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Lecture 3:

Lecture 3:. Nocturnal (Stably Stratified) Boundary Layer. Stable Stratification – Ri > 0. ;. Stable flows Richardson Number. Thermally Driven Slope Flows. Reproduced from Mountain Meteorology (2000). Courtesy of Dr. Whiteman, PNNL. Thermally Driven Valley flows.

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Lecture 3:

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  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

  7. A Typical Urban Experiment

  8. VTMX ASU Equipment

  9. Theta profile in the valley

  10. VTMX Measurements

  11. Downslope – Field Data

  12. Flow Analysis

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

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

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

  16. 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

  17. 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 )

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

  19. High Ri Entrainment is Unimportant

  20. Low Ri Entrainment is dominant

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

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

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

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

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

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

  27. CROSS SECTION SW-NE 45 deg.

  28. Temperature & Wind comparison

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

  30. 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).

  31. Downslope flow - Entrainment Entrainment coefficient Richardson number

  32. Entrainment Velocity Ellison and Turner, JFM, 1959

  33. Ellison & Turner Results

  34. Oquirrh Mountain

  35. ASU Doppler Lidar

  36. ENTRAINMENT

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

  38. Re vs. E

  39. Hydraulic Adjustment

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

  41. a) α= (10˚, 20˚) b) α= (0˚, 26˚)

  42. Applications Power plant emissions

  43. Phoenix Terrain

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