Transcript Large eddy simulation (LES)

LARGE EDDY SIMULATION
Chin-Hoh Moeng
NCAR
OUTLINE
• WHAT IS LES?
• APPLICATIONS TO PBL
• FUTURE DIRECTION
WHAT IS LES?
A NUMERICAL TOOL
FOR
TURBULENT FLOWS
Turbulent Flows
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governing equations, known
nonlinear term >> dissipation term
no analytical solution
highly diffusive
smallest eddies ~ mm
largest eddies --- depend on Renumber (U; L;  )
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
LES
Resolved large eddies
(important eddies)
turbulent flow
Subfilter scale, small
(not so important)
FIRST NEED TO SEPARATE THE
FLOW FIELD
• Select a filter function G
• Define the resolved-scale (large-eddy):
~
f ( x)   f ( x)G ( x, x)dx
• Find the unresolved-scale (SGS or SFS):
~
f ( x)  f ( x)  f ( x)
Examples of filter functions
Top-hat
Gaussian
Example: An 1-D flow field
f
~
f ( x)  f ( x)  f ( x)
large eddies
Reynolds averaged model (RAN)
f
f ( x)  f ( x)  f ' ( x)
non-turbulent
LES EQUATIONS
ui
ui
gi
 2ui
1 p
uj



2
t
x j
T0
 xi
x j
u~i   ui G dxdydz
~
~ u~ )
2~
~
~
~

(
u
u

u
u i ~ u i g i ~ 1 p
 ui
i j
i j
uj
  


2
t
x j T0
 xi
x j
x j
SFS
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
Geophysical turbulence
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PBL (pollution layer)
boundary layer in the ocean
turbulence inside forest
deep convection
convection in the Sun
…..
LES of PBL
km
m
resolved eddies
L

mm
SFS eddies
f
inertial range, 
energy input
5 / 3
dissipation
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
The premise of LES
• Large eddies, most energy and fluxes,
explicitly calculated
• Small eddies, little energy and fluxes,
parameterized, SFS model
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
Caution
• near walls, eddies small, unresolved
• very stable region, eddies
intermittent
• cloud physics, chemical reaction…
more uncertainties
A typical setup of PBL-LES
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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
Different PBL Flow Regimes
• numerical setup
• large-scale forcing
• flow characteristics
Clear-air convective PBL
Convective updrafts
Ug
z

Q
~ 5 km
Horizontal homogeneous CBL
LIDAR Observation
Local Time
Oceanic boundary layer


z
~ 300m
Add vortex force for Langmuir flows
McWilliam et al 1997
Oceanic boundary layer


z
~ 300m
Add vortex force for Langmuir flows
McWilliams et al 1997
Canopy turbulence
< 100 m
U0
z
~ 200m
Add drag force---leaf area index
Patton et al 1997
Comparison with observation
observation
LES
Shallow cumulus clouds
~ 12 hr
Ug

z
cloud layer
Q
~ 6 km
Add phase change---condensation/evaporation
COUPLED with SURFACE
• turbulence
• turbulence
heterogeneous land
ocean surface wave
Coupled with heterogeneous soil
Wet soil
LES model
z
Dry soil
the ground
Surface model
Land model
30 km
Coupled with heterogeneous soil
wet soil
dry soil
(Patton et al 2003)
Coupled with wavy surface
stably stratified
U-field
flat surface
stationary wave
moving wave
So far, idealized PBLs
• Flat surface
• Periodic in x & y
• Shallow clouds
Future Direction of LES
for PBL Research
• Realistic surface
–complex terrain, land use, waves
• PBL under severe weather
mesoscale model domain
500 km
50 km
LES domain
Computational challenge
Resolve turbulent motion in Taipei basin
~ 1000 x 1000 x 100 grid points
Massive parallel machines
Technical issues
• Inflow boundary condition
• SFS effect near irregular surfaces
• Proper scaling; representations of
ensemble mean
?
?
How to describe a turbulent inflow?
What do we do with LES
solutions?
Understand turbulence behavior
& diffusion property
Develop/calibrate PBL models
i.e. Reynolds average models
CLASSIC EXAMPLES
• Deardorff (1972; JAS)
- mixed layer scaling
• Lamb (1978; atmos env)
- plume dispersion
FUTURE GOAL
Understand PBL in complex environment
and improve its parameterization
for regional and climate models
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turbulent fluxes
air quality
cloud
chemical transport/reaction