Supercells - Severe Convective Storms and Tornadoes: Observations and Dynamics - page 172

Figure 4.5. (Top) One of the first illustrations of how boundary-layer horizontal vorticity
associated with vertical shear could be tilted onto the vertical as fluid parcels in the boundary
layer are tilted upward when they enter an updraft in a convective storm (from Barnes, 1970).
(Bottom) Idealized depiction of horizontal vorticity (green streamline points in the direction of
the 3D vorticity vector) associated with vertical shear of the horizontal wind being tilted onto
the vertical by an updraft (red vector).

According to the thermal wind relation, which is a consequence of the
observed approximate (geostrophic) balance between the large-scale (synoptic-
scale) pressure gradient force and the Coriolis force, and of hydrostatic balance,
the magnitude of the vertical shear of the geostrophic wind—which is approx-
imately the same as the vertical shear of the total wind (i.e., of the
geostrophic þ the ageostrophic wind)—is proportional to the horizontal gradient
of temperature normal to the vertical shear vector

@ v g =@ z g= fT k

TJ h T

ð 4 : 23 Þ