78
2
~
on
=>
e.
- ... 0
0
Co
'" C
~
...
';
-I
...
i
:c
global (II)
-2
-BO
-40
0
40
BO
Longitude
Figure 18. Poleward heat tranport (in 1015 Watts) in run III and in run II (dots) achieved by the
World Ocean. For run III, the contribution of the Atlantic is also given (dotted curve).
Appendix
A few ways of dealing with the external mode of an ocean model are outlined here.
Integrating the continuity equation over the whole water column, taking into account the
impermeability conditions of the surface and the bottom, we obtain
dry
-
= - V.U
dt
'
(AI)
where U is the horizontal transport, i.e., the depth-integral of the horizontal velocity.
The depth-integral of the horizontal momentum equation may be written as
dU
a; = -/ezxU - gHVry + F,
(A2)
where F encompasses many terms, the list of which does not need to be given here.
For simplicity, we have written equations (AI)-(A2) in the beta-plane: Earth's curvature is
neglected - so that cartesian coordinates may be used -, except in the Coriolis factor. The
latter is assumed to be a linear function of a space coordinate,
(A3)
where 10 and f3 are constants. For the beta-plane approximation to be valid, it is necessary that
the size of the domain of interest, characterized by length scale L, be much smaller than the
Earth's radius. In addition, we must also have f3L «/ 0 . Further details on the beta-plane
theory are given in classical treatises of geophysical fluid dynamics (e.g. Cushman-Roisin,
1994).