of thermohaline forcing) by the westward propagation of baroclinic Rossby waves generated at the
eastern boundary and on topographic features
(Anderson and Gill, 1975; Young, 1981). In fact,
as long as the mean flow is slow enough that
Rossby wave propagation is minimally affected, a
succession of Rossby waves of increasing vertical
mode number acts to confine the circulation to an
ever shallower depth. This only stops when the
flow speed becomes comparable to the Rossby
wave speed, for the wave mode with the same
depth scale as the current.
In the Southern Ocean, observation confirms
that the flow at all depths is strongly influenced by
bottom topography. From the above argument, this
would imply a flow speed comparable to the
Rossby wave mode with a vertical scale of 2000 m:
the first baroclinic mode. This is consistent with the
observation that mesoscale features seen in temperature and sea-surface height propagate eastwards in
the ACC, compared with westward propagation
elsewhere (Hughes et al., 1998). More importantly,
it implies that the Sverdrup balance must be upset
by interactions with bottom topography.
Nevertheless, several attempts have been made
to apply Sverdrup theory to the ACC by assuming
that various topographic features act as ‘effective
continents’, blocking the flow. Stommel (1957),
for example, suggested that the Scotia Island arc,
east of Drake Passage, effectively extended the
Antarctic Peninsula across the Drake Passage gap.
Southward interior flow in Sverdrup balance with
the wind stress curl was returned in an unusual
arrangement of boundary currents: a western
boundary current against South America, and an
eastern boundary current along the coast of the
Antarctic Peninsula and Scotia Island arc, the two
currents being joined in some unspecified way by
flow through Drake Passage. The transport is then
given by the zonally integrated wind stress curl
at the southernmost latitude of South America
(which is also the northernmost latitude of the
Scotia Island arc – there is no overlap; any overlap
would complicate this, since it would not then
be clear at which latitude the wind stress curl was
relevant). Baker (1982) found some support for
this argument in a comparison of wind stress curl
at 55°S with baroclinic transport through Drake
Passage from hydrography.
Webb (1993) suggested the Kerguelen Plateau
was a sufficient barrier effectively to block the
flow. Webb’s model is a highly idealized source–
sink flow in a homogeneous, flat-bottomed ocean,
but it can also be recognized as an application of
Godfrey’s (1989) ‘island rule’ to the geometry of
Antarctica, which immediately generalizes it to
the case of a stratified ocean obeying Sverdrup
dynamics except in specified western boundary
regions. The non-Sverdrup flow all occurs in western boundary currents off the eastern coasts of
South America and Kerguelen Plateau (and possibly the Antarctic Peninsula), resulting in a flow
around Antarctica that is proportional to an integral of the wind stress along a line encircling the
continent. This flow becomes infinite in the limit
where the northernmost latitude of Kerguelen
Plateau is equal to the southernmost latitude
of South America, with no overlap. With only
Sverdrup balance and western boundary currents
involved, Webb’s model is the most natural extension of wind-driven gyre dynamics to the Southern
Ocean.
While the Sverdrup models of Stommel (1957)
and Webb (1993) give reasonable values for the
ACC transport (about 120 Sv) when combined with
climatological wind stress estimates, the theories are
incomplete. There are latitudes at which neither of
the proposed ‘effective’ continental boundaries is
shallower than 2000 m, so the assumption that
these block the flow must at least be contingent
upon some assumption of the weakness of stratification at these latitudes. The dynamics allowing the
eastern and western boundary currents to join in
Stommel’s model are not clear. Perhaps most
importantly, these flat-bottomed Sverdrup models
ignore interaction between the flow and the bottom
topography.
The observation that the ACC penetrates to
great depth suggests this assumption is not justified. Topographic interactions link the horizontal
and meridional circulations, as can be seen most
clearly from the barotropic vorticity equation:
0 ⌿ x :kиٌp b ٌH;kиٌ;kиٌF (4.6.1)
where ⌿ is the barotropic streamfunction, p b is
bottom pressure, H is ocean depth, is wind
stress, and F represents frictional and non-linear
terms and k is the unit vector in the local vertical
(upwards). Integrating (4.6.1) over a zonal band
enclosed by two latitude lines 1 and 2 , there is
no net northward transport so the left-hand-side
4.6 The Antarctic Circumpolar Current System
281
Rintoul, Hughes and Olbers
eastern boundary and on topographic features
(Anderson and Gill, 1975; Young, 1981). In fact,
as long as the mean flow is slow enough that
Rossby wave propagation is minimally affected, a
succession of Rossby waves of increasing vertical
mode number acts to confine the circulation to an
ever shallower depth. This only stops when the
flow speed becomes comparable to the Rossby
wave speed, for the wave mode with the same
depth scale as the current.
In the Southern Ocean, observation confirms
that the flow at all depths is strongly influenced by
bottom topography. From the above argument, this
would imply a flow speed comparable to the
Rossby wave mode with a vertical scale of 2000 m:
the first baroclinic mode. This is consistent with the
observation that mesoscale features seen in temperature and sea-surface height propagate eastwards in
the ACC, compared with westward propagation
elsewhere (Hughes et al., 1998). More importantly,
it implies that the Sverdrup balance must be upset
by interactions with bottom topography.
Nevertheless, several attempts have been made
to apply Sverdrup theory to the ACC by assuming
that various topographic features act as ‘effective
continents’, blocking the flow. Stommel (1957),
for example, suggested that the Scotia Island arc,
east of Drake Passage, effectively extended the
Antarctic Peninsula across the Drake Passage gap.
Southward interior flow in Sverdrup balance with
the wind stress curl was returned in an unusual
arrangement of boundary currents: a western
boundary current against South America, and an
eastern boundary current along the coast of the
Antarctic Peninsula and Scotia Island arc, the two
currents being joined in some unspecified way by
flow through Drake Passage. The transport is then
given by the zonally integrated wind stress curl
at the southernmost latitude of South America
(which is also the northernmost latitude of the
Scotia Island arc – there is no overlap; any overlap
would complicate this, since it would not then
be clear at which latitude the wind stress curl was
relevant). Baker (1982) found some support for
this argument in a comparison of wind stress curl
at 55°S with baroclinic transport through Drake
Passage from hydrography.
Webb (1993) suggested the Kerguelen Plateau
was a sufficient barrier effectively to block the
flow. Webb’s model is a highly idealized source–
sink flow in a homogeneous, flat-bottomed ocean,
but it can also be recognized as an application of
Godfrey’s (1989) ‘island rule’ to the geometry of
Antarctica, which immediately generalizes it to
the case of a stratified ocean obeying Sverdrup
dynamics except in specified western boundary
regions. The non-Sverdrup flow all occurs in western boundary currents off the eastern coasts of
South America and Kerguelen Plateau (and possibly the Antarctic Peninsula), resulting in a flow
around Antarctica that is proportional to an integral of the wind stress along a line encircling the
continent. This flow becomes infinite in the limit
where the northernmost latitude of Kerguelen
Plateau is equal to the southernmost latitude
of South America, with no overlap. With only
Sverdrup balance and western boundary currents
involved, Webb’s model is the most natural extension of wind-driven gyre dynamics to the Southern
Ocean.
While the Sverdrup models of Stommel (1957)
and Webb (1993) give reasonable values for the
ACC transport (about 120 Sv) when combined with
climatological wind stress estimates, the theories are
incomplete. There are latitudes at which neither of
the proposed ‘effective’ continental boundaries is
shallower than 2000 m, so the assumption that
these block the flow must at least be contingent
upon some assumption of the weakness of stratification at these latitudes. The dynamics allowing the
eastern and western boundary currents to join in
Stommel’s model are not clear. Perhaps most
importantly, these flat-bottomed Sverdrup models
ignore interaction between the flow and the bottom
topography.
The observation that the ACC penetrates to
great depth suggests this assumption is not justified. Topographic interactions link the horizontal
and meridional circulations, as can be seen most
clearly from the barotropic vorticity equation:
0 ⌿ x :kиٌp b ٌH;kиٌ;kиٌF (4.6.1)
where ⌿ is the barotropic streamfunction, p b is
bottom pressure, H is ocean depth, is wind
stress, and F represents frictional and non-linear
terms and k is the unit vector in the local vertical
(upwards). Integrating (4.6.1) over a zonal band
enclosed by two latitude lines 1 and 2 , there is
no net northward transport so the left-hand-side
4.6 The Antarctic Circumpolar Current System
281
Rintoul, Hughes and Olbers