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