large eddy simulation chin-hoh moeng ncar outline what is les? applications to pbl future direction
TRANSCRIPT
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
• governing equations, known
• nonlinear term >> dissipation term
• no analytical solution
• highly diffusive
• smallest eddies ~ mm
• largest eddies --- depend on Re- number (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
turbulent flow
Resolved large eddies
Subfilter scale, small
(not so important)
(important eddies)
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
Examples of filter functions
Top-hat
Gaussian
Example: An 1-D flow field
)()(~
)( xfxfxf
f
Apply filter
large eddies
Reynolds averaged model (RAN)
)(')()( xfxfxf
f
Apply ensemble avg
non-turbulent
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
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
• PBL (pollution layer)
• boundary layer in the ocean
• turbulence inside forest
• deep convection
• convection in the Sun
• …..
LES of PBL
km m mm
resolved eddies SFS eddies
dissipationenergy input
fL inertial range, 3/5
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
• 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
gU
z
km5~
Q
Convective updrafts
~ 2
km
Horizontal homogeneous CBL
Local Time
LIDAR Observation
Oceanic boundary layer
z
m300~
Add vortex force for Langmuir flows McWilliam et al 1997
Oceanic boundary layer
z
m300~
Add vortex force for Langmuir flows McWilliams et al 1997
Canopy turbulence
0U
m200~
z
Add drag force---leaf area index Patton et al 1997
< 1
00 m
observation LES
Comparison with observation
Shallow cumulus clouds
gU
z
Q
layercloud
Add phase change---condensation/evaporation
~ 6 km
~3 k
m
~ 12 hr
COUPLED with SURFACE
• turbulence heterogeneous land
• turbulence ocean surface wave
Coupled with heterogeneous soil
Surface model
zWet soil
Dry soil
km30
the ground
LES model
Land model
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 LESfor PBL Research
• Realistic surface–complex terrain, land use, waves
• PBL under severe weather
500 km
50 km
LES domain
mesoscale model domain
Computational challenge
Massive parallel machines
Resolve turbulent motion in Taipei basin~ 1000 x 1000 x 100 grid points
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
– turbulent fluxes – air quality– cloud– chemical transport/reaction