Supercells - Severe Convective Storms and Tornadoes: Observations and Dynamics - page 208

Figure 4.29. (Top) Idealized illustration of how an updraft (green vector) in an environment of
westerly vertical shear (e.g., easterly winds below, westerly winds aloft, represented by red
vectors) tilts a vortex line pointing towards the north (dashed streamline) so that horizontal
vorticity is converted into cyclonic (C) vorticity south of anticyclonic (A) vorticity north of the
updraft. (Middle) Idealized illustration of how an updraft that deforms a e surface upward so
that there is a bulge/peak, also deforms a vortex line upward because the vortex line must
always lie on a surface of constant e (adapted from Davies-Jones, 1984). (Bottom) Idealized
illustration of how circulation (associated with vertical shear) in the vertical plane is advected
and tilted upward to produce cyclonic circulation (C) in the horizontal plane at mid-levels. The
dashed streamline indicates the motion of the vertical plane so that it becomes the horizontal
plane at the left.

dimensional vorticity equation (2.49) for a barotropic ( r B ¼ 0) and Boussinesq
(

r p 0 Þ¼ 0 because

JT ð 1

=

is not a function of x or y) atmosphere

D = Dt ð JT v Þ¼@=@ t ð JT v Þþ u @=@ x ð JT v Þþv @=@ y ð JT v Þþ w @=@ z ð JT v Þ

¼½ð JT v Þ EJ v ð 4 : 26 Þ

The term on the RHS of (4.26) represents tilting and stretching. So, in a