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Solid body rotation (XY):

Solid body rotation (XY):. low pressure. Divergent flow (XY):. high pressure. Shear flow (XY):. * no pressure perturbation. (stagnation pressures near saddle pts. in streamline pattern). Splat:. Spin:. (eddy rotation). For flow in solid body rotation:. 2D Supercells??. 2D Vorticity Eq.

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Solid body rotation (XY):

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  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

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