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perturbation wind acts to intensify the perturbation thickness field. This tendency
is also illustrated by the zonally oriented Q vectors shown at the 500 hPa-level in
Fig. 8.4.
The pattern of vertical motion forced by the divergence of the Q vector, as shown
in Fig. 8.4, is associated with a divergence-convergence pattern that contributes
a positive vorticity tendency near the 250-hPa trough and a negative vorticity
tendency near the 750-hPa ridge, with opposite tendencies at the 250-hPa ridge
and 750-hPa trough. Since in all cases these vorticity tendencies tend to increase
the extreme values of vorticity at the troughs and ridges, this secondary circulation
system will act to increase the strength of the disturbance.
The total vorticity change at each level is, of course, determined by the sum
of vorticity advection and vortex stretching due to the divergent circulation. The
relative contributions of these processes are indicated schematically in Figs. 8.5
and 8.6, respectively. As can be seen in Fig. 8.5, vorticity advection leads the
vorticity field by one-quarter wavelength. Since in this case the basic state wind
increases with height, the vorticity advection at 250 hPa is larger than that at
750 hPa. If no other processes influenced the vorticity field, the effect of this
differential vorticity advection would be to move the upper-level trough and ridge
pattern eastward more rapidly than the lower-level pattern. Thus, the westward tilt
of the trough-ridge pattern would quickly be destroyed. The maintenance of this
tilt in the presence of differential vorticity advection is due to the concentration of
vorticity by vortex stretching associated with the divergent secondary circulation.
Referring to Fig. 8.6, we see that concentration of vorticity by the divergence
effect lags the vorticity field by about 65
at 250 hPa and leads the vorticity field
by about 65
at 750 hPa. As a result, the net vorticity tendencies ahead of the
0
δζ
δ
δζ
δ t
250
<< 0
adv
>> 0
adv
t
500
δζ
δ t
δζ
δ t
750
< 0
> 0
adv
adv
1000
0
π
/2
3
π
/2
2
π
π
Phase (rad)
Fig. 8.5
Vertical cross section showing phase of vorticity change due to vorticity advection for an
unstable baroclinic wave in the two-level model.
 
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