Tornadoes - Severe Convective Storms and Tornadoes: Observations and Dynamics - page 391

Figure 6.55. Idealized illustration of the relationship between swirl ratio and vortex structure
in a tornado simulator. Vertical cross sections of the flow are shown. For very low swirl ratio
there is boundary-layer separation and there is no corner flow and no tornado; for low swirl
ratio, there is a laminar, one-cell vortex; for moderate swirl ratio, a laminar end-wall vortex
''erupts'' into a turbulent, wider, two-cell vortex above the level of vortex breakdown; for
moderate-high swirl ratio, the downdraft reaches the surface and there is a wide, turbulent,
two-cell vortex, with an annular corner region; for high swirl ratio, there are smaller, second-
ary, satellite vortices rotating about a common axis. The advectives ''low'', moderate'', ''high'',
etc. are relative descriptors—not absolute (based on Davies-Jones, 1986; Davies-Jones et al.,
2001; Wakimoto and Liu, 1998).

where the swirl ratio—defined as in (6.62)—is S ¼ v 0 = u 0 . Then

p 0

4

S 2 @ =@ r ð r = R Þ ð 6 : 67 Þ

At small r, the potential flow profile (6.65) is not valid because there is solid body
rotation, so we cannot interpret (6.67) for small radius within the core. However,
for relatively large radius where potential flow is a good approximation, we find
that for a given swirl ratio the radial pressure gradient force that is acting inward
(

<

0) decreases until at some radius the radial pressure gradient force vanishes and
then reverses (acts radially outward) at even larger radius. From (6.67) we see that