Geography Reference
In-Depth Information
Although the signs of the potential energy generation term and the potential
energy conversion term in (8.38) are always opposite for a developing baroclinic
wave, it is only the potential energy generation rate that determines the growth of
the total energy P
+
K
of the disturbance. This may be proved by adding (8.37)
and (8.38) to obtain
d
P
+
K
/dt
4λ
2
U
T
ψ
T
∂ψ
m
/∂x
=
Provided the correlation between the meridional velocity and temperature is
positive and U
T
> 0, the total energy of the perturbation will increase. Note that
the vertical circulation merely converts disturbance energy between the available
potential and kinetic forms without affecting the total energy of the perturbation.
The rate of increase of the total energy of the perturbation depends on the mag-
nitude of the basic state thermal wind U
T
. This is, of course, proportional to the
zonally averaged meridional temperature gradient. Because the generation of per-
turbation energy requires systematic poleward transport of warm air and equator-
ward transport of cold air, it is clear that baroclinically unstable disturbances tend
to reduce the meridional temperature gradient and hence the available potential
energy of the mean flow. This latter process cannot be described mathematically
in terms of the linearized equations. However, from Fig. 8.8 we can see qualita-
tively that parcels that move poleward and upward with slopes less than the slope
of the zonal mean potential temperature surface will become warmer than their
surroundings, and vice versa for parcels moving downward and equatorward. For
Fig. 8.8
Slopes of parcel trajectories relative to the zonal mean potential temperature surfaces for a
baroclinically unstable disturbance (solid arrows) and for a baroclinically stable disturbance
(dashed arrows).
