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NCAR TOY Workshop Geophysical Turbulence Phenomena Turbulence Theory and Modeling 29 February 2008. Requirements to Predict the Surface Layer with High Accuracy at High Reynolds Numbers using Large-eddy Simulation *. James G. Brasseur & Tie Wei Pennsylvania State University.

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NCAR TOY Workshop Geophysical Turbulence PhenomenaTurbulence Theory and Modeling

29 February 2008

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

James G. Brasseur & Tie WeiPennsylvania State University

*supported by the Army Research Office


Fundamental errors in les predictions in the surface layer of the atmospheric boundary layer

neutral boundary layer

U(z)

rough wall

z/

Fundamental Errors in LES Predictions in the Surface Layer of the Atmospheric Boundary Layer

1.0

neutral boundary layer

0.8

0.6

what should be predicted

0.4

0.2

surface layer

0

0

1


Fundamental errors in les predictions in the surface layer of the atmospheric boundary layer1

neutral boundary layer

U(z)

rough wall

z/

Fundamental Errors in LES Predictions in the Surface Layer of the Atmospheric Boundary Layer

1.0

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


The importance of the overshoot

U

w

w

horizontal integral scale of w

The Importance of the Overshoot

Moderately Convective

Atmospheric Boundary Layer

U

isosurfaces of vertical velocity:

up: w > 0 (yellow)

down: w < 0 (white or green)

Khanna & Brasseur 1998, JAS 55


Why the overshoot alters turbulence structure

u

Why the Overshoot Alters Turbulence Structure

Moderately 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


Consequences of the overshoot

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
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:


Clues from previous studies

resolution312831923

2. Inherent under-resolution at the first grid level

z

l ~ z

l ~ z

Juneja & Brasseur 1999, Phys. Fluids 11

Clues from Previous Studies

1. The overshoot is tied to the grid

Khanna & Brasseur 1997, JFM 345


Clues

Chow, Street, Xue & Ferziger 2005, JAS 62

z

l ~ z

l ~ z

Clues

1. 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
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.


The first discovery scaling mean smooth wall channel flow

U

inertial scaling:

integrate 0  z:

The First Discovery: ScalingMean Smooth-Wall Channel Flow

z

Ttot= Tt + T

Tt

inertia-dominated

T

friction-dominated

stationary, fully developed, mean:


Smooth wall channel flow

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 Flow

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

Ttot= Tt + T

Tt

m

m

T

peak at z+  10


The first discovery scaling mean les of high re or rough wall channel flow

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 Flow

z

Ttot= TR + TS

TR

U

inertia-dominated

throughout

TS

under-resolution of integral scalesat first few grid levels

stationary, fully developed, mean:


The first discovery a spurious frictional surface layer

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 Layer

Conclusion

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


The first discovery a requirement to eliminate the overshoot

The First Discovery:A Requirement to Eliminate the Overshoot

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 bl

U

The Second Discovery: Relative Inertia to Friction in the Real BL

z/

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


The second discovery relative inertia to les friction in the simulation

to support an inertial surface layer

Scaling

The Second Discovery: Relative Inertia to LES Friction in the Simulation

LES Reynolds Number

define


Numerical les viscous effects at the surface vertical grid resolution and t r vs t s
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
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
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

The Parameter Space

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


Designing high accuracy les

In the Parameter Space

  • 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 LES

For any SFS stress model:


Numerical experiments

1

N

0

Numerical Experiments

* from the literature


Numerical experiments1

N

Nz = 64

Nz = 32

Nz = 96

Nz = 128

Numerical Experiments


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


Resolution N

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


Numerical experiments2

1

N

0

Numerical Experiments


Designing high accuracy les1

Nz = 128

The Parameter Space

Nz = 96

Designing High-Accuracy LES


Nz = 128

Nz = 96



Conclusions
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
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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