246
DYNAMICAL OCEANOGRAPHY
equatorial thermocline is the second motivating problem of the material in this
chapter.
Temperature and salinity are plotted in Fig. 11.6 along the same meridional
section in the Pacific as in Fig. 11.3 (at 155 ◦ W). The north-south structure of the
20 ◦ isotherm indicates a shallowing of the thermocline near the equator. Slightly
north of the equator there is a region where the thermocline depth has a large
meridional gradient. The salinity distribution is fairly north-south asymmetric
with slightly higher salinities south of the equator. The Equatorial Under Current
is contained between the 15 ◦ C and 25 ◦ C isotherms and appears associated with
large meridional salinity gradients.
Additional Material
B: An elementary introduction on equatorial currents (with nice illustrations) is
given in chapter 5 of OU-staff (1989).
D: An extensive description of the tropical ocean circulation is given in chapter
4.3 (Godfrey et al.) of WOCE (2001) and in section 6.1 of Pedlosky (1996).
11.2. Equatorial ocean models
From the description of the phenomena in the previous section, it appears that
the characteristic zonal flow scale is the basin length, but the meridional scale is
much smaller. Furthermore, the vertical scale is only a few hundred meters. In
fact, most phenomena of interest are present only in a relatively small zone around
the equator. This motivates the use of the equatorial β-plane models; again, the
constant density case is considered first and then later extended to a layer-type
model.
11.2.1. Constant density equatorial β-plane model
For the case of constant density ρ, the starting equations are the dimensional
equations in chapter 4. The only thing to change for the equatorial case is the
value of the Coriolis parameter at the central latitude, which is the equator, hence
f 0 =0. In this way, the dimensional equations become
Du ∗
dt ∗
− β 0 y ∗ v ∗ = −
1
ρ
∂p ∗
∂x ∗
+
+A H
∂ 2 u ∗
∂x 2
∗
+
∂ 2 u ∗
∂y 2
∗
+ A V
∂ 2 u ∗
∂z 2
∗
,
(11.1a)
Dv ∗
dt ∗
+ β 0 y ∗ u ∗ = −
1
ρ
∂p ∗
∂y ∗
+
DYNAMICAL OCEANOGRAPHY
equatorial thermocline is the second motivating problem of the material in this
chapter.
Temperature and salinity are plotted in Fig. 11.6 along the same meridional
section in the Pacific as in Fig. 11.3 (at 155 ◦ W). The north-south structure of the
20 ◦ isotherm indicates a shallowing of the thermocline near the equator. Slightly
north of the equator there is a region where the thermocline depth has a large
meridional gradient. The salinity distribution is fairly north-south asymmetric
with slightly higher salinities south of the equator. The Equatorial Under Current
is contained between the 15 ◦ C and 25 ◦ C isotherms and appears associated with
large meridional salinity gradients.
Additional Material
B: An elementary introduction on equatorial currents (with nice illustrations) is
given in chapter 5 of OU-staff (1989).
D: An extensive description of the tropical ocean circulation is given in chapter
4.3 (Godfrey et al.) of WOCE (2001) and in section 6.1 of Pedlosky (1996).
11.2. Equatorial ocean models
From the description of the phenomena in the previous section, it appears that
the characteristic zonal flow scale is the basin length, but the meridional scale is
much smaller. Furthermore, the vertical scale is only a few hundred meters. In
fact, most phenomena of interest are present only in a relatively small zone around
the equator. This motivates the use of the equatorial β-plane models; again, the
constant density case is considered first and then later extended to a layer-type
model.
11.2.1. Constant density equatorial β-plane model
For the case of constant density ρ, the starting equations are the dimensional
equations in chapter 4. The only thing to change for the equatorial case is the
value of the Coriolis parameter at the central latitude, which is the equator, hence
f 0 =0. In this way, the dimensional equations become
Du ∗
dt ∗
− β 0 y ∗ v ∗ = −
1
ρ
∂p ∗
∂x ∗
+
+A H
∂ 2 u ∗
∂x 2
∗
+
∂ 2 u ∗
∂y 2
∗
+ A V
∂ 2 u ∗
∂z 2
∗
,
(11.1a)
Dv ∗
dt ∗
+ β 0 y ∗ u ∗ = −
1
ρ
∂p ∗
∂y ∗
+