James G. Brasseur & Tie Wei Pennsylvania State University

1. 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

2. 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

3. 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

4. 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

5.  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

6. 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

7. 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:

8. • 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

9. 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

10. 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.

11. 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:

12. 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

13. 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:

14. 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

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

16. U  The Second Discovery: Relative Inertia to Friction in the Real BL z/ DNS data from Iwamoto et al., Jimenez et al..

17. to support an inertial surface layer Scaling The Second Discovery: Relative Inertia to LES Friction in the Simulation LES Reynolds Number define

18. 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):

19. Why the Overshoot is Tied to the Grid z/zi increasing ReLES by increasing N  the overshoot cannot be “solved” with resolution

20. 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

21. 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

22. 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:

23. 1 N 0 Numerical Experiments * from the literature

24. N Nz = 64 Nz = 32 Nz = 96 Nz = 128 Numerical Experiments

25. 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

26. 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

27. 1 N 0 Numerical Experiments

28. Nz = 128 The Parameter Space Nz = 96 Designing High-Accuracy LES

29. Nz = 128 Nz = 96

30. A Current Issue: Numerical Instability

31. 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

32. Extra: Cs used in simulations

33. 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