Geoscience Reference
In-Depth Information
Figure 6.50b. As for Figure 6.50a, but vertical cross section of radar reflectivity in dBZ
e
(upper
left), co-polar cross-correlation coecient (
HV
) when the reflectivity factor is
>
10 dBZ
e
(upper
right), spectrum width (indicative of variance of wind speeds in radar volume; could represent
sharp gradients or turbulence or noise, if the signal is relatively weak) in m s
1
(lower left), and
the azimuthal wind speed in m s
1
(lower right), at constant azimuth, through the center of an
EF5 tornado in Oklahoma on May 24, 2011, as detected by RaXPol, a rapid-scan, X-band,
mobile Doppler radar. The center of the tornado is at 2.5 km from the origin, which is not
colocated with the radar (data processing courtesy of Jana Houser). The WEH closes up near
the ground in all cases, probably as a result of frictional inflow. The debris cloud is marked by
HV
<
0.8, the column of which lies inside the region of maximum azimuthal velocities near the
ground; the maximum spectrum width, indicative of turbulence, is located at low levels within
the radius of maximum azimuthal wind speed. Approximate scale of the radar cross-sectional
area is indicated by the purple square in the upper right-hand portions of the top panels.
for an assumed radial profile of azimuthal wind, radially inward in a hydrostatic
atmosphere beginning with the environment of
the tornado. In a combined
Rankine vortex ((6.27) and (6.28))
vð
r
Þ¼
ðv
c
=
r
c
Þ
r
for r
r
c
ð
6
:
47
Þ
ð
r
c
v
c
Þ=
>
ð
6
:
48
Þ
r
for r
r
c
where r
c
and
v
c
are the core radius and azimuthal velocity at the core radius,
respectively. Since
v
c
is also the maximum azimuthal velocity in the vortex, we re-
name it
v
max
. Substituting (6.47) into (6.46) and integrating the result from r
¼
r
c
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