Tornadoes - Severe Convective Storms and Tornadoes: Observations and Dynamics - page 400

where is the depth of the boundary layer in the limit as r ! 0. From (6.74) it is

then seen that the corner flow swirl ratio

S c ¼ r c =ð 2 : 6 Þ ð 6 : 77 Þ

The corner flow swirl ratio can therefore also be regarded as being a measure of
the relative size of the core radius in the parent vortex above to the thickness of
the boundary-layer inflow region below. Fiedler and Rotunno showed that the
azimuthal (swirl) velocity in a supercritical endwall vortex
v 1 ¼ 0

: G 1 = ð 6 :

78 Þ

5

while downstream (i.e., above) from the point of vortex breakdown the swirl is
v 2 0 : 25 G 1 = ð 6 : 79 Þ

If the swirl beyond the vortex breakdown level is equal to the swirl above in the
parent vortex ( v 2 ¼ v c ), then from (6.33) it follows that
r c ¼ 4

80 Þ
Then from (6.77) it is seen that the critical corner flow swirl ratio S c ¼ 1.5. (If the
flow rate across the vortex breakdown point is not exactly conserved, S c may be
slightly less.) This value of S c is in accord with a series of trial-and-error numer-
ical (LES) experiments performed by Dave Lewellen et al. To get the strongest
vortex, the depth of the boundary layer must be ''matched'' to the core radius of
the vortex imposed by the parent storm above. For larger values of S c , a central
downdraft reaches the surface, the core radius near the surface increases, and
maximum wind speeds are less; for smaller values of S c , vortex breakdown occurs
higher up and maximum wind speeds are higher up (there may be a central down-
draft, but it is elevated, above the height at which vortex breakdown occurs). As
S c is reduced even more, eventually there is no vortex breakdown at all. At the
critical corner flow swirl ratio, the thermodynamic speed limit is augmented by a
factor of 2. Thus, to get the strongest tornado possible for the parent vortex pro-
duced by the parent supercell above the boundary layer, there must be a ''match''
between the total depleted angular momentum flux into the corner region at the core
radius and angular momentum outside the core. When there is a ''match'', the
radially inward-accelerating air from the inertial layer penetrates the smallest radius
possible, as close to the surface as possible.
If a vortex is characterized by an S c that is less than S c , then the intensity of
the vortex may be enhanced if the total depleted angular momentum flux is
decreased; if S c is greater than S c , then the intensity of the vortex may be
enhanced if the total depleted angular momentum flux is increased. It has there-
fore been suggested that changes in the characteristics of boundary-layer inflow
away from the vortex can determine whether or not a parent mesocyclone can be
intensified and decreased in scale to tornado intensity and size.
Suppose that initially there is a mesocyclone at low levels that has a relatively
high (traditional) swirl ratio and a low corner flow swirl ratio. If boundary-layer
inflow at large radius is suddenly cut off, then the corner flow swirl ratio is

ð 6 :