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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

     Add phase change---condensation/evaporation
 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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posted:10/7/2011
language:English
pages:43