Geography Reference
In-Depth Information
isentropic transport and mixing by breaking planetary waves. Such eddy transport,
which is highly variable in space and time, must be included for quantitatively
accurate modeling of transport within the stratosphere.
In the mesosphere the residual circulation is dominated by a single circula-
tion cell with upward motion in the summer polar region, meridional drift from
the summer to the winter hemisphere, and subsidence in the winter polar region.
This circulation, like the residual circulation in the stratosphere, is eddy driven.
However, in the mesosphere it appears that the dominant eddies are vertically prop-
agating internal gravity waves, which have shorter scales in space and time than
the planetary waves that dominate the eddy activity in the stratosphere.
12.3
VERTICALLY PROPAGATING PLANETARY WAVES
In Section 12.1 we pointed out that the predominant eddy motions in the strato-
sphere are vertically propagating quasi-stationary planetary waves (Rossby waves)
and that these waves are confined to the winter hemisphere. In order to understand
the absence of synoptic-scale motions and the confinement of stationary planetary
waves to the winter hemisphere, it is necessary to examine the conditions under
which planetary waves can propagate vertically.
12.3.1
Linear Rossby Waves
To analyze planetary wave propagation in the stratosphere, it is convenient to
write the equations of motion in the log-pressure coordinate system introduced in
Section 8.4.1. For analysis of extratropical planetary wave motions in the middle
atmosphere, we may refer the motions to the midlatitude β-plane and use the quasi-
geostrophic potential vorticity equation (6.24), which in log-pressure coordinates
can be written as
∂
∂t
+
q
V
g
·∇
=
0
(12.10)
where
ρ
0
f
0
ρ
0
N
2
∂
∂z
∂ψ
∂z
2
ψ
q
≡∇
+
f
+
[Compare with Eq. (6.25)]. Here ψ
/f
0
is the geostrophic streamfunction
and f
0
is a constant midlatitude reference value of the Coriolis parameter. We
now assume that the motion consists of a small-amplit
ud
e disturbance
s
uperposed
on a constant zonal-mean flow. Thus, letting ψ
=
ψ
,q
q
, and
=−
uy
+
=
q
+
linearizing (12.10) we find that the perturbation q
field must satisfy
∂
∂t
+
q
+
β
∂ψ
∂
∂x
u
∂x
=
0
(12.11)
