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Accordingly, a tornado core is not formed from upward tilting of a horizontal
vortex tube by storm updrafts. Instead, it seems natural to assume that it orig-
inates in the storm from mid-levels at an altitude of several hundred meters or
a few kilometers above the ground, and with the wrap-around nonlinear mech-
anism, the tornado vortex tube hits the ground in the perpendicular direction,
satisfying the boundary condition of vanishing vertical velocity at the ground
surface.
18.7.2
High Relative Helicity and Stationary State
It is supported by successful numerical simulations (
Noda 2002
;
Noda and Niino
2005
,
2010
) that the relative helicity of a mature tornado is high, near one, implying
a stationary state SS (Fig.
18.2
) of a relatively long life time for the mature stage
of a tornado as discussed in Sects.
18.3
and
18.4
of this article. It should be noted
that the helicity is defined as given in (
18.8
) as the scale product (
v
!
) between
the flow velocity
v
and the vorticity
!
, and it is used to show the stationary state,
namely
.Todoso,itisassumed,asshownin(
18.10
) of Sect.
18.4
,that
the magnitude of the tem
@
t
!
0
.
v
!/
is sufficiently smaller than that of
.
v
!
/
.
Here the solenoid term r
..1=/
rp) and r
.
of (
18.23
) are neglected,
although both play important roles in supercell development stage (baroclinic),
but not after the transition to tornadic stage (barotropic), as discussed earlier in
Sasaki
(
2010
).
v
!/
18.7.3
Transition from Supercell to Mature Tornado
In the entropic balance theory, the flow velocity
v
is expressed by the diagnostic E-L
equation (
18.5
),
v
Dr
˛
Sr
ˇ:
same as (
18.5
)
(18.34)
The rotational term
, plays an important role in supercell stages including
tornadogenesis as discussed in the author's earlier article (
Sasaki 1999
,
2009
,
2010
)
and Sect.
18.5
of this article. This can also be been seen in the following vorticity,
!
.
Sr
ˇ/
, equation,
!
D
.1=
S
/
rS
.
Sr
ˇ/:
same as (
18.6
)
(18.35)
The helicity, however, uses only the first divergent term (-r
˛/
for the flow velocity
as shown in (
18.22
), as
H
˛
D
.
r
˛/
!:
same as (
18.22
)
(18.36)
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