 -0.015 -0.01 -0.005 00
50
100
150
200
subgridresolvedtotal
u'w' (m2/s2)
height (m)
Solution close to Smagorinsky model's solution
Smagorinsky subgrid TKE solution:
LES subgrid constants: cf=2.5 cm=0.12, ce=0.76
corresponding Smagorinsky constant: cs=0.22 €
e = 12
cm
cε
Δ2S2 1−chRig( ) = 12
c f2
4π 2 Δ2S2 1− chRig( )
0 0.02 0.04 0.06 0.08 0.10
0.02
0.04
0.06
0.08
0.1
LES subgrid TKE (m2/s2)Smagorinsky subgrid TKE solution (m
2 /s2 )
Changing the filter constant cf=2.52
Less filtering more resolved motions
263 264 265 266 267 2680
50
100
150
200
250
300
potential temperature (K)
height (m)
-0.008 -0.006 -0.004 -0.002 0 0.0020
50
100
150
200
250
300
subgrid
resolved
total
w'θ' (mKs)
height (m)
0 2 4 6 8 10 120
50
100
150
200
250
300
U
V
(m/s)
height (m)
-0.03 -0.02 -0.01 0 0.010
50
100
150
200
250
300
subgridresolvedtotal
u'w' (m2/s2)
height (m)
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Subgrid constants cm and ch
cm more mixing of hor. winds
c h
mor
e m
ixin
g of
pot
. te
mp.
€
Rig =
gθ
∂θv
∂z∂U∂z ⎛ ⎝ ⎜
⎞ ⎠ ⎟2
+ ∂V∂z ⎛ ⎝ ⎜
⎞ ⎠ ⎟2
Similarity relations
0
10
20
30
40
50
0 2 4 6 8 10
sub>ressub<res1+5z/Λ
zΛ
0
10
20
30
40
50
0 2 4 6 8 10
sub>ressub<res1+5z/Λ
zΛ
Solution if solution is 100% subgrid (Baas et al., 2008)
€
φh
φm
= cm
ch
= PrT = 13
Similarity relations: cf=2 (cm=0.096)
0
10
20
30
40
50
0 2 4 6 8 10
sub>ressub<res1+5z/Λ
zΛ
0
10
20
30
40
50
0 2 4 6 8 10
sub>ressub<res1+5z/Λ
zΛ
DNS Van der Wiel et al. (2008)
High resolution: x=y=z=1.5626m
0
10
20
30
40
50
0 2 4 6 8 10
sub>res
sub<res
1+5z/Λ
zΛ
0
10
20
30
40
50
0 2 4 6 8 10
sub>ressub<res1+5z/Λ
zΛ
12
Conclusions 1. =6.25 m resolution not enough
- Solution dictated by Smagorinsky subgrid TKE solution
- too much dependency on subgrid constants: bad simulation
- recommendation: refine grid resolution (smaller )
2. High resolution simulation
- smaller gradient for m and h compared to observations and DNS
€
e = 12
cm
cε
Δ2S2 1−chRig( ) = 12
cf2
4π 2 Δ2S2 1−chRig( )