Geography Reference
In-Depth Information
organized tropical convection can excite atmospheric equatorial waves, whereas
wind stresses can excite oceanic equatorial waves. Atmospheric equatorial wave
propagation can cause the effects of convective storms to be communicated over
large longitudinal distances, thus producing remote responses to localized heat
sources. Furthermore, by influencing the pattern of low-level moisture conver-
gence, atmospheric equatorial waves can partly control the spatial and temporal
distribution of convective heating. Oceanic equatorial wave propagation, however,
can cause local wind stress anomalies to remotely influence the thermocline depth
and the SST, as was discussed in Section 11.1.6.
11.4.1
Equatorial Rossby and Rossby-Gravity Modes
A complete development of equatorial wave theory would be rather complicated.
In order to introduce equatorial waves in the simplest possible context we here use
a shallow water model, analogous to that introduced in Section 7.3.2, and concen-
trate on the
horizontal
structure. Vertical propagation in a stratified atmosphere
is discussed in Chapter 12. For simplicity, we consider the linearized momentum
and continuity equations for a fluid system of mean depth h
e
in a motionless basic
state. Because we are interested only in the tropics, we utilize Cartesian geome-
try on an
equatorial
β
-plane
. In this approximation, terms proportional to cosφ
are replaced by unity, and terms proportional to sinφ are replaced by y/a, where
y is the distance from the equator and a is the radius of the earth. The Coriolis
parameter in this approximation is given by
f
≈
βy
(11.28)
where β
2/a, and is angular velocity of the earth. The resulting linearized
shallow water equations for perturbations on a motionless basic state of mean depth
h
e
may be written as
≡
∂u
/∂t
βyv
=−
∂
∂x
−
(11.29)
∂v
/∂t
βyu
=−
∂
∂y
+
(11.30)
gh
e
∂u
/∂x
∂v
/∂y
=
∂
/∂t
+
+
0
(11.31)
where
gh
is the geopotential disturbance, and primed variables designate
perturbation fields.
The x and t dependence may be separated by specifying solutions in the form
of zonally propagating waves:
=
u
v
u (y)
ˆ
ˆ
=
exp [i (kx
v (y)
ˆ
−
νt)]
(11.32)
(y)
