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