Tornadoes - Severe Convective Storms and Tornadoes: Observations and Dynamics - page 343

) in the vorticity equation (2.50), it
is seen that under the effect of a field of constant convergence at the base of a
convective storm of 10m s 1 /1 km ¼ 10 2 s 1 , which is consistent with a buoyant
updraft in a convective cloud above (

Considering only the divergence term (

y 10m s 1 /1 km),
the e-folding time for vorticity is 1/convergence 100 s, or on the order of a
minute. Considering the divergence term in (2.50) alone
t ¼ ln ½j f =j 0 =

@ w =@ z @ u =@ x and @v=@

ð 6 : 1 Þ

where the subscripts f and 0 represent the final and initial values. In 10min, the
vorticity of tornado intensity (1 s 1 ) can be ''grown'' from mesocyclone vorticity
( 1.5 10 3 s 1 )with10 2 s 1 convergence. In 10min, air flowing radially
inward at 10m s 1 from the outer edge of a mesocylone at the ground at 2.5 km
radius would have enough time to make it to near the center of the tornado and
then be transported upward.
Since vorticity is scale dependent, it is possible, for example, to identify
vortices such as dust devils, whose wind speeds can vary 10m s 1 over only
10m, having vorticity as high as that of tornadoes. Circulation is therefore a better
indicator of the intensity of tornadic vortices than vorticity because circulation is less
scale dependent. In addition, circulation is conserved if friction and baroclinic effects
are neglected, just like vorticity. This assertion must be accepted with extreme
caution, however, since friction does play a role and tornadoes are often
embedded in baroclinic environments, in which circulation may be further
enhanced, but not necessarily exponentially with time. The circulation enclosing
the core of a strong tornado, as noted earlier, is 30,000m 2 s 1 . In constrast, the
circulation of a dust devil is only 2 (10m)(10m s 1 ) 600m 2 s 1 . A 5 km wide

mesocyclone having a circulation of 30,000m 2 s 1 , with vorticity averaging
1.5 10 3 s 1 , could be shrunken to 100m radius in 4.5min by radial inflow of
just 10m s 1 . However, while circulation is a better measure of tornado intensity
than vorticity, circulation also is deficient because it depends on the precise loca-
tion of the material curve about which it is being computed. Since circulation is a
spatially averaged quantity, the wind speeds may be much higher inside the circuit
than they are outside the circuit and vice versa. Thus, depending on the radial
profile of the wind, much higher and more damaging winds may exist inside the
circuit or outside the circuit. To be a true measure of damage potential, the circuit
should be taken at the radius of maximum wind.
In addition, one must consider that tornado damage estimates and Doppler
wind measurements include both the wind speed associated with the tornado
vortex and that of the translation speed of the vortex. A weak vortex moving very
quickly can inflict strong damage, even though the azimuthal wind speeds in the
reference frame of the vortex are relatively low. It could be argued that one should
subtract out the translation speed to assess the ''true'' intensity of a tornado.
Earth's vorticity probably does not contribute directly to tornadogenesis. Con-
vergence of 10 2 s 1 (e.g., if convergence acts at cloud base, above which there is
an updraft 5 km in diameter and if the wind velocity varies linearly from zero at
the center of the cloud base to 20m s 1 radially inward at the perimeter, then
convergence is 8 10 3 s 1 ) would have to act on Earth's vorticity ( 10 4 s 1 )