# LARGE EDDY SIMULATION

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```					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

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    1 p      2 ui
uj                 
t      x j   T0     xi    x j
2

ui  ui G dxdydz
~ 

~
u i ~ u i
uj
~
  
~  (u i u j  u i u j )
g i ~ 1 p

~ ~~

~
 2 ui
t     x j T0     xi        x j              x j
2

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

•   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

L               f

inertial range,    5 / 3
energy input                                     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

•   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               

~ 300 m

Add vortex force for Langmuir flows   McWilliam et al 1997
Oceanic boundary layer



z


~ 300 m
Add vortex force for Langmuir flows   McWilliams et al 1997
Canopy turbulence

U0
< 100 m

z

~ 200 m

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

COUPLED with SURFACE

• turbulence   heterogeneous land
• turbulence   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
–   turbulent fluxes
–   air quality
–   cloud
–   chemical transport/reaction

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 views: 18 posted: 10/7/2011 language: English pages: 43