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LARGE EDDY SIMULATION Chin-Hoh Moeng NCAR

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OUTLINE WHAT IS LES? APPLICATIONS TO PBL FUTURE DIRECTION

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WHAT IS LES? A NUMERICAL TOOL FOR TURBULENT FLOWS

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**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; )

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**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

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**LES turbulent flow Resolved large eddies Subfilter scale, small**

(important eddies) Subfilter scale, small (not so important)

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**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):

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**Examples of filter functions**

Top-hat Gaussian

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**Example: An 1-D flow field**

Apply filter large eddies

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**Reynolds averaged model (RAN)**

f Apply ensemble avg non-turbulent

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LES EQUATIONS Apply filter G SFS

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**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

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**Geophysical turbulence**

PBL (pollution layer) boundary layer in the ocean turbulence inside forest deep convection convection in the Sun …..

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**LES of PBL inertial range, km m mm resolved eddies SFS eddies L**

energy input dissipation

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**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

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The premise of LES Large eddies, most energy and fluxes, explicitly calculated Small eddies, little energy and fluxes, parameterized, SFS model

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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

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**Caution near walls, eddies small, unresolved**

very stable region, eddies intermittent cloud physics, chemical reaction… more uncertainties

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**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

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**Different PBL Flow Regimes**

numerical setup large-scale forcing flow characteristics

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**Clear-air convective PBL**

Convective updrafts ~ 2 km

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**Horizontal homogeneous CBL**

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LIDAR Observation Local Time

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**Oceanic boundary layer**

Add vortex force for Langmuir flows McWilliam et al 1997

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**Oceanic boundary layer**

Add vortex force for Langmuir flows McWilliams et al 1997

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**Add drag force---leaf area index**

Canopy turbulence < 100 m Add drag force---leaf area index Patton et al 1997

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**Comparison with observation**

LES

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**Shallow cumulus clouds**

~ 12 hr ~3 km ~ 6 km Add phase change---condensation/evaporation

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**COUPLED with SURFACE turbulence heterogeneous land**

turbulence ocean surface wave

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**Coupled with heterogeneous soil**

Surface model Wet soil LES model Dry soil the ground Land model

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**Coupled with heterogeneous soil**

wet soil dry soil (Patton et al 2003)

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**Coupled with wavy surface**

stably stratified

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U-field flat surface stationary wave moving wave

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So far, idealized PBLs Flat surface Periodic in x & y Shallow clouds

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**Future Direction of LES for PBL Research**

Realistic surface complex terrain, land use, waves PBL under severe weather

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**mesoscale model domain**

500 km 50 km LES domain

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**Computational challenge**

Resolve turbulent motion in Taipei basin ~ 1000 x 1000 x 100 grid points Massive parallel machines

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**Technical issues Inflow boundary condition**

SFS effect near irregular surfaces Proper scaling; representations of ensemble mean

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**How to describe a turbulent inflow?**

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**What do we do with LES solutions?**

Understand turbulence behavior & diffusion property Develop/calibrate PBL models i.e. Reynolds average models

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CLASSIC EXAMPLES Deardorff (1972; JAS) - mixed layer scaling Lamb (1978; atmos env) - plume dispersion

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**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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