Geography Reference
In-Depth Information
transient growth of neutral waves
2
1
0
-1
-2
0
500
1000
1500
2000
2500
3000
x (km)
2
1
0
-1
-2
0
500
1000
1500
2000
2500
3000
x (km)
Fig. 8.11
Zonal distribution of the amplitude of a transient neutral disturbance initially confined
entirely to the upper layer in the two-layer model. Dashed lines show the initial distribution
of the baroclinic and barotropic modes; solid lines show the distribution at time of maximum
amplification.
8.5.2
Downstream Development
It was noted in Section 7.2.2 that under some circumstances the zonal group
velocity may exceed the zonal phase speed so that the energy of a wave group
propagates faster than the individual wave disturbances. This dispersion effect
was demonstrated for barotropic Rossby waves in Problem 7.19. The β effect is
not necessary, however, for the development of new disturbances to occur down-
stream of the original wave disturbances on the synoptic scale. The two-layer
channel model with constant Coriolis parameter can be used to demonstrate the
process of dispersion and downstream development of neutral waves in a simple
context.
Expressed in terms of wave frequency, the dispersion relation of (8.24) becomes
ν
=
kU
m
±
kµU
T
(8.76)
