A Molecular View of Vorticity & Turbulence Four Lectures at NCAR, 28-29 November 2007

1. A Molecular View of Vorticity & TurbulenceFour Lectures at NCAR, 28-29 November 2007 Adrian Tuck NOAA-ESRL/CSD6 Meteorological Chemistry Program Slide 1

2. CREDITS •Susan Hovde. •Many people in the erstwhile NOAA Aeronomy Laboratory. •Many people connected with the NASA ER-2 & WB57F, and the NOAA G4. Slide 2

3. Key References Alder & Wainwright (1970), Phys. Rev. A,1, 18-21. [emergence of fluid flow from molecular dynamics] Schertzer & Lovejoy (1987), J. Geophys. Res., 92, 9693-9714. [generalized scale invariance, statistical multifractals] Tuck et al. (2004), Q. J. R. Meteorol. Soc., 130, 2423-2444. [scale invariance in jet streams] Tuck et al. (2005), Faraday Discuss., 130, 181-193. [correlation between temperature intermittency and ozone photodissociation rate] Further references and bibliography are in slides 79-84 Some equations and text are in slides 70-78 Slide 3

4. Eady (1951), Q. J. R. Meteorol. Soc., 77, 316: Discussion remark. ‘I congratulate Dr. Batchelor on his scholarly presentation of the similarity theory of turbulence initiated by Kolmogoroff. The argument which derives the consequences of statistical “de-coupling” between the primary turbulence-producing processes and the secondary small-scale features of the turbulence appears to be sound but does it get us very far? In meteorology and climatology we are concerned principally with the transfer properties of the turbulence, determined mainly by the large-scale primary processes to which the similarity theory does not pretend to apply. It is the great virtue of similarity theories that no knowledge of the mechanism is involved and we do not have to assume anything about the nature of “eddies”; anything which has “size” (such as a Fourier component) will do in our description of the motion. But this emptiness of content is also their weakness and they give us very limited insight. It is true that a similarity theory that could be applied to the primary turbulence-producing processes would be of great value but there is no reason to expect that anything simple can be found; when several non-dimensional parameters can be formed, similarity theory, by itself, cannot do much.[continued] Slide 4

5. Similarity theories are attractive to those who follow Sir Geoffrey Taylor in rejecting crude hypotheses regarding “eddies”, mixing lengths, etc. But those who try to determine the properties of turbulence without such (admittedly unsatisfactory) concepts must show that they have sufficient material (in the shape of equations) to determine the answers. If this is not the case it will be necessary to develop some new principle in addition to the equations of motion and the nature of this principle may be brought to light in a study of the mechanism of the primary turbulence-producing process i.e. by trying to refine or modify what we mean by an “eddy” rather than by completely rejecting the concept.’ A wider context for the importance of understanding the mechanisms of turbulence can be found in Eady and Sawyer (1951), Q. J. R. Meteorol. Soc.,77, 531-551: ‘Dynamics of flow patterns in extratropical regions’. Slide 5

6. ER-2 flight into the polar night jet, Stavanger to Wallops Is.: T Slide 6

7. ER-2 flight into the polar night jet, Stavanger to Wallops Is.: √(u2+v2) Slide 7

8. 19890220 Wind VectorsCentred At (550 N,460 W) Slide 8

9. 19890220 Wind Shear Vectors Slide 9

10. Scaling Calculation for19890220 Wind Speed Slide 10

11. Scaling Calculation for19941005 Wind Speed(44°S,173°E) to (65°S,180°E) Slide 11

12. Dropsonde from NOAA G4: (15˚N, 166˚W), 20040304 Temperature & its H scaling exponent Slide 12

13. Dropsonde from NOAA G4: (15˚N, 166˚W), 20040304 Wind speed & its H scaling exponent Slide 13

14. All ER-2 flight segments, 1987 - 2000, 90˚N -72˚S ˚ Slide 15

15. All 261 dropsondes, 20040229 - 20040315, 10˚- 46˚N,140˚- 172˚W Slide 16

16. Figure 8 Alder & Wainwright (1970): A flux applied to an equilibrated population of Maxwellian molecules. Vortices and fluid flow emerge in 10-12s and 10-9 m. Slide 16

17. Intermittency, sharp gradients Slide 17

18. Intermittency, sharp gradients Slide 18

19. Intermittency, sharp gradients Slide 19

20. Long-tailed PDFs of temperature: millions of 5 Hz points from scores of ER-2 flight segments, Arctic summer 1997 & winter 2000. Slide 20

21. All ER-2 ‘horizontal’ segments >2000 s, 1987-2000 Slide 21

22. All WB57F ‘horizontal’ data near tropical tropopause 1998 - 1999 (WAM and ACCENT) Slide 22

23. All DC-8 ‘horizontal’ data, 44˚S - 90˚S, Aug-Sep 1987 (AAOE) Slide 23

24. All DC-8 total water, ‘horizontal’, 44˚S - 90˚S, Aug-Sep 1987 Slide 24

25. All NOAA G4 ‘horizontal’ data, 10˚N-46˚N, 140˚W-172˚W 20040229 - 20040315 Slide 25

26. All ER-2 ozone & nitrous oxide, 59˚N-70˚S, heavy SH weighting Slide 26

27. All 261 dropsondes, Winter Storms 2004, 10˚N-46˚N, 140˚W-172˚W, 20040229 - 20040314, NOAA G4 Slide 27

28. All 261 dropsondes, Winter Storms 2004, 10˚N-46˚N, 140˚W-172˚W, 20040229 - 20040314, NOAA G4 Slide 28

29. Aircraft ascents and descents,Jan-Mar 2004,10˚- 60˚N,84˚- 158˚W Gulfstream Ascents & Descents WB57F Ascents & Descents Slide 29

30. Scaling from G4 in Winter Storms 2004 Slide 30

31. Figure 18 Correlation of H for ER-2 wind speed and temperature with jet strength Slide 31

32. Correlation of H for dropsonde wind speed with jet strength, WS 2004 Slide 32

33. Dynamical stability [Ri>0.25] at 500 & 150 m(left),50 & 10 m(right) Dropsonde (25˚N,157˚W) on 20040229. The ‘Russian doll’ structure. Slide 33

34. Vertical scaling of horizontal wind, 235 dropsondes, Winter Storms 2004. Scaling is not Kolmogorov or gravity wave; Bolgiano-Obukhov applies in lower troposphere, but none are correct at jet altitudes. Slide 34

35. WB57F, Rocky Mountains 19980411. Severe turbulence & lee waves. Isentropes observed by MTP. Figure 22 Slide 35

36. Lee waves near Riverton, Wyoming. Severe turbulence (WAM). Slide 36

37. Figure 24 Scaling of WB57F observations and of MM5 simulation, 19980411. Slide 37

38. Scaling of WB57F and MM5, WAM Rocky Mountain Lee Wave Flight 19980411 Slide 38

39. Simulated monofractal signals: random, antipersistent & persistent. Slide 39

40. Simulated statistical multifractal signal, with typical observed values of generalized scale invariance exponents: conservation, intermittency and Lévy. Slide 40

41. ER-2 temperature data from SOLVE, Arctic Jan-Mar 2000. H1, C1 and . Archived (truncated) data spoils calculation of (T). Slide 41

42. Scaling exponents H1, C1and for SOLVE ER-2, full precision at 5 Hz Slide 42

43. ER-2, O3 SOLVE data. Scaling exponents H1, C1and. Slide 43

44. ER-2, O3 scaling exponents, AAOE, Antarctic vortex, Aug-Sep 1987. Slide 44

45. Long-tailed PDFs of temperature, Arctic winter & summer, trop. trop. Slide 45

46. Scaling & intermittency of temperature, ER-2, Arctic, 19970506 Slide 46

47. Correlation of the observed photodissociation rate of ozone with the intermittency of observed temperature. Arctic summer 1997 and winter 2000. Slide 47

48. Correlation of average temperature along an ER-2 flight segment with its intermittency. Arctic summer 1997 and winter 2000. Slide 48

49. ER-2, Arctic summer 1997. Racetrack segments in static air mass, crossing terminator. Temperature changes between night and day, nothing else does. Slide 49

50. ER-2, Arctic summer 1997. Unlike temperature, wind speed and nitrous oxide do not change across the terminator. Slide 50