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Thus, sinking motion is forced by negative advection of disturbance vorticity by
the basic state thermal wind (or alternatively, cold advection of the basic state
thermal field by the perturbation meridional wind), while rising motion is forced
by advection of the opposite sign.
We now have the information required to diagram the structure of a baroclini-
cally unstable disturbance in the two-level model. The lower part of Fig. 8.4 shows
schematically the phase relationship between the geopotential field and the diver-
gent secondary motion field for the usual midlatitude situation where U T >0.
Linear interpolation has been used between levels so that the trough and ridge
axes are straight lines tilted back toward the west with height. In this example the
ψ 1 field lags the ψ 3 field by about 65 in phase so that the trough at 250 hPa lies
65 in phase west of the 750-hPa trough. At 500 hPa the perturbation thickness
field lags the geopotential field by one-quarter wavelength as shown in the top part
of Fig. 8.4 and the thickness and vertical motion fields are in phase. Note that the
temperature advection by the perturbation meridional wind is in phase with the
500-hPa thickness field so that the advection of the basic state temperature by the
0
250
C O L
D
W A R M
500
δ T
δ
δ T
δ y
v
'
> 0
v
'
< 0
y
750
1000
0
π /2
π
3 π /2
2 π
Phase (rad)
Fig. 8.4
Structure of an unstable baroclinic wave in the two-level model. (Top) Relative phases
of the 500-hPa perturbation geopotential (solid line) and temperature (dashed line).
(Bottom) Vertical cross section showing phases of geopotential, meridional temperature
advection, ageostrophic circulation (open arrows), Q vectors (solid arrows), and temper-
ature fields for an unstable baroclinic wave in the two-level model.
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