Symmetric, 2-D Squall Line

1. Symmetric, 2-D Squall Line

2. Tropical Squall Lines: (Zipser, 1977) Severe Mid-Latitude Squall Lines: (Newton, 1963) Frontal Squall Lines: (Carbone, 1982)

3. Basic Equations: 2D Squall Line ⁄ *Also, no vortex tilting or stretching -- Or, more simply, consider the 2D horizontal vorticity equation: where

5. RKW Theory Rotunno et al. (JAS, 1988) C/∆u > 1 “Optimal”condition for cold pool lifting C/∆u = 1 C/∆u < 1

6. Early System Evolution “Optimal” C/∆u << 1 C/∆u ~ 1

7. Mature System: C/∆u > 1

10. 2D Convective System Evolution: C/∆u << 1 C/∆u ~ 1 C/∆u > 1 Weak shear, strong cold pool: rapid evolution Strong shear, weak cold pool: slow evolution

12. 2D Convective System Evolution: So, what’s optimal?? C/∆u ~ 1 C/∆u << 1 C/∆u > 1

13. RKW Theory: all other things being equal (e.g., same external forcing), squall line strength/longevity is “optimized” when the circulation associated with the system-generated cold pool remains “in balance” with the circulation associated with the low-level vertical wind shear. Issue: Squall-lines are observed to be strong and long-lived for a wider range of environments than suggested by the models (e.g., weaker shears, deeper shears,….). So, what is the utility of RKW theory?

14. Thorpe et al. (1982) (2D) Squall Lines steadiest when shear confined to low-levels!

15. Fovell (1988) (2D)

16. Weisman et al. (1988) (3D)

17. Weisman et al. (1988) (3D)

18. Weisman et al. (1988) (3D)

19. Weisman and Rotunno (2004)

20. Weisman and Rotunno (2004)

21. Weisman and Rotunno (2004)

22. Weisman and Rotunno (2004)

23. Weisman and Rotunno (2004)

24. Weisman and Rotunno (2004)

25. Wmax (ms-1) 3-6 h Total Rainfall 1-6 h Total Condensation 1-6 h

26. RKW Theory: all other things being equal (e.g., same external forcing), squall line strength/longevity is “optimized” when the circulation associated with the system-generated cold pool remains “in balance” with the circulation associated with the low-level vertical wind shear. Issue: Squall-lines are observed to be strong and long-lived for a wider range of environments than suggested by the models (e.g., weaker shears, deeper shears,….). So, what is the utility of RKW theory?

28. Now Consider a 3D Squall Line….without Coriolis: ⁄ ⁄ --

29. 20 ms-1 shear, no Coriolis forcing

31. 5 May 1996 18:48 GMT

32. How can we systematically produce the observed line-end vortex pattern?

33. Weisman and Davis (1998)

34. “Optimal” Mature System: C/∆u ~ 1 C/∆u > 1

35. Weisman and Davis (1998)

36. Weisman and Davis (1998)

37. Weisman and Davis (1998)

38. Weisman and Davis (1998) Vortex Lines: Us=20 ms-1 over 2.5 km t=4h

39. Weisman and Davis (1998)

40. Line-end vortex mechanisms: Mature Phase:

42. Weisman and Davis (1998) f=0

43. Vortex Tube Circulation:

44. ⁄ Vertical Vorticity: ⁄ …flux form ⁄ Circulation:

45. Weisman and Davis (1998) f=0

47. ⁄ ⁄

48. …tilting of system-generated horizontal vorticity Rear-inflow jet (Davis and Weisman, 1994; Weisman and Davis, 1998; Davis and Galarneau, 2009)

49. Role of Line-End Vortices Focuses and Intensifies Rear-Inflow Jet