Supercells - Severe Convective Storms and Tornadoes: Observations and Dynamics - page 216

Figure 4.33. Illustration of cyclostrophic balance. The azimuthal wind speed v may be cyclonic
as shown or anticyclonic. The pressure gradient must be positive, so that pressure increases
radially outward.

the vertical shear vector always points in the same direction; when the hodograph
is curved, the vertical shear vector changes direction with height. A straight (uni-
directional) hodograph may be associated with a wind profile in which the wind
direction changes with height, even though the vertical shear direction does not
vary with height (e.g., Figure 4.32 ). It is assumed in the following analyses that
R 1 (see (4.9)), so that the effects of the vertical perturbation pressure gradient

force are at least comparable with that of buoyancy and that the buoyancy is
substantial.
From (4.46) we see that for a localized updraft, the perturbation pressure is
relatively low on the downshear side of the updraft and relatively high on the
upshear side ( Figure 4.34, top). To understand this physically, consider an atmo-
sphere in which the wind is westerly and increases in speed with height. If
horizontal momentum is conserved (we ignore lateral mixing across the updraft),
then the weaker westerly momentum from below is advected upwards in an
updraft, so that an air parcel approaching the updraft aloft encounters lower
values of westerly momentum inside the updraft ( Figure 4.34, bottom panel). The
air parcel must therefore decelerate as it enters the updraft, which is consistent
with an adverse pressure gradient force (i.e., the pressure increases as it enters the
updraft, so that the horizontal pressure gradient force is directed in the direction
opposite that of the flow). Similarly, an air parcel leaving the updraft encounters
higher values of westerly momentum outside the updraft. The air parcel therefore
accelerates as it leaves the updraft, which is consistent with a pressure gradient
force that is directed along the flow. We now put together aspects of both the
linear and nonlinear pressure terms to see what happens to convective storms in
various environments.

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4.5.1 Convective storm dynamics for straight hodographs

At the onset of convection, a buoyant updraft in an environment of strong vertical
shear, most of which is concentrated in the lower half of the troposphere, and that
does not change direction (or magnitude) with height produces a couplet of