Geography Reference
In-Depth Information
Fig. 6.14
Orientation of
Q
vectors (bold arrows) for confluent (jet entrance) flow. Dashed lines are
isotherms. (After Sanders and Hoskins, 1990.)
change in
V
g
is parallel to the isotherms so that the
Q
vectors are normal to
the isotherms and are directed up the temperature gradient. Again rising motion
occurs where the
Q
vectors are convergent. Because such rising motion must imply
vorticity stretching in the column below, cyclonic vorticity will tend to increase
below a region of upper level convergent
Q
vectors.
6.4.3
The Ageostrophic Circulation
In the traditional form of quasi-geostrophic theory given in Section 6.3, the
ageostrophic velocity component is not explicitly determined. Rather, its role in the
secondary vertical circulation is implicitly included through diagnostic determi-
nation of the ω vertical motion field. Some dynamical aspects of the ageostrophic
motion are not, however, obvious from the analysis of vertical motion alone. In
particular, in some synoptic situations, advection by the ageostrophic wind may
be important in the evolution of the temperature and vorticity fields.
Because the ageostrophic wind generally has both irrotational and nondivergent
components, the total ageostrophic flow field cannot be obtained from knowledge
of the divergence alone. Rather, it is necessary to use the quasi-geostrophic momen-
tum equation (6.11). If for simplicity we neglect the β effect and solve (6.11) for
the ageostrophic wind, we obtain
k
×
V
g
·∇
V
g
1
f
0
D
g
V
g
Dt
∂
V
g
∂t
f
−
1
0
f
−
1
0
V
a
=
k
×
=
×
+
k
(6.56)
which shows that in the Northern Hemisphere the ageostrophic wind vector is
directed to the left of the geostrophic acceleration following the geostrophic motion.
