Establishment of the Abyssal Circulation
429
source configuration as discussed above, Kawase followed the evolution of the
flow field from a state of rest driven by the turning on the source in the
northwest corner of the basin. Figure 7.6.4 shows the evolution of the height
field for the case where bR/xe = 0.3 and bs/Xe = 0.0134. In the four panels of
the figure the height field is shown at 5, 10, 20, and 40 days after the source is
switched on. The development of the flow is striking. A coastal Kelvin wave
with characteristic speed (g"H2) 1 / 2 moves rapidly down the western boundary
away from the source with a southward fluid flow developing behind it. In the
second panel the Kelvin wave disturbance leaves the western boundary, as it
must, since it cannot travel southward in the southern hemisphere on the
western boundary. It starts to travel across the basin, trapped in the equatorial
wave guide. Upon reaching the eastern boundary, the signal splits evenly due
to the symmetry of the basin and the thermal disturbance, i.e. the displacement
of the interface, and moves poleward in each hemisphere. In the final panel the
disturbance along the eastern boundary enters the interior and propagates
westward as a baroclinic Rossby wave. Its penetration into the interior is well
estimated by the scale bR, which we recall is a function of latitude. The
propagation continues until the steady solution is established as shown in
Fig. 7.6.5 which agrees well with the analytical solution shown in Fig. 7.6.3.
It is particularly important to note how the anomaly introduced at the
western boundary enters the interior to establish the steady solution. It does so
in a very indirect way in which the propagation of Kelvin and Ross by waves is
instrumental in the establishment of the flow. Since the Kelvin waves move
only along the boundary and the equator , the interior flow is established by the
propagation of baroclinic Rossby waves inward from the eastern boundary
where the anomaly in the height field is set up by the Kelvin wave signal that
has carried the anomaly signal first along the equator and then poleward in
each hemisphere. The ability of the Rossby waves to penetrate westward is
what determines the structure of the interior flow and also the final equatorial
structure, even as here, when the source of the anomaly is in the west. The
dynamics is very nonlocal, and the response to the forcing is conditioned by the
wave properties of the flow so that even the nature of the steady solution
becomes clear only by considering the underlying wave dynamics.
As Fig. 7.6.5 shows, the interior response in each hemisphere is symmetric,
with the upwelling into the thermocline being equally divided between the two
hemispheres. This implies that half of the source flow crosses the hemisphere in
the western boundary layer to upwell in the southern hemisphere. The western
boundary current flows from a source in one hemisphere to the other
hemisphere in which there is no source but only the distributed sink of fluid
entering the thermocline. In agreement with the Stommel-Arons theory [see
equation (7.3.17)] the western boundary current has a stagnation point at half
the distance from equator to pole (at 30° in spherical coordinates) where the
boundary current transport changes direction.
The role of the dissipation and wave propagation is particularly clear in the
Kawase model, and this renders it particularly illuminating. Indeed, the
429
source configuration as discussed above, Kawase followed the evolution of the
flow field from a state of rest driven by the turning on the source in the
northwest corner of the basin. Figure 7.6.4 shows the evolution of the height
field for the case where bR/xe = 0.3 and bs/Xe = 0.0134. In the four panels of
the figure the height field is shown at 5, 10, 20, and 40 days after the source is
switched on. The development of the flow is striking. A coastal Kelvin wave
with characteristic speed (g"H2) 1 / 2 moves rapidly down the western boundary
away from the source with a southward fluid flow developing behind it. In the
second panel the Kelvin wave disturbance leaves the western boundary, as it
must, since it cannot travel southward in the southern hemisphere on the
western boundary. It starts to travel across the basin, trapped in the equatorial
wave guide. Upon reaching the eastern boundary, the signal splits evenly due
to the symmetry of the basin and the thermal disturbance, i.e. the displacement
of the interface, and moves poleward in each hemisphere. In the final panel the
disturbance along the eastern boundary enters the interior and propagates
westward as a baroclinic Rossby wave. Its penetration into the interior is well
estimated by the scale bR, which we recall is a function of latitude. The
propagation continues until the steady solution is established as shown in
Fig. 7.6.5 which agrees well with the analytical solution shown in Fig. 7.6.3.
It is particularly important to note how the anomaly introduced at the
western boundary enters the interior to establish the steady solution. It does so
in a very indirect way in which the propagation of Kelvin and Ross by waves is
instrumental in the establishment of the flow. Since the Kelvin waves move
only along the boundary and the equator , the interior flow is established by the
propagation of baroclinic Rossby waves inward from the eastern boundary
where the anomaly in the height field is set up by the Kelvin wave signal that
has carried the anomaly signal first along the equator and then poleward in
each hemisphere. The ability of the Rossby waves to penetrate westward is
what determines the structure of the interior flow and also the final equatorial
structure, even as here, when the source of the anomaly is in the west. The
dynamics is very nonlocal, and the response to the forcing is conditioned by the
wave properties of the flow so that even the nature of the steady solution
becomes clear only by considering the underlying wave dynamics.
As Fig. 7.6.5 shows, the interior response in each hemisphere is symmetric,
with the upwelling into the thermocline being equally divided between the two
hemispheres. This implies that half of the source flow crosses the hemisphere in
the western boundary layer to upwell in the southern hemisphere. The western
boundary current flows from a source in one hemisphere to the other
hemisphere in which there is no source but only the distributed sink of fluid
entering the thermocline. In agreement with the Stommel-Arons theory [see
equation (7.3.17)] the western boundary current has a stagnation point at half
the distance from equator to pole (at 30° in spherical coordinates) where the
boundary current transport changes direction.
The role of the dissipation and wave propagation is particularly clear in the
Kawase model, and this renders it particularly illuminating. Indeed, the