Geography Reference
In-Depth Information
Fig. 6.7
Schematic 500-hPa geopotential field showing regions of positive and negative advections
of relative and planetary vorticity.
βυ
g
and that the divergence of the ageostrophic wind can be eliminated in favor of ω
using (6.12), we can rewrite (6.18) as
Noting that because f depends only on y so that D
g
f/Dt
=
V
g
·∇
f
=
V
g
·∇
ζ
g
+
f
+
∂ζ
g
∂t
=−
∂ω
∂p
f
0
(6.19)
which states that the local rate of change of geostrophic vorticity is given by the
sum of the advection of the absolute vorticity by the geostrophic wind plus the
concentration or dilution of vorticity by stretching or shrinking of fluid columns
(the divergence effect).
The vorticity tendency due to vorticity advection [the first term on the right in
(6.19)] may be rewritten as
V
g
·∇
ζ
g
+
f
=−
−
V
g
·∇
ζ
g
−
βv
g
The two terms on the right represent the geostrophic advections of relative
vorticity and planetary vorticity, respectively. For disturbances in the westerlies,
these two effects tend to have opposite signs, as illustrated schematically in Fig. 6.7
for an idealized 500-hPa flow.
In region I upstream of the 500-hPa trough, the geostrophic wind is directed from
the relative vorticity minimum at the ridge toward the relative vorticity maximum
at the trough so that -V
g
·∇
ζ
g
< 0. However, at the same time, because v
g
< 0in
region I, the geostrophic wind has its y component directed down the gradient of
