Geoscience Reference
In-Depth Information
imposed from above in the parent storm (the mesocyclone) and the vortex in the
corner region below affected by the boundary layer. Downward-propagating cen-
trifugal waves from above cannot continue to propagate downward into the
supercritical region, so wave energy is reflected upward and standing waves are
produced. Standing centrifugal waves above the jet, in the subcritical regime, must
reduce the upstream flow force so that a steady state can be maintained. When the
transition between supercritical and subcritical regimes is sharp, the lead centrifu-
gal wave breaks and there are standing waves downstream. When the transition is
sharper, even downstream waves break. Because downward-propagating centrifu-
gal waves from the mesocyclone in the parent storm cannot propagate into the
supercritical region below, information about the mesocyclone aloft is not ''com-
municated'' to the supercritical corner region.
Doppler radars cannot easily document the vortex breakdown phenomenon
because it is dicult for radars to detect motions near the surface where vortex
breakdown often occurs. Radars cannot detect motions very close to the surface
owing to the curvature of the Earth and because the half-power beamwidths of
radar antennas are too wide; as a result of the latter there is ground clutter con-
tamination. Vortex breakdown has been seen in nature, especially from airborne
platforms that permit a look downward into the corner region of a tornado,
which may otherwise be hidden from view at the surface by a debris cloud or a
condensation funnel. It perhaps could be verified by observing the spectrum width
(a measure of the variation of Doppler wind speeds in a radar volume) and deter-
mining if the spectrum width increases with height at the level at which vortex
breakdown is expected. It may be, however, that the region of vortex breakdown
may not have a high enough density of scatterers to be detected or that scatterers
are too small to be detected, or both.
The most important parameter defining idealized vortex behavior in a
simulated laboratory vortex, based on many experiments, is the ''swirl ratio'' (S):
S ¼ð R
GÞ=ð 2M Þ
ð 6
:
58 Þ
where R is the radius of the updraft hole;
G
is circulation at the edge of the
updraft ( v 0 2
R) (i.e., angular momentum multiplied by 2
); and M is the volume
R 2
flow rate of the updraft (w
Rhu 0 ), where h is the height of the inflow area,
v 0 is the azimuthal wind component at the outer edge of the updraft hole (the edge
of the updraft), u 0 is the radial inflow velocity at the edge of the chamber (note
that u 0 is positive for radial inflow, the reverse of convention, according to which
the radial wind component is negative for radial inflow), and w is the mean ver-
tical velocity in the updraft hole. The swirl ratio is therefore also given by the
following:
¼ 2
R 2
S ¼ R ðv 0 2
R Þ=
2 ð w
Þ¼v 0 =
w
ð 6
:
59 Þ
From mass continuity consideration, the flux of mass into the chamber from all
sides must equal the flux of mass out of the chamber through the updraft hole, as
noted earlier, so that
w ¼ð 2hu 0 Þ=
R
ð 6
:
60 Þ
Search WWH ::




Custom Search