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In-Depth Information
vanishes (u
−
c
x
=
0). In that case (12.19a) cannot be satisfied even for small
amplitude waves.
For understanding of wave behavior near critical lines it is helpful to generalize
the Rossby wave analysis of Section 12.3.1 to a situation such as that shown in
the seasonal mean c
ro
ss
se
ctions of Fig. 12.2 in which the zonal wind depends on
latitude and height, u
u (y, z). The x and t dependence in (12.11) can then be
separated by seeking solutions of the form
=
e
z/2H
Re
(y, z) e
ik(x
−
c
x
t)
ψ
=
(12.20)
we obtain
∂
2
∂y
2
f
0
N
2
∂
2
∂z
2
n
k
+
+
=
0
(12.21)
where the small vertical variation of N
2
is neglected, and
f
0
/
4HN
2
n
k
(y, z)
c
x
)
−
1
∂q/∂y
k
2
=
(u
−
−
−
(12.22)
Equation (12.21) has a form similar to that of the equation governing the two-
dimensional propagation of light waves in a medium with variable refractive index,
n
k
. The propagation of linear Rossby wave EP flux in that case can be shown to
be along rays that behave somewhat like light rays. Thus, wave activity will tend
to propagate along rays that bend toward regions of large positive n
k
and avoid
regions of negative n
k
. For stationary Rossby waves (c
x
0) of low zonal wave
number, n
k
is positive in a region with westerly winds that are not too strong and
increases to infinity along a critical surface where the mean flow vanishes. Thus,
the index of refraction for wave activity is positive in the winter hemisphere, but
increases rapidly toward the equatorial zero wind line. As a result Rossby wave
activity tends to propagate upward and equatorward, and wavebreaking occurs in
the vicinity of the equatorial critical line.
=
12.4
SUDDEN STRATOSPHERIC WARMINGS
In the lower stratosphere the temperature is a minimum at the equator and has
maxima at the summer pole and at about 45
◦
latitude in the winter hemisphere (see
Fig. 12.2). From thermal wind considerations the rapid decrease of temperature
poleward of 45
◦
in winter requires a zonal vortex with strong westerly shear with
height.
In the Northern Hemisphere, every other year or so this normal winter pattern of
a cold polar stratosphere with a westerly vortex is interrupted in a spectacular man-
ner in midwinter. Within the space of a few days the polar vortex becomes highly
distorted and breaks down (see Fig. 12.10) with an accompanying large-scale
