Geography Reference
In-Depth Information
(hPa)
X = 0
250
p
500
X > 0
X < 0
750
1000
Equator
N
Fig. 10.1
Relationship of the Eulerian mean meridional stream function to vertical and meridional
motion.
The relationship of the sign of the streamfunction χ to the sense of the mean
meridional circulation is show
n
schematically in Fig. 10.1.
The diagnostic equation for χ is derived by first taking
∂
∂z
(
10.11
)
R
H
∂
∂y
f
0
+
(
10.12
)
and then using (10.13) to eliminate the ti
m
e derivatives and (10.14) to express the
mean meridional circulation in terms of χ . The resulting elliptic equation has the
form
∂
∂y
κJ
H
−
v
T
1
ρ
0
∂
2
χ
∂y
2
f
0
∂
∂z
∂χ
∂z
ρ
0
N
2
R
H
∂
∂y
+
N
2
ρ
0
=
∂
2
∂z∂y
(10.15)
u
v
∂X
∂z
−
f
0
−
Equation (10.15)
ca
n be used to qualitatively diagnose the mean meridional
circulation. Because χ must vanish on the boundaries it can be represented by a
double Fourier series in y and z. Hence, the elli
p
tic operator on the left-hand side
of (10.15) is approximately proportional to
−
χ and (10.15) states qualitatively
that
∂
2
∂y
2
∂
∂y
(
diabatic heating
)
χ
∝−
+
(
large-scale eddy heat flux
)
∂
2
∂y∂z
(large-scale eddy momentum flux)
∂
∂z
(zonal drag force)
+
+
