Geoscience Reference
In-Depth Information
boundary layer is Ekman-like as we have discussed earlier, but with the caveat that
in tornado-like vortices the friction term is actually negligible. Air rises most rapidly
just inside the RMW and sinks relatively slowly outside the core.
The reader is reminded that the idealized solutions presented for the Rankine,
Burgers-Rott, and Sullivan vortices are for free-slip lower-boundary conditions.
Kuo included the effects of ''surface stress''. It is more complicated to find solu-
tions for free-slip boundary conditions or for those intermediate between no slip
and free slip. It might be that ''partial'' no-slip boundary conditions are most
realistic, but there is no assurance that this is the case. In the case of partial slip
(chunks of earth may be hurled), we have some semblance of a boundary layer.
We now come back to discuss the corner region in more detail. At the surface,
where w ¼ 0, we find from (6.22) that
2
p 0
u
@
u
=@
r v
=
r ¼ 0 @
=@
r
ð 6
:
45 Þ
In the corner region, since radial inflow must decelerate (unlike in the inertial
layer, in which the flow accelerates radially inward), u
@
u
=@
r
>
0, since u
<
0 and
2
@
u
=@
r
<
0. The second term on the LHS of (6.45), the centripetal term ( v
=
r)is
always
0. It follows that acceleration due to the radial pressure gradient force
(the RHS of (6.45)) is radially outward (acting to decelerate radial inflow; p 0
decreases with radius, so that there is an ''adverse'' pressure gradient) for rela-
tively large radius within the corner region or when v is small (i.e., when there is
''low swirl''). For small radius or when v is large (i.e., when there is ''high swirl'')
the pressure gradient force may vanish (there is a stagnation point) or reverse,
becoming negative (acting to accelerate radial inflow; p 0 increases with radius).
For increasing swirl (value of v ), a reversal occurs at greater radius. There are a
number of possible configurations of the radial velocity field that vary as a function
of swirl ( v ) and radial pressure gradient. If the radial pressure gradient is held fixed,
then the radial velocity field depends on the swirl and distance from the axis of rota-
tion. The behavior of the wind field in the corner region using (6.45) will be
discussed in more detail subsequently.
In the corner region, there can be ''inertial overshoot'', which is manifested by
a bulge toward the axis of rotation in the lines of constant angular momentum,
such that there is a layer in which the angular momentum is greater than the
angular momentum aloft in the core region at the same radii ( Figure 6.41b ).
The inertial overshoot in the corner region is associated with the highest azimuthal
velocities (swirl) in a tornado. There will be a further discussion on the effects of
swirl in the corner region later when we try to find the condition(s) under
which tornado intensity is optimized.
A climatology of the core radius in tornadoes (and other characteristics) based
on mobile Doppler radar data from Doppler on Wheels (DOW) radars has been
compiled by Curtis Alexander for many tornadoes. The author and his mobile
radar group at OU, using mobile Doppler radars from the University of
Massachusetts, have also made measurements of core radius. The median core
radius for tornadoes in the Great Plains of the U. S. is 150m, while the core
radius may be as narrow as 100m and as wide as 500m.
<
Search WWH ::




Custom Search