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James G. Brasseur & Tie Wei Pennsylvania State UniversityPowerPoint Presentation

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### Requirements to Predict the Surface Layer with High Accuracy at High Reynolds Numbers using Large-eddy Simulation*

NCAR TOY Workshop Geophysical Turbulence PhenomenaTurbulence Theory and Modeling

29 February 2008

James G. Brasseur & Tie WeiPennsylvania State University

*supported by the Army Research Office

U(z)

rough wall

z/

Fundamental Errors in LES Predictions in the Surface Layer of the Atmospheric Boundary Layer1.0

neutral boundary layer

0.8

0.6

what should be predicted

0.4

0.2

surface layer

0

0

1

U(z)

rough wall

z/

Fundamental Errors in LES Predictions in the Surface Layer of the Atmospheric Boundary Layer1.0

neutral boundary layer

0.8

0.6

neutral boundary layer

what should be predicted

0.4

0.2

surface layer

0

0

1

what is actually predicted

Chow, Street, Xue, Ferziger JAS 62, 2005

w

w

horizontal integral scale of w

The Importance of the OvershootModerately Convective

Atmospheric Boundary Layer

U

isosurfaces of vertical velocity:

up: w > 0 (yellow)

down: w < 0 (white or green)

Khanna & Brasseur 1998, JAS 55

u

Why the Overshoot Alters Turbulence StructureModerately Convective ABL

z/zi = 0.10

z/zi = 0.05

z/zi = 0.10

z/zi = 0.05

U

z/zi = 0.25

z/zi = 0.50

z/zi = 0.25

z/zi = 0.50

Khanna & Brasseur 1998, JAS 55

horizontal integral scale

Consequences of the Overshoot- Over-prediction of mean shear in the surface layer produces poor predictions throughout the ABL of:
- turbulence production
- thermal eddying structure (e.g., rolls)
- vertical transport, dispersion and eddy structure of momentum, temperature, humidity, contaminants, toxins, …
- correlations, turbulent kinetic energies,…
- cloud cover, CO2 transport, radiation, …

Moderately

Convective ABL

16-year History of the Overshoot

- Mason & Thomson 1992, JFM 242.
- Sullivan, McWilliams & Moeng 1994, BLM 71.
- Andren, Brown, Graf, Mason, Moeng, Nieuwstadt & Schumann 1994 QJR Meteor Soc 120 (comparison of 4 codes: Mason, Moeng, Neiustadt, Schumann).
- Khanna & Brasseur 1997, JFM 345.
- Kosovic 1997, JFM 336.
- Khanna & Brasseur 1998, JAS 55.
- Juneja & Brasseur 1999 Phys Fluids 11.
- Port-Agel, Meneveau & Parlange 2000, JFM 415.
- Zhou, Brasseur & Juneja 2001 Phys Fluids 13.
- Ding, Arya, Li 2001, Environ Fluid Mech 1.
- Reselsperger, Mahé & Carlotti 2001, BLM 101.
- Esau 2004 Environ Fluid Mech 4.
- Chow, Street, Xue & Ferziger 2005, JAS 62
- Anderson, Basu & Letchford 2007, Environ Fluid Mech 7.
- Drobinski, Carlotti, Redelsperger, Banta, Masson & Newson 2007, JAS 64.
- Moeng, Dudhia, Klemp & Sullivan 2007 Monthly Weather Rev 135.

Relevant toany LES of boundary layers where the viscous sublayer is unresolved or nonexistent.

… enhanced with direct exchange between inner and outer boundary layer:

resolution312831923

•

2. Inherent under-resolution at the first grid level

z

l ~ z

l ~ z

Juneja & Brasseur 1999, Phys. Fluids 11

Clues from Previous Studies1. The overshoot is tied to the grid

Khanna & Brasseur 1997, JFM 345

Chow, Street, Xue & Ferziger 2005, JAS 62

z

l ~ z

l ~ z

Clues1. The overshoot is tied to the grid

3. The overshoot is sensitive to the SFS model

•

Smag

•

Sullivan, McWilliams & Moeng 1994, BLM 71

2. Inherent under-resolution at the first grid level

4. Lack of grid independence

not strictly a modeling issue.

Juneja & Brasseur 1999, Phys. Fluids 11 Khanna & Brasseur 1997, JFM 345

Into the Future

- What is known after 15 years:
- The overshoot is fundamental to LES of shear-dominated surface layers.
- The overshoot is somehow connected to the grid.
- The overshoot is somehow connected to the SFS stress model.

- Mason & Thomson 1992, JFM 242.
- Sullivan, McWilliams & Moeng 1994, BLM 71.
- Andren, Brown, Graf, Mason, Moeng, Nieuwstadt & Schumann 1994 QJR Meteor Soc 120 (comparison of 4 codes: Mason, Moeng, Neiustadt, Schumann).
- Khanna & Brasseur 1997, JFM 345.
- Kosovic 1997, JFM 336.
- Khanna & Brasseur 1998, JAS 55.
- Juneja & Brasseur 1999 Phys Fluids 11.
- Port-Agel, Meneveau & Parlange 2000, JFM 415.
- Zhou, Brasseur & Juneja 2001 Phys Fluids 13.
- Ding, Arya, Li 2001, Environ Fluid Mech 1.
- Reselsperger, Mahé & Carlotti 2001, BLM 101.
- Esau 2004 Environ Fluid Mech 4.
- Chow, Street, Xue & Ferziger 2005, JAS 62
- Anderson, Basu & Letchford 2007, Environ Fluid Mech 7.
- Drobinski, Carlotti, Redelsperger, Banta, Masson & Newson 2007, JAS 64.
- Moeng, Dudhia, Klemp & Sullivan 2007 Monthly Weather Rev 135.

- Today’s Discussion:
- We have (finally) found the source(s) of the overshoot and its consequences.
- The solution is a framework in which high-accuracy LES can be developed.
- The framework involves and interplay between: (1) grid resolution, (2) SFS model, (3) numerical algorithm, (4) grid aspect ratio.

inertial scaling:

integrate 0 z:

The First Discovery: ScalingMean Smooth-Wall Channel Flowz

Ttot= Tt + T

Tt

inertia-dominated

T

friction-dominated

stationary, fully developed, mean:

z+ 2.5

Conclusions

1. In the smooth-wall channel flow the overshoot in m is real.

2. The real overshoot in m arises from applying inertial scale z in a frictional layer that has characteristic viscous scale

Smooth-Wall Channel FlowDNS data from Iwamoto et al., Jimenez et al..

Ttot= Tt + T

Tt

m

m

T

peak at z+ 10

Extract Viscous Contentof SGS Model:define “LES viscosity”

for strong shear flow

Inertial Scaling… integrate 0 z:

The First Discovery: ScalingMean LES of high Re or Rough-Wall Channel Flowz

Ttot= TR + TS

TR

U

inertia-dominated

throughout

TS

under-resolution of integral scalesat first few grid levels

stationary, fully developed, mean:

DNS: Smooth-wall Channel Flow

LES: Rough-wall ABL

Ttot= TR + TS

Ttot= Tt + T

Tt

Reynolds

stess

TR

resolved

stess

T

viscous

stress

TS

SFS

stress

~10

~10

where parameterizes

real friction

where LESparameterizes

friction in the (inertial) SFS stress

The First Discovery:A Spurious Frictional Surface LayerConclusion

The overshoot in m arises from applying an inertial scaling to a numerical LES “viscous” layer

- To eliminate the overshoot the ratio TR/TS must exceed a critical value ~ O(1) at the first grid level.

LES of the Rough-wall ABL

a numerical LES “viscous” scale

Ttot= TR + TS

TR

resolved

stess

TS

SFS

stress

LESis a “numerical-LES viscosity”

~10

The overshoot arises from “numerical-LES friction” at the surfaceakin to the real frictional layer on smooth walls

The Second Discovery: Relative Inertia to Friction in the Real BLz/

DNS data from Iwamoto et al., Jimenez et al..

to support an inertial surface layer

Scaling

The Second Discovery: Relative Inertia to LES Friction in the SimulationLES Reynolds Number

define

Numerical LES Viscous Effects at the Surface: Vertical Grid Resolution and TR vs. TS

subcritical

ReLES from insufficient resolution

TR

TS

z/zi

z/zi

increasing ReLES

by increasing N

LES, Eddy Viscosity (Smag):

Why the Overshoot is Tied to the Grid

z/zi

increasing ReLES

by increasing N

the overshoot cannot be “solved” with resolution

Putting the two Discoveries Together

1. For the simulation to have the possibility of producing a complete inertial surface layer,an LES Reynolds Number

must exceed a critical value, requiring a minimum vertical resolution

2. To remove the overshoot in mean gradient,the resolved to SFS stressat the first grid level

must exceed a critical value

The Third Discovery

In general,

1.0

0.8

2

0.6

0.4

increasing N

The LES must reside here toeliminate the overshootandresolve a full surface layer

0.2

0

1

0

0

0

- Moving the simulation into the “High-Accuracy Zone (HAZ):
- 1.Adjust resolution in the vertical so that
- 2. Adjust AR + model constant together until

2

HAZ

increasing N

If using the Smagorinsky model:

0

0

Designing High-Accuracy LESFor any SFS stress model:

Nz = 32

N 15

Nz = 64

N 30

N0.2 3

N0.2 6

Resolution N

Nz = 96

N 45

Nz = 128

N 60

N0.2 12

N0.2 9

under-resolution alters the entire boundary layer structure

~ 9 points in surface layer required

Nz = 32

N 15

Nz = 64

N 30

N0.2 3

N0.2 6

Resolution N

Nz = 96

N 45

Nz = 128

N 60

N0.2 12

N0.2 9

Nz = 128

Nz = 96

Conclusions

- High-accuracy LES
- 1. removal of the overshoot in mean gradient
- 2. sufficient resolution of the surface layer

- We have created a framework for developing high-accuracy LES:
- To create high-accuracy LES the simulation must move into a “High-Accuracy Zone” (HAZ) through variation of
- vertical grid resolution
- grid aspect ratio
- friction in model (e.g., model constant) and algorithm

- Instability arises as the simulation moves into the HAZ:
- Tie will discuss next

Extra: AR used in simulations

Effective AR

Note: For this plot, Tie used the effective AR based on explicit dealiasing filter. To get true AR, each of these should be divided by 1.5

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