Tornadoes - Severe Convective Storms and Tornadoes: Observations and Dynamics - page 387

6.6.2.2 Dynamic effects on the intensity of tornadoes: the swirl ratio
Owing to the stability of the core of a tornado vortex with respect to
displacements in the radial direction, centrifugal wave motion is possible. Centri-
fugal waves can be produced in tornadoes when there is an imbalance between the
radially inward-directed pressure-gradient force and the radially outward-directed
centrifugal force. The resultant restoring force (cf. (6.9)) can be explained as
follows: imagine squeezing a vortex of solid body rotation radially inward locally
and then letting go; the vortex will then experience a radially outward-directed
restoring force and pop back outward and overshoot its equilibrium level, a con-
sequence of the conservation of angular momentum, when there is no friction
( Figure 6.53 ). Above and below, coupled vertical motions and the resultant radial
flow will cause the vortex above and below to be squeezed, and vertical wave
propagation will follow.
Above the upward jet in an end-wall vortex upward vertical velocity
eventually is reduced and may even switch sign (turn into a downdraft) since vor-
ticity decreases with height there and therefore a dynamically induced downdraft
above the level at which azimuthal winds are greatest is induced. If rising air in
the upward, frictionally induced jet ascends more rapidly than the phase speed of
vertically propagating centrifugal waves, then the flow is said to be ''supercritical''
(with respect to centrifugal waves). Above the jet, vertical velocity becomes less
than the phase speed of centrifugal waves, so the flow becomes ''subcritical''.
The transition from supercritical to subcritical flow can lead to a phenomenon
known as ''vortex breakdown'', which the fluid dynamicist T. Benjamin in a
Figure 6.53. Idealized illustration of vertically propagating centrifugal waves in a stable
vortex. Streamlines show alternating compression and expansion (based on Shapiro, 2001).