large eddy simulation
TRANSCRIPT
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LARGE EDDY SIMULATION
Chin-Hoh Moeng
NCAR
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OUTLINE
• WHAT IS LES?
• APPLICATIONS TO PBL
• FUTURE DIRECTION
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WHAT IS LES?
A NUMERICAL TOOL
FOR
TURBULENT FLOWS
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Turbulent Flows
• governing equations, known
• nonlinear term >> dissipation term
• no analytical solution
• highly diffusive
• smallest eddies ~ mm
• largest eddies --- depend on Re- number (U; L; )
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Numerical methods of studying turbulence
• Reynolds-averaged modeling (RAN)
model just ensemble statistics
• Direct numerical simulation (DNS)
resolve for all eddies
• Large eddy simulation (LES)
intermediate approach
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LES
turbulent flow
Resolved large eddies
Subfilter scale, small
(not so important)
(important eddies)
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FIRST NEED TO SEPARATE THE
FLOW FIELD
• Select a filter function G• Define the resolved-scale (large-eddy):
• Find the unresolved-scale (SGS or SFS):
xdxxGxfxf ),()()(~
)(~
)()( xfxfxf
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Examples of filter functions
Top-hat
Gaussian
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Example: An 1-D flow field
)()(~
)( xfxfxf
f
Apply filter
large eddies
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Reynolds averaged model (RAN)
)(')()( xfxfxf
f
Apply ensemble avg
non-turbulent
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LES EQUATIONS
2
2
0
1
j
i
i
i
j
ij
i
x
u
x
p
T
g
x
uu
t
u
dxdydzGuu ii ~
2
2
0
~)~~(~1~~~
~
j
i
j
jiji
i
i
j
ij
i
x
u
x
uuuu
x
p
T
g
x
uu
t
u
~
SFS
Apply filter G
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Different Reynolds number turbulent flows
• Small Re flows: laboratory (tea cup) turbulence; largest eddies ~ O(m); RAN or DNS
• Medium Re flows: engineering flows; largest eddies ~ O(10 m); RAN or DNS or LES
• Large Re flows: geophysical turbulence; largest eddies > km; RAN or LES
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Geophysical turbulence
• PBL (pollution layer)
• boundary layer in the ocean
• turbulence inside forest
• deep convection
• convection in the Sun
• …..
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LES of PBL
km m mm
resolved eddies SFS eddies
dissipationenergy input
fL inertial range, 3/5
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Major difference between engineer and geophysical
flows: near the wall
• Engineering flow: viscous layer
• Geophysical flow: inertial-subrange layer; need to use surface-layer theory
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The premise of LES
• Large eddies, most energy and fluxes, explicitly calculated
• Small eddies, little energy and fluxes, parameterized, SFS model
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The premise of LES
• Large eddies, most energy and fluxes, explicitly calculated
• Small eddies, little energy and fluxes, parameterized, SFS model
LES solution is supposed to be insensitive to SFS model
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Caution
• near walls, eddies small, unresolved• very stable region, eddies
intermittent • cloud physics, chemical reaction…
more uncertainties
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A typical setup of PBL-LES
• 100 x 100 x 100 points• grid sizes < tens of meters • time step < seconds • higher-order schemes, not too diffusive• spin-up time ~ 30 min, no use• simulation time ~ hours• massive parallel computers
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Different PBL Flow Regimes
• numerical setup
• large-scale forcing
• flow characteristics
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Clear-air convective PBL
gU
z
km5~
Q
Convective updrafts
~ 2
km
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Horizontal homogeneous CBL
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Local Time
LIDAR Observation
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Oceanic boundary layer
z
m300~
Add vortex force for Langmuir flows McWilliam et al 1997
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Oceanic boundary layer
z
m300~
Add vortex force for Langmuir flows McWilliams et al 1997
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Canopy turbulence
0U
m200~
z
Add drag force---leaf area index Patton et al 1997
< 1
00 m
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observation LES
Comparison with observation
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Shallow cumulus clouds
gU
z
Q
layercloud
Add phase change---condensation/evaporation
~ 6 km
~3 k
m
~ 12 hr
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COUPLED with SURFACE
• turbulence heterogeneous land
• turbulence ocean surface wave
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Coupled with heterogeneous soil
Surface model
zWet soil
Dry soil
km30
the ground
LES model
Land model
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Coupled with heterogeneous soil
wet soil dry soil(Patton et al 2003)
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Coupled with wavy surface
stably stratified
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U-field
flat surface stationary wave moving wave
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So far, idealized PBLs
• Flat surface
• Periodic in x & y
• Shallow clouds
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Future Direction of LESfor PBL Research
• Realistic surface–complex terrain, land use, waves
• PBL under severe weather
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500 km
50 km
LES domain
mesoscale model domain
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Computational challenge
Massive parallel machines
Resolve turbulent motion in Taipei basin~ 1000 x 1000 x 100 grid points
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Technical issues
• Inflow boundary condition
• SFS effect near irregular surfaces
• Proper scaling; representations of ensemble mean
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???
How to describe a turbulent inflow?
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What do we do with LES solutions?
Understand turbulence behavior & diffusion property
Develop/calibrate PBL models i.e. Reynolds average models
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CLASSIC EXAMPLES
• Deardorff (1972; JAS)
- mixed layer scaling
• Lamb (1978; atmos env)
- plume dispersion
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FUTURE GOAL
Understand PBL in complex environment and improve its parameterization for regional and climate models
– turbulent fluxes – air quality– cloud– chemical transport/reaction