Tornadoes - Severe Convective Storms and Tornadoes: Observations and Dynamics - page 397

increases, owing to the increase in centrifugal force inhibiting the radial pressure
gradient force and forcing air upward at an even greater radius. The vortex is now
a relatively wide, two-cell vortex, and the radial profile of azimuthal wind is such
that there is an annulus of strong shear vorticity flanked by a downdraft at
smaller radii and an updraft at higher radii.
In nature, the swirl ratio is probably controlled by the updraft magnitude in
the convective cloud above, which is related to both buoyancy in the cloud and
dynamic vertical pressure gradients, and to the dimensions (depth and width) of
the inflow layer. A change in updraft intensity while a convective cloud grows or
decays or a change in the nature of surface roughness characteristics or a change
in how much vorticity is produced in the parent storm or a change in the depth of
the moist boundary layer feeding the updraft in the parent storm may change the
swirl ratio. It is dicult to relate the swirl ratio defined for a vortex simulator to
the swirl ratio in nature because critical swirl transitions depend on the Reynolds
number, which is different in the real atmosphere, and because there is uncertainty
as to how to interpret the parameters defined in the simulator based on measure-
ments in the real atmosphere; nevertheless, it has been attempted with some
claimed success in mesocyclones and tornadoes.
We will now relate the swirl ratio to the maximum intensity of tornadoes.
Lewellen et al. in 2000 argued that the conventional definition of swirl ratio in
simulators (or in their ''virtual'' representation) is deficient because '' other

physical parameters also affect the structure of the central vortex corner flow, so
that flows that share the same large-scale swirl ratio can produce different corner
flow structures.'' Lewellen et al. therefore defined a swirl ratio for the corner flow
region only: this parameter describes the ratio of azimuthal velocities in the core
region to radial inflow velocities (cf. (6.62)) in the tornado boundary layer only at
the outer boundaries of the corner region. The more conventional swirl ratio
includes radial inflow at a much larger radius; since radial inflow outside the core
radius in the inertial layer is accelerated, it depends on what radius one chooses to
measure inflow. In addition, the value used for the azimuthal wind is not neces-
sarily the one at the location of the radius of maximum wind or at the core radius
or at some radius that marks some particular characteristic of the flow field;
moreover, the azimuthal wind varies with height in the boundary layer. The swirl
ratio for the corner region is defined as

...

S c ¼ r c G 1 = M ð 6 : 71 Þ

where r c is the core radius ( G 1 is a measure of the angular momentum

outside the core (i.e., at infinity) and above the boundary layer; and M is a
measure of the mass flux flowing into the corner region from the boundary layer.
M must be chosen for some conserved quantity such that it does not matter what
the radius is in the boundary layer or what the height is in the core region at
which we measure

G 1 =v c );

it. Lewellen et al. therefore define ''depleted angular

momentum'' as

G d ¼ G 1 G ð 6 : 72 Þ