Tornadoes - Severe Convective Storms and Tornadoes: Observations and Dynamics - page 396

height and in the clockwise direction as a result of the increase in radial inflow
with height near the ground ( Figure 6.29, top right panel). The vortex line initially
is therefore vertical above the boundary layer, but leans inward and in the clock-
wise direction with height near the surface. It then moves more quickly in the
counterclockwise direction with height owing to increase in cyclonic flow with
height. The net effect is that the vortex line curls with height in the clockwise
direction and near the surface, forming a helix about the central axis. Secondary
vortices are located near the radius of maximum wind (RMW) and propagate
more slowly than the mean flow (approximately half the speed, based on observa-
tions in a vortex chamber) so that they retrograde with respect to the mean flow.
When the swirl ratio is very low, from (6.67) it is seen that

p 0

4

@ =@ r ð r = R Þ ð 6 : 70 Þ

In other words, since the RHS of (6.70) is 0 and increases with r, the radial

pressure gradient force acts radially outward, and from (6.69) we find that when
v

>

2

r can be neglected (for low v and/or high r) inertial acceleration is radially
outward. In this case, radial inflow decreases inward and is forced upward at the
very far radius and a strong vortex cannot occur at low levels ( Figure 6.55 ).
Boundary-layer flow is forced to ''separate'' at high radius beyond the core radius,
beyond the corner region.
So, we have described what happens at the two extremes, when there is a high
swirl ratio and a very low swirl ratio. What happens when there is a ''low swirl
ratio'', a swirl ratio intermediate between that of ''very low swirl ratio'' and ''high
swirl ratio''? At low swirl ratio the radius at which the radial pressure gradient
force reverses from radially outward to radially inward occurs at small radius—
cf. the discussion immediately following (6.45). If it occurs near the core radius,
the air will be accelerated inward into the corner region and then it decelerates
and turns upward there. In this case, there is rising motion near the axis of
rotation and sinking motion beyond the core radius. The resultant circulation is
that of a ''one-cell vortex''.
The reader is reminded that the behavior of an idealized tornado-like vortex
in a vortex simulator is summarized in Figure 6.55. Idealized force diagrams at
various swirl ratios are illustrated for summary purposes in Figure 6.59. At very
low swirl ratio, there is boundary-layer separation at large radius and an intense
low-level vortex does not occur.
At low swirl ratio, a one-cell vortex forms, in which there is rising motion
along the central axis of the tornado and sinking motion far from the central axis.
In the corner region, rapidly rising air along the central axis weakens and en-
counters the central downdraft and vortex breakdown may occur. Above the level
of vortex breakdown, there is a two-cell vortex, in which there is sinking motion
along the central axis, rising motion outside of the central axis, and sinking
motion far from the central axis. At some higher swirl ratio, the level of vortex
breakdown lowers to just above the surface and is referred to as a ''drowned
vortex jump''.
As the swirl ratio is increased some more, the width of the core of the vortex

=