Download - Solid body rotation (XY):
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Solid body rotation (XY):
Divergent flow (XY):
Shear flow (XY):
low pressure
high pressure
*no pressure perturbation
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Splat:
Spin:
(stagnation pressures near saddle pts. in streamline pattern)
(eddy rotation)
For flow in solid body rotation:
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2D Supercells??
2D Vorticity Eq.
2D Diagnostic Pressure:
No tilting, stretching!!
No rotationally-induced mid-level mesolow
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A Simple “Model” of a Tornado:
Rankine Combined Vortex:
Cyclostrophic balance:
Solid-body rotation in core:
Potential vortex outside:
*For core region:
For full vortex:
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Vmax=10 ms-1
Vmax=20 ms-1
Vmax=40 ms-1
.5 hPa
2 hPa
8 hPa
.5 K
2 K
8 K
For Vortex at 3 km AGL:*
*simply assuming pressure change from inner-core region
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at rmax:
beyond rmax:
…for Rankine vortex:
Vrmax=40 ms-1 V20= 20 ms-1
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Ordinary Cell:
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Multicell:
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Supercell:
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•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)
Physical processes controlling cell types:
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Basic Equations:
(Buoyancy)--
+ ice….
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Buoyant Processes:
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Buoyancy is Scale-Dependent!!!
…real bubble in 3D simulation
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Theoretical speed of propagation:
Density Currents
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“Optimal” condition for cold pool lifting
C/∆u > 1
C/∆u = 1
C/∆u < 1
RKW Theory
Rotunno et al. (JAS, 1988)
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Dynamic Pressure Effects:
Dynamic pressure Buoyancy pressure
Vertical momentum:
(take divergence)
diagnostic pressure eq.
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~
Updraft growing in sheared environment:
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Vorticity Equation:
Vertical Vorticity:
tilting stretching
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Vortex Tube
Circulation:
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Supercell processes are Galilean invariant!!!
Supercell Hodographs:
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Bunkers et al. WAF 2000
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Potential Vorticity:
= 0 for isentropic motions
Equivalent Potential Vorticity:
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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
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Storm-relative Environmental Helicity (SREH)
(actually, streamwise vorticity)
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Thompson et al., WAF 2012
EBWD
EBWD: Effective Bulk Wind Difference (half storm depth)
Convective Modes
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Thompson et al., WAF 2012
Convective Modes
ESRH
ESRH: Effective Storm-Relative Helicity (effective inflow layer)
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Vortex Tube
Circulation:
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Adlerman and Droegemeier, MWR, 2005
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Ward Tornado Chamber (1972)
Ingredients for a tornado: 1) source of rotation
2) updraft
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Swirl Ratio: S = Vo / Wo
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McCaul MWR 1991
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McCaul and Weisman MWR 1996
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McCaul and Weisman MWR 1996
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Thompson et al., WAF 2012
STP
STP: Sig. Tornado Parameter
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