Geography Reference
In-Depth Information
Fig. 11.15
Plan view of horizontal velocity and height perturbations associated with an equatorial
Kelvin wave. (Adapted from Matsuno, 1966.)
which may be integrated immediately to yield
u
o
exp
βy
2
/2c
u
ˆ
=
−
(11.48)
where u
0
is the amplitude of the perturbation zonal velocity at the equator. Equation
(11.48) shows that if solutions decaying away from the equator are to exist, the
phase speed must be positive (c>0). Thus, Kelvin waves are eastward propagating
and have zonal velocity and geopotential perturbations that vary in latitude as
Gaussian functions centered on the equator. The e-folding decay width is given by
1/2
Y
K
= |
2c/β
|
30 m s
−
1
which for a phase speed c
1600 km.
The perturbation wind and geopotential structure for the Kelvin wave are shown
in plan view in Fig. 11.15. In the zonal direction the force balance is exactly that
of an eastward propagating shallow water gravity wave. A vertical section along
the equator would thus be the same as that shown in Fig. 7.9. The meridional
force balance for the Kelvin mode is an exact geostrophic balance between the
zonal velocity and the meridional pressure gradient. It is the change in sign of the
Coriolis parameter at the equator that permits this special type of equatorial mode
to exist.
=
gives Y
K
≈
11.5
STEADY FORCED EQUATORIAL MOTIONS
Not all zonally asymmetric circulations in the tropics can be explained on the
basis of inviscid equatorial wave theory. For quasi-steady circulations the zonal
pressure gradient force must be balanced by turbulent drag rather than by inertia.
The Walker circulation may be regarded as a quasi-steady equatorially trapped
circulation that is generated by diabatic heating. The simplest models of such
circulations specify the diabatic heating and use the equations of equatorial wave
