Tornadoes - Severe Convective Storms and Tornadoes: Observations and Dynamics - page 350

Figure 6.34. Illustration of the dynamic pipe effect. A steady vortex in an inviscid fluid (curved
streamline) is associated with a dynamic perturbation central pressure deficit ''L'' (it does not
matter if the vortex is cyclonic or anticyclonic). There are therefore downward and upward-
directed vertical dynamic peturbation pressure gradient forces (PGFs) above and below the
vortex, respectively. Fluid converges inward and vorticity is increased both above and below
( þ ) (while divergence (not shown) occurs at the center of the vortex, where vorticity is
decreased). When a stable vortex is squeezed inward locally, centrifugal waves are generated.
this occurs probably depends on the vertical gradient in vorticity or, in other
words, how localized in height the mesocyclone is: the shorter the vertical scale of
the mesocyclone, the sharper the vertical gradient in vorticity, the more intense the
vertical perturbation pressure gradient force, and the faster the propagation speed.
However, the propagation speed of the mid-level vortex could depend on the
speed of vertically propagating centrifugal waves, which for solid body rotation
(solid body rotation and centrifugal waves are discussed in more detail later in
this chapter) that is height dependent and with no mean updraft or downdraft
superimposed, the vertical phase speed as shown by Alan Shapiro depends upon
the rate of rotation divided by the wavenumber: the fastest vertically propagating
centrifugal waves are those with the longest vertical wavelength. For a vertical
wavelength of 10 km and vorticity of 10 2 s 1 , the phase speed is around 50m s 1 ,
which is comparable with vertical velocity in supercell updrafts; at this propaga-
tion speed, waves can travel half the depth of the troposphere in just a few
minutes. In nature, vortices may not be in solid body rotation, may be confined to
a layer, and there may be an updraft or downdraft embedded, so that the problem
of determining the centrifugal wave speed is more complicated.
It has been found from Doppler radar observations on time scales of minutes
that many ''tornadic vortex signatures'' (and hence tornadoes) begin at mid-levels
and then propagate downward. Numerical experiments have demonstrated how
when the buoyancy driving the updraft in a supercell is greatest at mid-levels,
there is the highest potential for the DPE to propagate mid-level vortices down-
ward; on the other hand, when buoyancy is greatest at low levels, vorticity
increases throughout the vertical column simultaneously.
More recent rapid scan Doppler radar observations of the formation and
subsequent behavior of a few mid-level mesocyclones on time scales of 10 s