Tornadoes - Severe Convective Storms and Tornadoes: Observations and Dynamics - page 377

The core radius, as explained earlier, is in part controlled by the amount of
work needed to bring a ring of air in towards the center of the tornado; the
amount of work available is due in large part to buoyancy above in the updraft:
The stronger the buoyancy, the closer in air can be brought. Thermodynamic
buoyancy, however, is not the only significant vertical force. Lou Wicker and Bob
Wilhelmson showed numerically how non-hydrostatic, upward-directed, dynamic
pressure gradient forces could also be significant below the level of free convection
if vorticity increases with height below the cloud base (cf. (4.48)): it is natural for
vorticity to increase with height below the cloud base as a result of frictional
pumping. Within the core radius, where angular momentum increases from zero
at the origin, there is approximate solid body rotation and cyclostrophic balance.
In this region, the ''core region'' ( Figure 6.41a ), radial gradients are much greater
than vertical gradients and the core of solid body rotation is advected upward by
air flowing upward from the corner region.
Beginning at lower levels in the core region, near the center of the vortex,
there is also a friction layer that Wilson and Rotunno have referred to as a
''viscous subcore'' ( Figure 6.41a ). This type of friction layer, which may be found
when air flows past an aircraft wing and is associated with the core of a ''leading
edge vortex'', was discussed by M. G. Hall in 1961, but is not of any great con-
sequence for us. This viscous core forms about the central axis of the core region
so that the azimuthal component of vorticity (6.13) does not tend to infinity as

r ! 0. This viscous subcore is unlike the boundary layer beyond the core radius in
that there is no solid surface slowing down the flow. However, u and v must be
zero at r ¼ 0 owing to axisymmetry.
To summarize ( Figure 6.41 ), we re-state that there are four main regions in
and just surrounding a tornado. (1) The outer flow, which lies beyond the core
radius and above the boundary layer, is inviscid and characterized by constant
angular momentum, potential flow, and non-zero swirl (there is an azimuthal com-
ponent to the wind). (2) The boundary layer is composed of an inertial layer and a
friction layer. The former is inviscid, has low swirl, and angular momentum sur-
faces are horizontally oriented. The friction layer, which is in contact with the
surface and is much thinner than the inertial layer, has almost no swirl. (3) The
corner region, which encircles the axis of rotation of the tornado, but lies within
the core radius, is inviscid and has high swirl. Angular momentum surfaces turn
from horizontal at the interface with the boundary layer to vertical at the top of
the layer. (4) The core is inviscid, except for a thin, conical region centered on the
axis of the tornado; angular momentum surfaces are vertically oriented.
Since dual-Doppler analyses of tornadoes are very dicult to obtain, but
many tornadoes have been probed at close range by mobile Doppler radars, tech-
niques have been developed to make good use of these single-Doppler datasets. To
measure the characteristics of real tornadoes using just one Doppler radar, one
can deduce the structure based on a simple, circularly symmetric model and fitting
the observations to the model. Observational data using mobile Doppler radars
have been used to estimate the dimensions and characteristics of tornado vortices.
In particular, Wen-Chau Lee at NCAR and collaborators have shown how to fit