Geography Reference
In-Depth Information
Fig. 12.12
Longitude-height section along the equator showing pressure, temperature, and wind
perturbations for a thermally damped Kelvin wave. Heavy wavy lines indicate material
lines; short blunt arrows show phase propagation. Areas of high pressure are shaded.
Length of the small thin arrows is proportional to the wave amplitude, which decreases with
height due to damping. The large shaded arrow indicates the net mean flow acceleration
due to the wave stress divergence.
0 we again recover the dispersion relationship for hydrostatic inter-
nal gravity waves. The role of the β effect in (12.42) is to break the symmetry
between eastward (ν > 0) and westward (ν < 0) propagating waves. Eastward
propagating modes have shorter vertical wavelengths than westward propagating
modes. Vertically propagating n
When β
=
β/k
2
.
=
0 modes can exist only for c
=
ν/k >
−
Because k
s/a, where s is the number of wavelengths around a latitude circle,
this condition implies that for ν<0 solutions exist only for frequencies satisfying
the inequality
=
|
ν
|
< 2/s
(12.43)
For frequencies that do not satisfy (12.43), the wave amplitude will not decay away
from the equator and it is not possible to satisfy boundary conditions at the pole.
After some algebraic manipulation, the meridional structure of the horizontal
velocity and geopotential perturbations for the n
=
0 mode can be expressed as
exp
N
−
1
νy
1
iνy
u
ˆ
ˆ
i
|
m
|
y
2
β
|
m
|
=
v
ˆ
v
0
−
(12.44)
2N
The westward propagating n
=
0 mode is generally referred to as the Rossby-
gravity mode.
2
For upward energy propagation this mode must have downward
2
Some authors use this term to describe both eastward and westward n
=
0 waves.
