448
Abyssal Circulation
the north, the barotropic velocity is small there for all x, and we can expect that
the meridional velocity has a very small vertical average compared with the
baroclinic velocity. Figure 7.7.4 shows the meridional velocity profiles again at
zonal locations across the basin at y = 0.9L. Again, the dashed-dotted line
shows the Stommel-Arons, barotropic component to the velocity and it is seen
to be small at each x location with respect to the baroclinic velocity. The flow in
the upper part of the water column is now equatorward at each zonal position
as vortex compression in the upper part of the water column is induced by the
midlevel source, and the small upwelling at z = 0 at this latitude.
Thus for the interior velocity field the combination of Rossby and Kelvin
wave dynamics leads to a velocity structure at every location which is quite
different than that indicated by the sources. The source is important for the
structure of the velocity field, especially at the bottom of the water column, but
only for spatially featureless wo is the velocity field's structure dominated by
the source structure.
Edwards and Pedlosky (1995) also investigated the boundary layer
structure required to close the circulation. They added horizontal mixing of
both momentum (in the equation for the flow component parallel to the
boundary) and horizontal mixing for density. The reader is referred to their
paper for the details of the calculation. The boundary layer structure is
complex. The barotropic component of the flow in this linear model always has
the lateral structure of the Munk layer while the baroclinic portion of the flow
has a double boundary layer structure that depends on the level of
stratification. If the Munk layer is thicker than the Rossby deformation
radius, the baroclinic structure has an inner scale of the order of the Rossby
deformation radius, which exists on all boundaries, and an outer scale, which
dominates the baroclinic flow structure, which occurs only on the western
boundary and has a characteristic width for the nth baroclinic mode equal to
bw = (n 2 j 2 Kh/f3H 2 N 2 ) (Warren 1981). Edwards and Pedlosky show that the
vertical structure of the velocity field in the boundary layer depends not only
on the local source structure of the flow entering the basin through the
boundary but also on the integrated properties of the source and the upwelling
over the entire basin. This occurs because the western boundary current must
carry not only the flow entering from the sources but also accept the interior
recirculating flow which impinges on the boundary. The boundary layer turns
the impinging flow to bring its normal velocity to zero so that the current flows
along the boundary. Since the interior flow and its vertical structure depends,
as we have seen, on nonlocal properties of the source distribution and the
upwelling, the boundary layer flow also has its structure determined by remote
forcing.
Thus in both the interior and the boundary layer the flow pattern at any
level can be expected to differ significantly from that predicted by the classical
Stommel-Arons model although, at least in models with no topography, the
barotropic mode which carries the total transport is still given by the StommelArons theory. The layering of the velocity field is not explainable simply in
Abyssal Circulation
the north, the barotropic velocity is small there for all x, and we can expect that
the meridional velocity has a very small vertical average compared with the
baroclinic velocity. Figure 7.7.4 shows the meridional velocity profiles again at
zonal locations across the basin at y = 0.9L. Again, the dashed-dotted line
shows the Stommel-Arons, barotropic component to the velocity and it is seen
to be small at each x location with respect to the baroclinic velocity. The flow in
the upper part of the water column is now equatorward at each zonal position
as vortex compression in the upper part of the water column is induced by the
midlevel source, and the small upwelling at z = 0 at this latitude.
Thus for the interior velocity field the combination of Rossby and Kelvin
wave dynamics leads to a velocity structure at every location which is quite
different than that indicated by the sources. The source is important for the
structure of the velocity field, especially at the bottom of the water column, but
only for spatially featureless wo is the velocity field's structure dominated by
the source structure.
Edwards and Pedlosky (1995) also investigated the boundary layer
structure required to close the circulation. They added horizontal mixing of
both momentum (in the equation for the flow component parallel to the
boundary) and horizontal mixing for density. The reader is referred to their
paper for the details of the calculation. The boundary layer structure is
complex. The barotropic component of the flow in this linear model always has
the lateral structure of the Munk layer while the baroclinic portion of the flow
has a double boundary layer structure that depends on the level of
stratification. If the Munk layer is thicker than the Rossby deformation
radius, the baroclinic structure has an inner scale of the order of the Rossby
deformation radius, which exists on all boundaries, and an outer scale, which
dominates the baroclinic flow structure, which occurs only on the western
boundary and has a characteristic width for the nth baroclinic mode equal to
bw = (n 2 j 2 Kh/f3H 2 N 2 ) (Warren 1981). Edwards and Pedlosky show that the
vertical structure of the velocity field in the boundary layer depends not only
on the local source structure of the flow entering the basin through the
boundary but also on the integrated properties of the source and the upwelling
over the entire basin. This occurs because the western boundary current must
carry not only the flow entering from the sources but also accept the interior
recirculating flow which impinges on the boundary. The boundary layer turns
the impinging flow to bring its normal velocity to zero so that the current flows
along the boundary. Since the interior flow and its vertical structure depends,
as we have seen, on nonlocal properties of the source distribution and the
upwelling, the boundary layer flow also has its structure determined by remote
forcing.
Thus in both the interior and the boundary layer the flow pattern at any
level can be expected to differ significantly from that predicted by the classical
Stommel-Arons model although, at least in models with no topography, the
barotropic mode which carries the total transport is still given by the StommelArons theory. The layering of the velocity field is not explainable simply in