that the potential vorticity becomes fixed at the
point where the water in each density layer loses
contact with the surface and remains constant
until either the water upwells again into the surface layer or it becomes changed in the western
boundary current. The theory also predicts the
existence of shadow zones, regions where the characteristics intersect solid boundaries, so there is no
flow, and regions of closed characteristics. In the
latter case, the mesoscale eddy field eventually
homogenizes the potential vorticity.
The theory helps to explain the main features of
the potential vorticity field calculated by Keffer
(1985) from hydrographic data. Keffer shows that
the potential vorticity is reset wherever the water
returns to the surface mixed layer. He also finds
regions of homogenized potential vorticity but his
results show that even outside these regions diffusion has a significant effect.
de Szoeke (1987) used a three-layer version of
the Luyten et al. (1983) model to investigate the
structure of the subtropical gyre in the South
Pacific. At depth the results agree well with both
the float and hydrographic data discussed previously, including the southward movement of the
gyre with depth. The agreement is less satisfactory
at the surface, especially in the tropics.
Similarly Talley (1985) was able to use the
model to explain the large-scale features of the
shallow salinity minimum in the North Pacific.
However, the theory could not explain many of
the observed small-scale structures.
Recently Robbins et al. (2000) have used tracers
to study the ventilated flows in the North Atlantic.
In the surface layers they find good agreement
with the theory but in layers that intersect the
Azores Current they find that there is little advection across the current, only diffusion. This is consistent with Jia’s (2000) isopycnal model study of
the North Atlantic, which shows that the Azores
Current entrains these water masses into the
Mediterranean Outflow.
4.2.3.2 The effect of topography
In the subtropical gyres there is now general agreement between results from hydrographic data,
autonomous floats and the Sverdrup and ventilation theories of gyre circulation. At high latitudes
this is not so, primarily because the reduced stratification means that topographic effects can no
longer be ignored.
Rotating flows in the limit of weak or zero stratification have been investigated by Taylor (1917),
Hogg (1973), Huppert (1975), Huppert and Bryan
(1976) and many others. When there is no stratification the flow is independent of depth. In most
geophysical flows the vorticity (ٌu) is small
compared with f, so from (4.2.4) the flow must
follow lines of constant (f/H).
With stratification, the effect of topography
drops off with height, the vertical scale distance
being proportional to Lf/N, where L is the horizontal scale of the topography and N is the
Brunt–Väisälä frequency (9g
91
Ѩ/Ѩz) .
In the main thermocline at mid-latitudes, f is
approximately 1/4 h
91 and N is 10 h
91 . So for features with horizontal scales of less than 100 km,
the vertical scale will be less than 2.5 km. As a
result, the near-surface circulation rarely sees the
effect of deep topography. (The converse is also
true, so in the subtropics the surface forcing has
little effect at depth. However one of us, Suginohara,
has found that a model ocean with a flat bottom can
generate weak zonal flows at 2.5 km below the
subtropical gyre.) At 60°N, the Brunt–Väisälä frequency is nearer 3 h
91 so features with horizontal
scales of 100 km have a vertical influence of order
8 km. As this is larger than the depth of the ocean,
all such features have strong effects on the surface
circulation.
Hughes et al. (1998) recently showed that the
current speed is also involved. In the Antarctic
Circumpolar Current, the mean current is larger
than the first mode Rossby wave speed and so density compensation never has a chance to become
established.
The importance of topography at high latitudes
is seen in surface dynamic height plots of the
North Atlantic where the surface currents cross
the Mid-Atlantic Ridge just south of Iceland. The
FRAM (Fine Resolution Antarctic Model) atlas
(Webb et al., 1991) also shows the effect of topography on a numerical model where the Antarctic
Circumpolar Current skirts Kerguelen and the
Campbell Plateau.
Topography can further complicate the picture
through the Sverdrup transport produced by
the bottom friction due to other currents. Dewar
(1998) considers this problem analytically. Deep
zonal jets seen in the OCCAM (Ocean Circulation
and Climate Advanced Modelling Project) model
results may be due to this mechanism.
1
ᎏ
2
SECTION 4 THE GLOBAL FLOW FIELD
210
point where the water in each density layer loses
contact with the surface and remains constant
until either the water upwells again into the surface layer or it becomes changed in the western
boundary current. The theory also predicts the
existence of shadow zones, regions where the characteristics intersect solid boundaries, so there is no
flow, and regions of closed characteristics. In the
latter case, the mesoscale eddy field eventually
homogenizes the potential vorticity.
The theory helps to explain the main features of
the potential vorticity field calculated by Keffer
(1985) from hydrographic data. Keffer shows that
the potential vorticity is reset wherever the water
returns to the surface mixed layer. He also finds
regions of homogenized potential vorticity but his
results show that even outside these regions diffusion has a significant effect.
de Szoeke (1987) used a three-layer version of
the Luyten et al. (1983) model to investigate the
structure of the subtropical gyre in the South
Pacific. At depth the results agree well with both
the float and hydrographic data discussed previously, including the southward movement of the
gyre with depth. The agreement is less satisfactory
at the surface, especially in the tropics.
Similarly Talley (1985) was able to use the
model to explain the large-scale features of the
shallow salinity minimum in the North Pacific.
However, the theory could not explain many of
the observed small-scale structures.
Recently Robbins et al. (2000) have used tracers
to study the ventilated flows in the North Atlantic.
In the surface layers they find good agreement
with the theory but in layers that intersect the
Azores Current they find that there is little advection across the current, only diffusion. This is consistent with Jia’s (2000) isopycnal model study of
the North Atlantic, which shows that the Azores
Current entrains these water masses into the
Mediterranean Outflow.
4.2.3.2 The effect of topography
In the subtropical gyres there is now general agreement between results from hydrographic data,
autonomous floats and the Sverdrup and ventilation theories of gyre circulation. At high latitudes
this is not so, primarily because the reduced stratification means that topographic effects can no
longer be ignored.
Rotating flows in the limit of weak or zero stratification have been investigated by Taylor (1917),
Hogg (1973), Huppert (1975), Huppert and Bryan
(1976) and many others. When there is no stratification the flow is independent of depth. In most
geophysical flows the vorticity (ٌu) is small
compared with f, so from (4.2.4) the flow must
follow lines of constant (f/H).
With stratification, the effect of topography
drops off with height, the vertical scale distance
being proportional to Lf/N, where L is the horizontal scale of the topography and N is the
Brunt–Väisälä frequency (9g
91
Ѩ/Ѩz) .
In the main thermocline at mid-latitudes, f is
approximately 1/4 h
91 and N is 10 h
91 . So for features with horizontal scales of less than 100 km,
the vertical scale will be less than 2.5 km. As a
result, the near-surface circulation rarely sees the
effect of deep topography. (The converse is also
true, so in the subtropics the surface forcing has
little effect at depth. However one of us, Suginohara,
has found that a model ocean with a flat bottom can
generate weak zonal flows at 2.5 km below the
subtropical gyre.) At 60°N, the Brunt–Väisälä frequency is nearer 3 h
91 so features with horizontal
scales of 100 km have a vertical influence of order
8 km. As this is larger than the depth of the ocean,
all such features have strong effects on the surface
circulation.
Hughes et al. (1998) recently showed that the
current speed is also involved. In the Antarctic
Circumpolar Current, the mean current is larger
than the first mode Rossby wave speed and so density compensation never has a chance to become
established.
The importance of topography at high latitudes
is seen in surface dynamic height plots of the
North Atlantic where the surface currents cross
the Mid-Atlantic Ridge just south of Iceland. The
FRAM (Fine Resolution Antarctic Model) atlas
(Webb et al., 1991) also shows the effect of topography on a numerical model where the Antarctic
Circumpolar Current skirts Kerguelen and the
Campbell Plateau.
Topography can further complicate the picture
through the Sverdrup transport produced by
the bottom friction due to other currents. Dewar
(1998) considers this problem analytically. Deep
zonal jets seen in the OCCAM (Ocean Circulation
and Climate Advanced Modelling Project) model
results may be due to this mechanism.
1
ᎏ
2
SECTION 4 THE GLOBAL FLOW FIELD
210