70
and Roach, 1987). A corresponding temperature and salinity flux is also prescribed. The
parameterizations are tuned so that the northward water flow be of order 10 6 m 3 s-l.
The meridional streamfunction. It is not easy to understand the results of an OGCM,
because of the complexity of the phenomena taking place in the World Ocean, and because of
the large amount of real numbers generated by an OGCM. An example of an interpretation
technique based on little graphical skill but considerable physical skill is the meridional
strearnfunction approach. This technique, which has now become a standard for visualising and
discussing the results of OGCMs (e.g. Bryan 1982, 1987; Toggweiler et al., 1989; Killworth
et al., 1991; Marotzke and Willebrand, 1991; England 1992; Semtner and Chervin, 1992) since
it allows visualizing the "conveyor belt" circulation - which is described below. It consists in
integrating the velocity in meridional planes over the longitudinal width of the ocean basin
under study. Assuming that there is no water flux across me land and sea boundaries, the
resulting two-dimensional vector field is divergenceless, implying that it may be represented
with the help of a streamfunction, termed "meridional streamfunction" since the longitudinal
velocity component is ignored. Contours of the streamfunction are drawn, and the difference
between me strearnfunction values associated with two given isolines corresponds to the water
flux flowing between these isolines.
Assume that the domain of interest is defined as
(52)
where, for simplicity, the ocean surface is assumed flat (7J = 0); y _ and y + are constants. The
two components of the transport that we want to represent are
x+(y)
(U, W) =
f (h v, h h w) dx .
x
x y
(53)
xJy)
The lateral boundaries of the domain of interest, located at x_(y) and x/y), are either
impermeable or periodic - if x _ (y) corresponds to the same location of the terrestrial sphere as
x+(y).
The continuity equation
a
a
a
- (h u) + - (h v) + - (h h w) = 0,
ax Y
ay x
az x Y
(54)
is integrated over x, from x _ (y) to x /y), and, taking into account the lateral boundary
conditions, it may be seen that
av
ay
+
aw
az
o.
The transport (V, W) is defined in the domain
[y_,-d(y)] ~ (y,z) ~ [Y+,O],
where the depth d is given by
d(y)
max h(x,y).
x ~X'>x
-
+
(55)
(56)
(57)
and Roach, 1987). A corresponding temperature and salinity flux is also prescribed. The
parameterizations are tuned so that the northward water flow be of order 10 6 m 3 s-l.
The meridional streamfunction. It is not easy to understand the results of an OGCM,
because of the complexity of the phenomena taking place in the World Ocean, and because of
the large amount of real numbers generated by an OGCM. An example of an interpretation
technique based on little graphical skill but considerable physical skill is the meridional
strearnfunction approach. This technique, which has now become a standard for visualising and
discussing the results of OGCMs (e.g. Bryan 1982, 1987; Toggweiler et al., 1989; Killworth
et al., 1991; Marotzke and Willebrand, 1991; England 1992; Semtner and Chervin, 1992) since
it allows visualizing the "conveyor belt" circulation - which is described below. It consists in
integrating the velocity in meridional planes over the longitudinal width of the ocean basin
under study. Assuming that there is no water flux across me land and sea boundaries, the
resulting two-dimensional vector field is divergenceless, implying that it may be represented
with the help of a streamfunction, termed "meridional streamfunction" since the longitudinal
velocity component is ignored. Contours of the streamfunction are drawn, and the difference
between me strearnfunction values associated with two given isolines corresponds to the water
flux flowing between these isolines.
Assume that the domain of interest is defined as
(52)
where, for simplicity, the ocean surface is assumed flat (7J = 0); y _ and y + are constants. The
two components of the transport that we want to represent are
x+(y)
(U, W) =
f (h v, h h w) dx .
x
x y
(53)
xJy)
The lateral boundaries of the domain of interest, located at x_(y) and x/y), are either
impermeable or periodic - if x _ (y) corresponds to the same location of the terrestrial sphere as
x+(y).
The continuity equation
a
a
a
- (h u) + - (h v) + - (h h w) = 0,
ax Y
ay x
az x Y
(54)
is integrated over x, from x _ (y) to x /y), and, taking into account the lateral boundary
conditions, it may be seen that
av
ay
+
aw
az
o.
The transport (V, W) is defined in the domain
[y_,-d(y)] ~ (y,z) ~ [Y+,O],
where the depth d is given by
d(y)
max h(x,y).
x ~X'>x
-
+
(55)
(56)
(57)