1. Solid body rotation (XY):
low pressure
Divergent flow (XY):
high pressure
Shear flow (XY):
*no pressure perturbation

2. (stagnation pressures near saddle pts. in streamline pattern)
Splat:
Spin:
(eddy rotation)
For flow in solid body rotation:

3. 2D Supercells?? 2D Vorticity Eq. No tilting, stretching!!
2D Diagnostic Pressure:
No rotationally-induced mid-level mesolow

4. A Simple “Model” of a Tornado:
Cyclostrophic balance:
Rankine Combined Vortex:
Solid-body rotation in core:
Potential vortex outside:
For full vortex:
*For core region:

5. For Vortex at 3 km AGL:* Vmax=10 ms-1 .5 hPa 2 K 2 hPa Vmax=20 ms-1
*simply assuming pressure change from inner-core region

6. …for Rankine vortex:
at rmax:
beyond rmax:
V20= 20 ms-1
Vrmax=40 ms-1

7. Ordinary Cell:

8. Multicell:

9. Supercell:

11. Physical processes controlling cell types:
Buoyancy processes: basic updraft/downdraft, (ordinary cells)
Gust front processes: triggering of new cells, upscale growth, (multicells)
Dynamic processes: rotating updraft, dynamic vertical pressure gradient forcing, (supercells)

12. Basic Equations: --
(Buoyancy)
+ ice….

13. Buoyant Processes:

14. Buoyancy is Scale-Dependent!!!
…real bubble in 3D simulation
Buoyancy is Scale-Dependent!!!

16. Density Currents
Theoretical speed of propagation: 

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

19. Dynamic Pressure Effects:
(take divergence)
diagnostic pressure eq.
Dynamic pressure
Buoyancy pressure
Vertical momentum:

20. ~
Updraft growing in sheared environment:

21. Vorticity Equation:
Vertical Vorticity:
tilting
stretching

22. Vortex Tube
Circulation:

26. ~

29. Supercell Hodographs:
Supercell processes are Galilean invariant!!!

30. Bunkers et al. WAF 2000

31. Equivalent Potential Vorticity:
= 0 for isentropic motions
Equivalent Potential Vorticity:

32. Davies-Jones, 1984 *assumes steady-state, propagating storm
…from linear theory of circular, convective cells in a sheared environment, covariance of vertical velocity and vertical vorticity is proportional to the storm-relative environmental helicity
*assumes steady-state, propagating storm

33. Storm-relative Environmental Helicity (SREH)
(actually, streamwise vorticity)

34. EBWD Convective Modes Thompson et al., WAF 2012
EBWD: Effective Bulk Wind Difference (half storm depth)

35. ESRH Convective Modes Thompson et al., WAF 2012
ESRH: Effective Storm-Relative Helicity (effective inflow layer)

37. Vortex Tube
Circulation:

42. Adlerman and Droegemeier, MWR, 2005

46. Ward Tornado Chamber (1972)
Ingredients for a tornado: 1) source of rotation
2) updraft

49. Swirl Ratio: S = Vo / Wo

53. McCaul MWR 1991

54. McCaul and Weisman MWR 1996

55. McCaul and Weisman MWR 1996

56. Thompson et al., WAF 2012
STP
STP: Sig. Tornado Parameter