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the advective part of the ageostrophic wind. For baroclinic waves in the jetstream
the advective term is dominated by zonal advection so that
×
V
g
·∇
V
g
≈
∂x
k
V
g
=−
∂
∂
∂x
(
f
−
1
0
×
∇
k
u
u
)
where u is the mean zonal flow, and we have used the definition of the geostrophic
wind (6.7). The advective contribution to the ageostrophic flow is shown by the
open arrows in Fig. 6.15. Note that due to the strong jetstream at 300 hPa at
the center of the waves the advective contribution dominates over the isallobaric
contribution. On the flanks of the waves at 300 hPa the two contributions are of
comparable amplitude so that the net ageostrophic wind is small. At the 850-hPa
level, however, the two contributions nearly cancel at the center of the perturba-
tions, whereas the advective contribution is nearly zero on the flanks. The net result
is that the ageostrophic motion for baroclinic waves is primarily zonal in the upper
troposphere and primarily meridional in the lower troposphere.
6.5
IDEALIZED MODEL OF A BAROCLINIC DISTURBANCE
Section 6.2 showed that for synoptic-scale systems the fields of vertical motion
and geopotential tendency are determined to a first approximation by the three-
dimensional distribution of geopotential. The results of our diagnostic analyses
using the geopotential tendency and omega equations can now be combined to
illustrate the essential structural characteristics of a developing baroclinic wave.
In Fig. 6.16 the relationship of the vertical motion field to the 500- and 1000-hPa
geopotential fields is illustrated schematically for a developing baroclinic wave.
Also indicated are the physical processes that give rise to the vertical circulation
in various regions.
Additional structural features, including those that can be diagnosed with the
tendency equation, are summarized in Table 6.1. In Table 6.1 the signs of various
physical parameters are indicated for vertical columns located at the position of
(A) the 500-hPa trough, (B) the surface low, and (C) the 500-hPa ridge. It can be
seen from Table 6.1 that in all cases the vertical motion and divergence fields act
to keep the temperature changes hydrostatic and vorticity changes geostrophic in
order to preserve thermal wind balance.
Following the nomenclature of Chapter 5, we may regard the vertical and diver-
gent ageostrophic motions as constituting a secondary circulation imposed by the
simultaneous constraints of geostrophic and hydrostatic balance. The secondary
circulation described in this chapter is, however, completely independent of the
circulation driven by boundary layer pumping. In fact, it is observed that in midlat-
itude synoptic-scale systems, the vertical velocity forced by frictional convergence
in the boundary layer is generally much smaller than the vertical velocity due to
