Solid body rotation (XY):

# Solid body rotation (XY):

## Solid body rotation (XY):

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##### Presentation Transcript

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 .5 K 2 K 2 hPa Vmax=20 ms-1 8 hPa 8 K Vmax=40 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:

10. 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)

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

12. Buoyant Processes:

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

14. Density Currents Theoretical speed of propagation: 

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

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

17. ~ Updraft growing in sheared environment:

18. Vorticity Equation: Vertical Vorticity: tilting stretching

19. Vortex Tube Circulation:

20. ~

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

22. Bunkers et al. WAF 2000

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

24. Davies-Jones, 1984 …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

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

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

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

28. Vortex Tube Circulation:

29. Adlerman and Droegemeier, MWR, 2005

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

31. Swirl Ratio: S = Vo / Wo