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 (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 Apply filter  large eddies

Reynolds averaged model (RAN) f Apply ensemble avg  non-turbulent

LES EQUATIONS Apply filter G 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 inertial range, km m mm resolved eddies SFS eddies L 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

Horizontal homogeneous CBL

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

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

Comparison with 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

Coupled with heterogeneous soil Surface model 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 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