1. Shawnee/
Moore, Oklahoma May 20, 2013

2. MPEX Mobile Soundings 19 May 2013
CSU 19 UTC
CSU 21 UTC
CSU 23 UTC
WRF OUN 19 UTC
WRF OUN 23 UTC
WRF OUN 00 UTC

3. Trier et al. MWR 2015
Ensemble-analyzed circulation along dry line: 19 May 2013

4. Supercells

11. MICRO-
PHYSICS

12. 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)

14. 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)

16. Momentum Eq.
Dynamic Pressure Eq. --

17. Linearise pressure eq. about U(z), V(z) (environmental vertical wind shear)
So, since

18. 2D Updraft in Sheared Environment:

19. Vorticity Equation:
Vertical Vorticity:
tilting
stretching

22. Vortex Tube
Circulation:

23. Theorems for inviscid fluids with conservative external forces (e. g
Theorems for inviscid fluids with conservative external forces (e.g., no baroclinicity, buoyancy) (Helmholtz, 1858)
….Vortex lines (tubes) are material lines that are frozen into the fluid.
….The circulation (strength) of a vortex tube is invariant
…The circulation on any curve around a vortex tube is constant along the tube.

25. Tilting:
Linearized about a mean vertical wind shear:

26. Vertical Momentum Eq. (rewritten)
(dynamic) (buoyancy)

27. (H = horizontal shearing deformation)
So, for a wind profile in pure rotation:
So, again, since

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

36. Linearise pressure eq. about U(z), V(z) (environmental vertical wind shear)
So, since

42. Bunkers et al. WAF 2000

43. Weisman and Rotunno, Jas 2000