Geography Reference
In-Depth Information
=−
√
gh
e
, corresponding to a westward propagating gravity
wave, is not permitted, as the second term in parentheses in (11.41) was implicitly
assumed not to vanish when (11.36) and (11.37) were combined to eliminate
The root ν/k
ˆ
.
The roots given by the first term in parentheses in (11.41) are
1
2
±
1/2
(11.42)
1
k
gh
e
1
2
4β
k
2
√
gh
e
ν
=
+
The positive root corresponds to an eastward propagating equatorial inertia-
gravity wave, whereas the negative root corresponds to a westward propagating
wave, which resembles an inertia-gravity wave for long zonal scale (k
0) and
resembles a Rossby wave for zonal scales characteristic of synoptic-scale distur-
bances. This mode is generally referred to as a
Rossby-gravity
wave. The horizon-
tal structure of the westward propagating n
→
0 solution is shown in Fig. 11.13,
whereas the relationship between frequency and zonal wave number for this and
several other equatorial wave modes is shown in Fig. 11.14.
=
11.4.2
Equatorial Kelvin Waves
In addition to the modes discussed in the previous section, there is another equa-
torial wave that is of great practical importance. For this mode, which is called the
equatorial
Kelvin wave
, the meridional velocity perturbation vanishes and (11.33)-
(11.35) are reduced to the simpler set
ik
ˆ
−
iν
u
ˆ
=−
(11.43)
∂
ˆ
βy
u
ˆ
=−
/∂y
(11.44)
gh
e
ik
u
=
iν
ˆ
−
+
ˆ
0
(11.45)
Fig. 11.13
Plan view of horizontal velocity and height perturbations associated with an equatorial
Rossby-gravity wave. (Adapted from Matsuno, 1966.)
