Lecture 3:

1. Lecture 3: Nocturnal (Stably Stratified) Boundary Layer

2. Stable Stratification – Ri > 0 ;

3. Stable flows Richardson Number

4. Thermally Driven Slope Flows Reproduced from Mountain Meteorology (2000). Courtesy of Dr. Whiteman, PNNL.

5. Thermally Driven Valley flows Reproduced from Mountain Meteorology (2000). Courtesy of Dr. Whiteman, PNNL.

6. Salt Lake City

8. A Typical Urban Experiment

9. VTMX ASU Equipment

10. Theta profile in the valley

11. VTMX Measurements

12. Downslope – Field Data

13. Flow Analysis

14. Entrainment Coefficient, Ri = Dbh/U2 X X Idealized Slope Flow Analysis X X X X X X X X

15. Downslope flow - Pulsation Linearized governing equations with neglected flux divergence and the entrainment-rate, have oscillatory solution with the frequency or period

16. T=55 min Downslope flow - Pulsation ACS a = 4.7 deg: T=20 – 50 min SS a = 1.8 deg: T=50 – 130 min

17. Other Observations • the Riviera valley (Gorsel et al., ICAM/MAP proceedings, 2003) • Cobb Mountain (Doran and Horst, JAM, 20(4), 361-364, 1981) • Phoenix valley (Keon, Master Thesis, ASU, 1982) • Slope and ACS sites of the VTMX campaign in Salt Lake City (Doran et al., BAMS, 83(4), 537-554). American Scientist 2004

18. Manin and Sawford’s (1978) Solutions(Combining with Briggs formula) For ( is the slope angle, the stabilizing buoyancy flux driving the flow and s the along-slope distance measured downward, hI integral scales of katabatic layer depth, UI velocity and DbI buoyancy )

19. Flow Velocity High Ri Entrainment is Unimportant Low Ri Entrainment is dominant

20. High Ri Entrainment is Unimportant

22. Low Ri Entrainment is dominant

23. D P B Flux Richardson Number Gradient Richardson Number Diffusion Coefficients e.g.. Parameterization of Vertical Mixing

24. Flux versus Gradient Richardson Numbers J. Fluid Mech. 2002

25. Eddy Coefficients for the entire range of Rig; for Rig > 1 for Rig < 1 and

26. Normalization of the eddy coefficients in the VTMX J. Atmospheric Sci., 2003

27. for Rig < 1 and for Rig > 1 Eddy Diffusivity (Semi Empirical)

28. Inverse Prandtl Number Inverse Prandtl Number Eddy Diffusivity Ratio • J. Physical Oceanography 2001 • Boundary layer Meteor. 2005

29. CROSS SECTION SW-NE 45 deg.

30. Temperature & Wind comparison

31. (averaged over 1-h, at 10 km inland versus simulations) RAMS uses Therry and Lacarrere’s (1983) parameterization (200x200 km domain, including Rome)

32. Due to a normal mean flow Entrainment Coefficient U Characteristic velocity Entrainment -- Encroachment of nearby fluid across a boundary Boundary entrainment velocity (rate of propagation of a bounding surface due to turbulence). Flux entrainment velocity (characteristic velocity the scales cross across an interface – boundary stationary).

33. Downslope flow - Entrainment Entrainment coefficient Richardson number

34. Entrainment Velocity Ellison and Turner, JFM, 1959

35. Ellison & Turner Results

36. Oquirrh Mountain

37. ASU Doppler Lidar

38. ENTRAINMENT

39. Entrainment Coefficient Mixing Transition -- above a certain critical Reynolds number, entrainment increases J. Fluid Mech. 2005,

41. Re vs. E

42. Hydraulic Adjustment

43. Steady state, small angle Ri < 1 Hydraulic Equation Ri > 1

45. a) α= (10˚, 20˚) b) α= (0˚, 26˚)

46. Applications Power plant emissions

47. Phoenix Terrain