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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 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