Craig Smith

Fernando Porte-Agel

WIRE, EPFL, Switzerland

craig.smith@epfl.ch

Craig SmithWIRE, EPFL

Subgrid models in LES of drainage flows

Craig SmithWIRE, EPFL

Why study drainage flows?

Source: Whiteman 2008

zzjetjet = 5-10m – requires very fine = 5-10m – requires very fine resolution, or highly anisotropic resolution, or highly anisotropic gridsgrids

Craig SmithWIRE, EPFL

Science questions

• Predictability of drainage flowsPredictability of drainage flows

• Subgrid model performanceSubgrid model performance

• Monin Obukov similarity (MOS)Monin Obukov similarity (MOS)

Rattlesnake Ridge – SE WA, USAHoran and Dorst, 1983

Craig SmithWIRE, EPFL

Observations

Rattlesnake Ridge – SE WA, USAHoran and Dorst, 1983

x = 7m, y = 10m

Craig SmithWIRE, EPFL

A B

A

B CNumerical setup

x = 20m, z = 2.5-3.8m

500x20x400

x = 13.3m, z = 1.6-2.4m

900x30x620

WIRE LES code – spectral difference in horizontal, center difference in vertical, 2nd order Adams Bashforth in time, z0 = 0.1 m, qsfc = -15-40 Wm-2 (not at peak)Subgrid models – Smagorinsky (wall corrected), Dynamic, Lagrangian scale dependent dynamic

Craig SmithWIRE, EPFL

SGS models

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• Smagorinsky (wall corrected) – model Smagorinsky (wall corrected) – model coefficients are constant (isotropic coefficients are constant (isotropic homogenous TKE)homogenous TKE)

• Dynamic – uses a 2Dynamic – uses a 2ndnd test filter to dynamically test filter to dynamically optimize model coefficientsoptimize model coefficients

• Scale dependent dynamic – allows model Scale dependent dynamic – allows model coefficients to vary with filter size coefficients to vary with filter size

Oregon State UniversityCollege of Oceanic and Atmospheric Sciences

log(Elog(Ekk))

log(k)log(k)kkc c ==

Inertial Inertial subrangesubrange

resolved resolved scalesscales

DissipationDissipation subrangesubrange

unresolved unresolved scalesscales

SGS models

1.0sC 4.0

1.0Pr 12 sgssC

ss CC

ss CC

Craig SmithWIRE, EPFL

Scale dependent Lagrangian dynamic after 45 minutes of integration

Velocity

Results

Potential temperature

Craig SmithWIRE, EPFL

U TKE

Scale dependent Lagrangian dynamic after 45 minutes of integration

Results

Craig SmithWIRE, EPFL

Rattlesnake ridge observations comparison

Results

Craig SmithWIRE, EPFL

U TKE

Smagorinsky ->low near surface temperature -> 10-20% more cold air flux

Craig SmithWIRE, EPFL

dzumhsfc

sfc

T

0

Smagorinsky ->low near surface temperature -> 10-20% more cold air flux

U TKE

Craig SmithWIRE, EPFL

Results

Smagorinksy1.0sC

Dynamic

Scale dependent dynamic

ss CC

ss CC

Assumption of constant model coefficients in Smagorinsky

Craig SmithWIRE, EPFL

Results

Dynamic

Scale dependent dynamic

12

2

2

s

s

C

C

2

422

2

2

2

s

s

s

s

C

C

C

C

Assumption of scale invariance in dynamic model

Craig SmithWIRE, EPFL

In contextObservations suggest zObservations suggest zjj = 5- = 5-

10m10m

Author bc

Burkholder et al 2010 - very small periodic many

Axelsen 2009 glacial 2.6x2.6x0.4 periodic ???

Skyllingstad 2003 SE WA 0.75x0.75x0.75 slope FSF

Smith and Skyllingstad 2005 VTMX 3x3x3 slope FSF100x100x5 valley 1.5 TKE (ARPS)

Chow et al 2006 MAP 150x150x20 valley 1.5 TKE and DRM (ARPS)

Catalano and Cenedese 2010 - 50x50x2 valley WRF in LES mode

Zhong and Whiteman 2008 VTMX 250x250x2.1 valley 2.5 TKE (RAMS)

location sgs

Craig SmithWIRE, EPFL

Future work• Numerical setupNumerical setup

• Grid aspect ratioGrid aspect ratio

• Spanwise heterogeneitySpanwise heterogeneity

Smagorinsky model for katabatic winds – constant Smagorinsky model for katabatic winds – constant PrPrsgssgs

Craig Smith

Fernando Porte-Agel

WIRE, EPFL, Switzerland

craig.smith@epfl.ch

Craig SmithWIRE, EPFL

Subgrid models in LES of drainage flows

Craig SmithWIRE, EPFL

Smagorinsky – original vs wall corrected

Results