Numerical Models
373
sign of the rather large dissipation affecting the current, which also is responsible for its artificially low speed. In panel c the velocity vectors in the x-z
plane are superimposed on the isotherms, and we observe a rather stronger
than expected cross-isopycnal flux except at the very core of the current. In
spite of these discrepancies with regard to observations the model is dynamically consistent and reproduces the overall length and velocity scales seen in
observations.
Wacongne carefully analysed the balances in the zonal momentum equation, and her results are shown in Fig. 6. 7 .4. In the upper panel the zones of
eastward flow are shown in white, with the region of the equatorial thermocline
superimposed as cross-hatching. The core of the model EUC is shown by the
dot-dashed heavy line while a heavy dashed line indicates a boundary below
which both the zonal pressure gradient and the vertical mixing of momentum
are negligible.
A heavy dark line in panel a delineates the region (2) in panel b in which
the momentum equation reduces to a balance between the zonal pressure
gradient and the eastward acceleration. In this region the simple adiabatic,
inertial model of the EUC discussed in Section 6.4 is applicable. As the core of
the undercurrent flows eastward it enters a region, labeled (3) in which the
horizontal pressure gradient vanishes, and in which the eastward acceleration is
small. This is reminiscent of the nonaccelerating region east of the intersection
of the shadow zone boundary with the equator discussed in Section 6.5. Above
this region vertical mixing penetrates, and the strong vertical mixing is responsible for the deceleration of the current. Indeed, in the center of the basin
the core of the model undercurrent falls beneath the thermocline, and here the
otherwise free jet is restrained by horizontal mixing.
The numerical model describes a rather more dissipative EUC than either
observations or the inertial theory suggest, but it does indicate the regime
boundaries anticipated from the simple theories.
This has been further emphasized by the very illuminating analysis of the
particle trajectories in the model by Liu et al. (1994) who used the Philander
and Pacanowski model in an idealized domain but with similar parameter
settings and domain sizes as in the study of Wacongne (1989). Figure 6.7.5
shows the streamline pattern (indicated by the arrows and the dot-dashed lines)
and the isolines of potential vorticity (light solid lines) on three density surfaces
corresponding to (a) the region somewhat above the core of the EUC, (b) the
region of the core, and (c) the region beneath the undercurrent core. We see
that water in the core (panel b) reaches the EUC from the interior of the
subtropical gyre along paths that nearly conserve potential vorticity in the
interior. The fluid reaches the EUC along a path through the western boundary
current. The model current receives little water along its flanks in the core, and
its acceleration on this surface is limited, and this is consistent with the analysis
ofWacongne. Water somewhat above the core flows into the current from both
the western boundary layer and the interior although its path in the interior is a
contorted zig-zag curve between the subtropical gyre and the EUC. In the
373
sign of the rather large dissipation affecting the current, which also is responsible for its artificially low speed. In panel c the velocity vectors in the x-z
plane are superimposed on the isotherms, and we observe a rather stronger
than expected cross-isopycnal flux except at the very core of the current. In
spite of these discrepancies with regard to observations the model is dynamically consistent and reproduces the overall length and velocity scales seen in
observations.
Wacongne carefully analysed the balances in the zonal momentum equation, and her results are shown in Fig. 6. 7 .4. In the upper panel the zones of
eastward flow are shown in white, with the region of the equatorial thermocline
superimposed as cross-hatching. The core of the model EUC is shown by the
dot-dashed heavy line while a heavy dashed line indicates a boundary below
which both the zonal pressure gradient and the vertical mixing of momentum
are negligible.
A heavy dark line in panel a delineates the region (2) in panel b in which
the momentum equation reduces to a balance between the zonal pressure
gradient and the eastward acceleration. In this region the simple adiabatic,
inertial model of the EUC discussed in Section 6.4 is applicable. As the core of
the undercurrent flows eastward it enters a region, labeled (3) in which the
horizontal pressure gradient vanishes, and in which the eastward acceleration is
small. This is reminiscent of the nonaccelerating region east of the intersection
of the shadow zone boundary with the equator discussed in Section 6.5. Above
this region vertical mixing penetrates, and the strong vertical mixing is responsible for the deceleration of the current. Indeed, in the center of the basin
the core of the model undercurrent falls beneath the thermocline, and here the
otherwise free jet is restrained by horizontal mixing.
The numerical model describes a rather more dissipative EUC than either
observations or the inertial theory suggest, but it does indicate the regime
boundaries anticipated from the simple theories.
This has been further emphasized by the very illuminating analysis of the
particle trajectories in the model by Liu et al. (1994) who used the Philander
and Pacanowski model in an idealized domain but with similar parameter
settings and domain sizes as in the study of Wacongne (1989). Figure 6.7.5
shows the streamline pattern (indicated by the arrows and the dot-dashed lines)
and the isolines of potential vorticity (light solid lines) on three density surfaces
corresponding to (a) the region somewhat above the core of the EUC, (b) the
region of the core, and (c) the region beneath the undercurrent core. We see
that water in the core (panel b) reaches the EUC from the interior of the
subtropical gyre along paths that nearly conserve potential vorticity in the
interior. The fluid reaches the EUC along a path through the western boundary
current. The model current receives little water along its flanks in the core, and
its acceleration on this surface is limited, and this is consistent with the analysis
ofWacongne. Water somewhat above the core flows into the current from both
the western boundary layer and the interior although its path in the interior is a
contorted zig-zag curve between the subtropical gyre and the EUC. In the