1. Internal Gravity Waves and Turbulence Closure Model for SBL Sergej Zilitinkevich Division of Atmospheric Sciences, Department of Physical Sciences University of Helsinki and Finnish Meteorological Institute Helsinki, Finland Tov Elperin, Nathan Kleeorin and Igor Rogachevskii Department of Mechanical Engineering The Ben-Gurion University of the Negev Beer-Sheba, Israel Victor L’vov Department of Chemical Physics, Weizmann Institute of Science, Israel L. N. Gutman Conference on Mesoscale Meteorology and Air Pollution, Odessa, Ukraine, September 15-17, 2008

2. Boussinesq Approximation

3. Laminar and Turbulent Flows Laminar Boundary Layer Turbulent Boundary Layer

4. Why Turbulence? Number degrees of freedom Why Not DNS?

5. Turbulent Eddies

6. Laboratory Turbulent Convection Before averaging After averaging

7. Velocity Fields

8. SBL Equations

9. Total Energy

10. Total Budget Equations: BL-case

11. Total Budget Equations for SBL

12. Total Budget Equations: BL-case

13. Total Energy The source: The turbulent potential energy:

14. Steady-state of Budget Equations for SBL

15. Total Energy Deardorff (1970)

16. Steady-State Form of the Budget Equations Turbulent temperature diffusivity Our model Old classical theory

17. vs. vs.

18. Turbulent Prandtl Number

19. Total Budget Equations: BL-case in Presents of Gravity Waves

20. vs. (Waves) vs. (Waves)

21. Turbulent Prandtl Number

22. Anisotropy vs.

23. vs. vs.

24. vs. (Waves) vs. (Waves)

25. Conclusions - Total turbulent energy (potential and kinetic) is conserved - No critical Richardson number - Reasonable turbulent Prandtl number from theory - Reasonable explanation of scattering of the observational data by the influence of the large- scale internal gravity waves.

26. References  Elperin, T., Kleeorin, N., Rogachevskii, I., and Zilitinkevich, S. 2002 Formation of large-scale semi-organized structures in turbulent convection. Phys. Rev. E, 66, 066305 (1--15)  Elperin, T., Kleeorin, N., Rogachevskii, I., and Zilitinkevich, S. 2006 Tangling turbulence and semi-organized structures in convective boundary layers. Boundary Layer Meteorology, 119, 449-472.  Zilitinkevich, S., Elperin, T., Kleeorin, N., and Rogachevskii, I, 2007 "Energy- and flux-budget (EFB) turbulence closure model for stably stratified flows. Boundary Layer Meteorology, Part 1: steady-state homogeneous regimes. Boundary Layer Meteorology, 125, 167-191.  Zilitinkevich S., Elperin T., Kleeorin N., Rogachevskii I., Esau I., Mauritsen T. and Miles M., 2008, "Turbulence Energetics inStably Stratified Geophysical Flows: Strong and Weak Mixing Regimes". Quarterly Journal of Royal Meteorological Societyv. 134, 793-799.

27. Many Thanks to

28. THE END

30. Tturbulence and Anisotropy IsotropyAnisotropy

31. Total Energy

32. Anisotropy in Observations Isotropy

33. Equations for Atmospheric Flows

34. Budget Equation for TKE Balance in R-space Balance in K-space ( Heisenberg, 1948 ) Isotropy

35. Mean Profiles

36. Turbulent Prandtl Number

38. Total Budget Equations  Turbulent kinetic energy:  Potential temperature fluctuations:  Flux of potential temperature :

39. Boundary Layer Height Momentum flux derived Heat flux derived

40. Calculation

41. vs. vs.

42. Total Budget Equations  Turbulent kinetic energy:  Potential temperature fluctuations:  Flux of potential temperature :

43. vs. vs.

44. Temperature Forecasting Curve Forecasting Curve

45. Anisotropy vs.