Supercells - Severe Convective Storms and Tornadoes: Observations and Dynamics - page 210

vertically: thus, in order that the potential vorticity vector remain zero, the
vorticity vector must become directed upward (and poleward) on the equatorward
side and downward (and poleward) on the poleward side ( Figure 4.29, middle
panel).
Finally, one can use circulation analysis to understand mid-level vortices in
supercells. For example, consider a circuit in a horizontal plane encompassing a
mesocyclone at mid-levels. How did this configuration come about? There must
have been a gradient in vertical motion and the plane had been advected so that a
circuit in the vertical plane had been tilted upward onto the horizontal ( Figure
4.29, bottom panel). In the case of a mid-level mesocyclone, circulation analysis,
potential vorticity analysis, and vortex line analysis are all useful.
In nature, cyclonic-anticyclonic couplets are observed in Doppler radar
observations of the mid-levels of supercells. When a (single) Doppler radar scans a
supercell at mid-levels, the signature of a cyclonic-anticyclonic couplet is usually
evident ( Figure 4.30 ). These cyclonic-anticyclonic couplets are usually most pro-
nounced at mid-levels because (1) updrafts in supercells are strongest at upper
levels in the troposphere, so that horizontal vertical velocity gradients are
also strongest there and (2) vertical shear is usually strongest in the lower half of
the troposphere. The net result is that the tilting of horizontal vorticity is strongest
at mid-levels. When these vortices are intense and long lived they are called
''mesocyclones'' and ''meso-anticyclones''; mesocyclones are usually the focus of
attention rather than meso-anticyclones because they are associated more

frequently with severe weather.

4.5 INTERACTION OF VERTICAL SHEAR WITH UPDRAFTS/

DOWNDRAFTS FORCED BY BUOYANCY: LINEAR AND
NONLINEAR PRESSURE EFFECTS

In the previous section the vorticity equation (and vortex line analysis and
potential vorticity analysis) was used to explain the formation of a counter-rotat-
ing vortex pair when a strong updraft interacts with horizontal environmental
vorticity. The divergence equation (2.62) is now used to examine the effects of the
interaction between a buoyant updraft and environmental vertical shear on the
pressure field. It turns out these counter-rotating vortices play an important role in
updraft propagation. An analysis of (2.62) can be used to explain how and why
supercell updrafts propagate because in regions of upward-directed dynamic per-
turbation pressure gradients, air is accelerated upward and updrafts may be
triggered when the LFC is reached, while in regions of downward-directed pertur-
bation pressure gradients air is accelerated downward and updrafts are suppressed
or downdrafts are forced.
The propagation velocity of updrafts triggered by upward-directed dynamic
perturbation pressure gradients can be determined using Petterssen's formula for
the motion of extrema in scalar fields (see pp. 47-54 of Bluestein, 1992),
which depends on the horizontal gradient of the field of the vertical dynamic