The crucial role of transient eddies or non-ideal
fluid behaviour beneath the mixed layer is also
clear in realistic conditions. Consider a contour of
constant time-averaged PV on some density surface beneath the mixed layer but above topography. Since PV and potential density are both
materially conserved for an ideal fluid, any steadystate flow can have no component across the PV
contour. Thus if there is a return flow at this density, since it must cross this PV contour (assumed
to close around Antarctica), either friction or transient eddies are required to permit this.
Analytical theories of the ACC in which the
baroclinic pressure field, and thus the bottom
stress, is established by thermohaline forcing are
still lacking. Several numerical studies (e.g. Olbers
and Wübber, 1991; Cai and Baines, 1996; Gent
et al., 2000; Gnanadesikan and Hallberg, 2000)
with coarse-resolution models have recently investigated the dependence of transport on the buoyancy forcing at the surface. The state of the ACC
in these models is generally intermediate between
the extreme cases I and II described in Section
4.6.3.2. There is conversion of deep to lighter
water masses to allow for a deeper (than Ekman
layer) reaching meridional cell but there is also a
parameterized interfacial stress of some kind. It is
likely that the barotropic and baroclinic form
stresses are not solely created by thermohaline
processes because the topographic resonance
mechanism should be operating as well.
An increase of the ACC transport by an
increase of the buoyancy loss by increased brine
release off the Antarctic shelf was documented
in primitive equation models by Olbers and
Wübber (1991) and clearly described in Gent et al.
(2000). Using restoring boundary conditions for
heat and salt and different wind fields, Gnanadesikan and Hallberg (2000) found a similar strong
increase of the ACC transport with strengthening
of the overturning circulation (linked to a deeper
thermocline and increased water mass transformation in the northern hemisphere). As shown by Cai
and Baines (1996) and Gent et al. (2000), parameterizations of sub-grid mixing play an essential
role: the ACC transport and the overturning transport are larger in the presence of a larger vertical
diffusivity and a smaller isopycnal diffusivity. The
latter is in qualitative agreement with the baroclinic transport models (4.6.7) and (4.6.15). It also
agrees with the baroclinic Charney–DeVore model
described above, where the transport strongly
decreases with friction between the layers (see
Fig. 4.6.10b).
Topographic steering
The important role of submarine topography in
the dynamics of the ACC was discussed in the preceding sections. The topography also acts to steer
the current, as noted very early on by Sverdrup
et al. (1942, pp. 468; 606–607) and described by
Gordon et al. (1978) (see also the pressure maps in
Webb et al., 1991, and the steric height maps in
Olbers et al., 1992). Steering by bathymetry has
also been detected in the sea surface topography obtained from altimeter data, as reported by
Chelton et al. (1990) and Gille (1994). A laboratory model of homogeneous and linearly stratified
flow over realistic topography is reported by Boyer
et al. (1993). The resulting flow is in fair agreement
with observations regarding steering by the major
ridges and troughs, but it also shows significant
discrepancies that are traced back to inadequate
representation of small-scale passages and fracture
zones, unrealistic forcing (which was simulated by
sources and sinks of mass) and neglect of the planetary effect. Early models of topographic effects
on the ACC were homogeneous (Kamenkovich,
1962; Johnson and Hill, 1975), so that f/H contours inevitably dominated the flow pattern. The
breaking of f/H or bathymetry control by stratification is demonstrated in many simple numerical
models (e.g. Klinck, 1993) and the coarse- and
high-resolution models of the circumpolar circulation discussed above.
Theory suggests the flow may be steered
along bathymetry contours, latitude circles or the
geostrophic contours f/H. The conditions under
which one of these effects will dominate can be clarified by use of the balance (4.6.1) of integrated
vorticity. If the deep ocean is motionless,
0 f ku b :9(ٌp) b :0 , the bottom torque term in
(4.6.1) vanishes because (ٌp) b :ٌp b 9g b ٌH. This
allows a ‘free mode’ in the transport streamfunction following f contours; in case of locally weak
stress curl the flow would follow such a path.
However, a motionless abyss requires strong stratification to shield the flow from the influence of
topography. The ACC is far from such a state but
the converse condition of a homogeneous water
SECTION 4 THE GLOBAL FLOW FIELD
290
fluid behaviour beneath the mixed layer is also
clear in realistic conditions. Consider a contour of
constant time-averaged PV on some density surface beneath the mixed layer but above topography. Since PV and potential density are both
materially conserved for an ideal fluid, any steadystate flow can have no component across the PV
contour. Thus if there is a return flow at this density, since it must cross this PV contour (assumed
to close around Antarctica), either friction or transient eddies are required to permit this.
Analytical theories of the ACC in which the
baroclinic pressure field, and thus the bottom
stress, is established by thermohaline forcing are
still lacking. Several numerical studies (e.g. Olbers
and Wübber, 1991; Cai and Baines, 1996; Gent
et al., 2000; Gnanadesikan and Hallberg, 2000)
with coarse-resolution models have recently investigated the dependence of transport on the buoyancy forcing at the surface. The state of the ACC
in these models is generally intermediate between
the extreme cases I and II described in Section
4.6.3.2. There is conversion of deep to lighter
water masses to allow for a deeper (than Ekman
layer) reaching meridional cell but there is also a
parameterized interfacial stress of some kind. It is
likely that the barotropic and baroclinic form
stresses are not solely created by thermohaline
processes because the topographic resonance
mechanism should be operating as well.
An increase of the ACC transport by an
increase of the buoyancy loss by increased brine
release off the Antarctic shelf was documented
in primitive equation models by Olbers and
Wübber (1991) and clearly described in Gent et al.
(2000). Using restoring boundary conditions for
heat and salt and different wind fields, Gnanadesikan and Hallberg (2000) found a similar strong
increase of the ACC transport with strengthening
of the overturning circulation (linked to a deeper
thermocline and increased water mass transformation in the northern hemisphere). As shown by Cai
and Baines (1996) and Gent et al. (2000), parameterizations of sub-grid mixing play an essential
role: the ACC transport and the overturning transport are larger in the presence of a larger vertical
diffusivity and a smaller isopycnal diffusivity. The
latter is in qualitative agreement with the baroclinic transport models (4.6.7) and (4.6.15). It also
agrees with the baroclinic Charney–DeVore model
described above, where the transport strongly
decreases with friction between the layers (see
Fig. 4.6.10b).
Topographic steering
The important role of submarine topography in
the dynamics of the ACC was discussed in the preceding sections. The topography also acts to steer
the current, as noted very early on by Sverdrup
et al. (1942, pp. 468; 606–607) and described by
Gordon et al. (1978) (see also the pressure maps in
Webb et al., 1991, and the steric height maps in
Olbers et al., 1992). Steering by bathymetry has
also been detected in the sea surface topography obtained from altimeter data, as reported by
Chelton et al. (1990) and Gille (1994). A laboratory model of homogeneous and linearly stratified
flow over realistic topography is reported by Boyer
et al. (1993). The resulting flow is in fair agreement
with observations regarding steering by the major
ridges and troughs, but it also shows significant
discrepancies that are traced back to inadequate
representation of small-scale passages and fracture
zones, unrealistic forcing (which was simulated by
sources and sinks of mass) and neglect of the planetary effect. Early models of topographic effects
on the ACC were homogeneous (Kamenkovich,
1962; Johnson and Hill, 1975), so that f/H contours inevitably dominated the flow pattern. The
breaking of f/H or bathymetry control by stratification is demonstrated in many simple numerical
models (e.g. Klinck, 1993) and the coarse- and
high-resolution models of the circumpolar circulation discussed above.
Theory suggests the flow may be steered
along bathymetry contours, latitude circles or the
geostrophic contours f/H. The conditions under
which one of these effects will dominate can be clarified by use of the balance (4.6.1) of integrated
vorticity. If the deep ocean is motionless,
0 f ku b :9(ٌp) b :0 , the bottom torque term in
(4.6.1) vanishes because (ٌp) b :ٌp b 9g b ٌH. This
allows a ‘free mode’ in the transport streamfunction following f contours; in case of locally weak
stress curl the flow would follow such a path.
However, a motionless abyss requires strong stratification to shield the flow from the influence of
topography. The ACC is far from such a state but
the converse condition of a homogeneous water
SECTION 4 THE GLOBAL FLOW FIELD
290