The steady state circulation in a bounded basin under
steady wind stress curl driving is governed by the
following special case of (14) with
:
The classical Sverdrup, Stommel and Munk analyses (Proc. Nat. Acad., 1947; AGU Trans., 1948; J. Met., 1950) represent the following special cases of balance:
or 
) in particular)
None of these considered topographic effects of the sea floor.
It wasn't until the advent of numerical models in the early
1960s and more importantly in the 1970s (the work of Holland
and Rhines in particular) that the importance of topographic
coupling was fully appreciated.
We will give here an analysis which illustrates the importance
of such coupling in the context of the simplest of all
regimes, namely the Sverdrup interior regime.
Before doing this, a summary of the important results of the Sverdrup/Stommel/Munk analyses is useful as background. As in the above analyses, we consider for simplicity a rectangular basin of constant depth D, zonal dimension a and meridional dimension b. The wind stress is considered purely zonal and dependent only on y, i.e.
for which
For the Sverdrup regime, taking 
on the
eastern boundary we get
which is linear in x with maximum 
along the western wall
at 
. For the barotropic mode 
, and the
result is usually expressed in terms of a barotropic stream
function 
.
The Stommel analysis, which uses
for term 5, essentially gives
result (18) except for a frictional boundary jet near the western wall having a scale
. The Munk analysis also verifies the
Sverdrup regimes, as is appropriate in the interior, but has
a western frictional boundary jet of scale
.
In summary, for the interior region friction is essentially
negligible; its importance in the western boundary region is
due to the large gradient of velocity which exists in that
region (see Stommel's 1965 book The Gulf Stream for
further insight).