Geography Reference
In-Depth Information
with height, but phase lines tend to be vertical. Although nonlinear processes
may be significant in the formation and maintenance of stationary waves, the
climatological stationary wave pattern can to a first approximation be described
in terms of forced barotropic Rossby waves. When superposed on zonal-mean
circulation, such waves produce local regions of enhanced and diminished time
mean westerly winds, which strongly influence the development and propagation
of transient weather disturbances. They thus represent essential features of the
climatological flow.
10.5.1
Stationary Rossby Waves
The most significant of the time mean zonally asymmetric circulation features is
the pattern of stationary planetary waves excited in the Northern Hemisphere by
the flow over the Himalayas and the Rockies. It was shown in Section 7.7.2 that the
quasi-stationary wave pattern along 45
◦
latitude could be accounted for to a first
approximation as the forced wave response when mean westerlies impinge on the
large-scale topography. More detailed analysis suggests that zonally asymmetric
heat sources also contribute to the forcing of the climatological stationary wave
pattern. Some controversy remains, however, concerning the relative importance
of heating and orography in forcing the observed stationary wave pattern. The
two processes are difficult to separate because the pattern of diabatic heating is
influenced by orography.
The discussion of topographic Rossby waves in Section 7.7.2 used a β-plane
channel model in which it was assumed that wave propagation was parallel to lati-
tude circles. In reality, however, large-scale topographic features and heat sources
are confined in latitude as well as longitude, and the stationary waves excited by
such forcing may propagate energy meridionally as well as zonally. For a quanti-
tatively accurate analysis of the barotropic Rossby wave response to a local source
it is necessary to utilize the barotropic vorticity equation in spherical coordinates
and to include the latitudinal dependence of the mean zonal wind. The mathemat-
ical analysis for such a situation is beyond the scope of this topic. It is possible,
however, to obtain a qualitative notion of the nature of the wave propagation for
this case by generalizing the β-plane analysis of Section 7.7. Thus, rather than
assuming that propagation is limited to a channel of specified width, we assume
that the β plane extends to plus and minus infinity in the meridional direction and
that Rossby waves can propagate both northward and southward without reflection
from artificial walls.
The free barotropic Rossby wave solution then has the form of (7.90) and satisfies
the dispersion relation of (7.91) where l is the meridional wave number, which is
now allowed to vary. From (7.93) it is clear that for a specified zonal wave number,
k, the free solution is stationary for l given by
l
2
k
2
=
β/u
−
(10.65)
