Tornadoes - Severe Convective Storms and Tornadoes: Observations and Dynamics - page 368

result of these processes is that there is a level at which the azimuthal wind is
greatest and this level is elevated at a height just above the depth of the boundary
layer. So, we would expect to find maximum wind speeds in tornadoes just above
the friction layer—not at the surface—if there is solid body rotation.
Alas, evidence from numerical simulations is that where solid body rotation is
found in a tornado-like vortex the turbulent friction term is relatively small com-
pared with the other terms. It therefore appears as if the boundary layer under
solid body rotation is not applicable to tornadoes; it seems, on the other hand, to
be applicable to the hurricane/typhoon/tropical cyclone boundary layer. However,
that a rotating boundary layer for solid-body rotation is inviscid may not be a
correct inference if one takes into account that the effect of turbulent viscosity
itself might be to reduce the friction term to zero, so that just because the friction
term is negligible does not mean that it is not important in bringing the boundary
layer into a steady state. (One can say the same for a convective boundary layer in
which stratification is dry adiabatic. One might incorrectly conclude that since
stratification is neutral there are no turbulent eddies; in reality local, short-lived
episodes of super-adiabatic flow occur and the vertical exchange of eddies stabil-
izes the atmosphere so that it appears as if the atmosphere is inviscid.)
Burggraf, Stewartson, and Belcher, in their 1971 paper, showed that for
potential flow there is a layer of radial inflow, whose intensity is a maximum
above the surface, but then decreases with height; there is no layer of radial
outflow. As r gets smaller and smaller, the level at which the intensity of radial
inflow begins to decrease with height lowers. Most importantly, it is found that
there is no overshooting of azimuthal velocity with respect to the cyclostrophic
value of the azimuthal velocity as there was when the radial profile of azimuthal
wind is that of potential flow; the azimuthal wind is always less than the

cyclostrophic value.
The flow in tornadoes in nature and in idealized simulations contains aspects
of both solid body rotation and potential flow. In the inertial region air flows
radially inward and angular momentum is conserved (there is no turbulent
friction). So

vð r Þ r ¼ G ð 6 : 26 Þ

where is a constant given by the angular momentum, and air parcels therefore

spin up as they approach the center of the vortex. It follows that when

G

G is

spatially uniform outside of some radius the radial profile of azimuthal wind is

vð r Þ¼G= r ð 6 : 27 Þ

In the outer flow and inertial regions, then, there is potential flow (no vorticity),
and the azimuthal wind weakens rapidly with distance from the center of the
vortex. The curvature vorticity of the vortex is counterbalanced by shear vorticity
of the opposite sign ( Figure 6.44 ). Formally, the potential vortex is a solution to
the inviscid forms of (6.9) and (6.10) when w ¼ u ¼ 0.