Role of the Shadow Zone in the Undercurrent Structure
357
that the shadow zone boundary strikes the equator before reaching the western
boundary can be written as:
-r(O)L > y,H:j
X -
2
( 6.5.3)
where Lx is the width of the basin. If the basin is wide enough, or equivalently,
if the westward wind stress at the edge of the equatorial boundary layer is large
enough to satisfy (6.5.3), the shadow zone boundary strikes the equator in the
interior in the basin as shown in Fig. 6.5.la.
When this occurs, the solution in the region west of the longitude ¢ = ¢eq
is qualitatively similar to that discussed in the previous section. The model's
EUC is fed from both the western boundary current and the interior and
increases in transport and maximum velocity as it flows eastward until it
reaches the longitude ¢eq· At this longitude, as at every longitude west of this
point, (6.4.26) is solved for the current structure matching the subtropical value
of h in the region outside the equatorial boundary layer and matching B0 on
the equator. This yields the current structure entering the region east of ¢eq· In
this eastern region the undercurrent is no longer fed by from the interior, and
its total transport is constant as a function of longitude as it flows through the
equatorial margin of the shadow zone. The structure of the current, however,
alters in this region since although the boundary condition for his independent
of longitude in this region, h1 in the shadow zone diminishes eastward. As h1
becomes small compared with H 2 even this variation becomes negligible, and
the system of equations yields essentially the same boundary value problem at
each longitude so that even the structure of the current tends to become independent of longitude. Thus in the region ¢ ::::> ¢eq the solution of the model's
EUC yields a zonal current whose transport is constant. It is important to keep
in mind that this leveling off of the transport is a purely adiabatic effect produced by the shielding of the undercurrent from additional mass input after it
crosses the shadow zone boundary. In the region east of the intersection of the
shadow zone boundary with the equator the depth h of the thermocline base is
nearly level, ignoring the small effect of the variation in h1 in determining u2
and h in (6.4.26), and therefore in this region the eastward pressure force in the
lower layer is nearly zero. The EUC glides eastward in this region as a free,
unaccelerating jet.
On the other hand if, as in Fig. 6.5.1 b, the shadow zone boundary strikes
the western boundary before it reaches the equator and strikes it south of the
bifurcation latitude of the western boundary layer, the model's EUC has its
transport in layer 2 fixed at the western boundary by the mass flux delivered to
the equator in the boundary current. It then flows eastward along the entire
equatorial extent of the basin with no change in transport since there is no flow
into the undercurrent from the interior.
For the shadow zone boundary to strike the western boundary at or south
of the bifurcation latitude where f =f.:
357
that the shadow zone boundary strikes the equator before reaching the western
boundary can be written as:
-r(O)L > y,H:j
X -
2
( 6.5.3)
where Lx is the width of the basin. If the basin is wide enough, or equivalently,
if the westward wind stress at the edge of the equatorial boundary layer is large
enough to satisfy (6.5.3), the shadow zone boundary strikes the equator in the
interior in the basin as shown in Fig. 6.5.la.
When this occurs, the solution in the region west of the longitude ¢ = ¢eq
is qualitatively similar to that discussed in the previous section. The model's
EUC is fed from both the western boundary current and the interior and
increases in transport and maximum velocity as it flows eastward until it
reaches the longitude ¢eq· At this longitude, as at every longitude west of this
point, (6.4.26) is solved for the current structure matching the subtropical value
of h in the region outside the equatorial boundary layer and matching B0 on
the equator. This yields the current structure entering the region east of ¢eq· In
this eastern region the undercurrent is no longer fed by from the interior, and
its total transport is constant as a function of longitude as it flows through the
equatorial margin of the shadow zone. The structure of the current, however,
alters in this region since although the boundary condition for his independent
of longitude in this region, h1 in the shadow zone diminishes eastward. As h1
becomes small compared with H 2 even this variation becomes negligible, and
the system of equations yields essentially the same boundary value problem at
each longitude so that even the structure of the current tends to become independent of longitude. Thus in the region ¢ ::::> ¢eq the solution of the model's
EUC yields a zonal current whose transport is constant. It is important to keep
in mind that this leveling off of the transport is a purely adiabatic effect produced by the shielding of the undercurrent from additional mass input after it
crosses the shadow zone boundary. In the region east of the intersection of the
shadow zone boundary with the equator the depth h of the thermocline base is
nearly level, ignoring the small effect of the variation in h1 in determining u2
and h in (6.4.26), and therefore in this region the eastward pressure force in the
lower layer is nearly zero. The EUC glides eastward in this region as a free,
unaccelerating jet.
On the other hand if, as in Fig. 6.5.1 b, the shadow zone boundary strikes
the western boundary before it reaches the equator and strikes it south of the
bifurcation latitude of the western boundary layer, the model's EUC has its
transport in layer 2 fixed at the western boundary by the mass flux delivered to
the equator in the boundary current. It then flows eastward along the entire
equatorial extent of the basin with no change in transport since there is no flow
into the undercurrent from the interior.
For the shadow zone boundary to strike the western boundary at or south
of the bifurcation latitude where f =f.: