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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
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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 turbulent flow (important eddies) Subfilter scale, small (not so important)
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):
Examples of filter functions Top-hat Gaussian
Example: An 1-D flow field f Apply filter large eddies
Reynolds averaged model (RAN) f Apply ensemble avg non-turbulent
LESEQUATIONS Apply filter G SFS
Different Reynolds number turbulent flows • Small Re flows: laboratory (tea cup) turbulence; largest eddies ~ O(m); RAN orDNS • Medium Re flows: engineering flows; largest eddies ~ O(10 m); RAN orDNS or LES • Large Re flows: geophysical turbulence; largest eddies > km; RAN orLES
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 inertial range, 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 ~ 2 km
LIDAR Observation Local Time
Oceanic boundary layer Add vortex force for Langmuir flows McWilliam et al 1997
Oceanic boundary layer Add vortex force for Langmuir flows McWilliams et al 1997
Canopy turbulence < 100 m Add drag force---leaf area index Patton et al 1997
Comparison with observation observation LES
Shallow cumulus clouds ~ 12 hr ~3 km ~ 6 km Add phase change---condensation/evaporation
COUPLED with SURFACE • turbulence heterogeneous land • turbulence ocean surface wave
Surface model Coupled with heterogeneous soil Wet soil LES model Dry soil the ground 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
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