Tornadoes - Severe Convective Storms and Tornadoes: Observations and Dynamics - page 369

Figure 6.44. Cancellation of shear and curvature vorticity in a potential vortex. The rotation
(red curved streamline) induced by shear associated with the decrease in azimuthal wind speed
with radius from the center of the vortex (black curved streamlines; wind speed is proportional
to the length of each curved streamline) is equal and opposite to the rotation induced by the
curvature of the flow.

0and
vðGÞ is nonzero everywhere beyond the origin (r ¼ 0). However, the vorticity in a
potential vortex is zero. Since vorticity is circulation divided by the area of the
material curve about which circulation is computed, there must be infinite vorticity
at r ¼ 0 (as a point source or line source), and this vorticity is averaged along with
the zero vorticity for r a >

The circulation (2.52) about a potential vortex (6.27) is finite, since r >

0, where r a is the radius of the material curve when
circulation is computed. So, if we compute circulation using (2.52) and take the
limit as the area of the material curve approaches zero, we find that circulation is
due entirely to the point or line source of vorticity at the origin. If, on the other
hand, we choose as our material curve one that excludes the center of the vortex,
then circulation in the potential vortex is zero ( Figure 6.45 ).
At the center of the tornado, by symmetry there must be zero azimuthal
velocity and angular momentum. Beyond the ''core'' of the tornado the angular
momentum is a constant ( Figure 6.41a ) fixed set by environmental flow (cf.
(6.26)). If air parcels were brought towards the center of the vortex, without any
turbulent mixing, the azimuthal velocity would approach infinity and so would its
radial gradient. So, an air parcel transported radially inward toward the center

r >