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