Geography Reference
In-Depth Information
Fig. 11.14
Dispersion diagram for free equatorial waves. Frequency and zonal wave numbers have
been nondimensionalized by defining
ν
∗
≡
ν/
β
gh
e
1/2
k
∗
≡
k
gh
e
/β
1/2
Curves show dependence of frequency on zonal wave number for eastward and westward
gravity modes and for Rossby and Kelvin modes. (k
∗
axis tic marks at unit interval with
0 on left.)
ˆ
Combining (11.43) and (11.45) to eliminate
, we see that the Kelvin wave dis-
persion equation is identical to that for ordinary shallow water gravity waves:
c
2
(ν/k)
2
≡
=
gh
e
(11.46)
According to (11.46), the phase speed c can be either positive or negative. However,
if (11.43) and (11.44) are combined to eliminate
ˆ
, we obtain a first-order equation
for determining the meridional structure:
βy
u
ˆ
=−
c∂
u/∂y
ˆ
(11.47)
