366
Equatorial Dynamics of the Thermocline: The Equatorial Undercurrent
y;
1-x =-Ax= 2 ; .
(6.6.18)
Equation (6.6.18) can be thought of as determining the particular characteristic
(i.e., the value of Ye) which strikes the equator at this location. The value oft{! 1
is determined by integrating along the characteristic and in particular its value
on the equator at that longitude is then known. This determines the value of B2
at the equator from (6.6.16). Then the system (6.4.26) can be integrated in
latitude at this longitude which is one step in x west of the eastern boundary.
This determines hand ht along the latitude corresponding to the first zonal step
from the eastern boundary. With the layer thicknesses known on this meridian
the equation (6.6.14) can then be recalculated another step westward along the
characteristic and the process iterated until the western boundary is reached.
At each step the Bernoulli function is determined on the equator.
This method of determining the Bernoulli function on the equator appears
inconsistent with the suggestion of the previous section in which the Bernoulli
function on the equator is determined in the west by the value carried to the
equator by the western boundary current. The inconsistency really reflects the
overidealization of each partial attempt to deal with the dynamics. The previous specification of the Bernoulli function most likely overidealizes the
conservative nature of the dynamics which should have a limited range of
validity near the western boundary before the effect of cross-isopycnal flux
become significant. The linear dynamics of the upper layer discussed in this
section is probably more relevant to the eastern regime of the upper density
layers of the undercurrent. There does not currently exist an analytical model
which joins the two regimes.
Figure 6.6.4 shows the results of the calculation of Pedlosky and Samelson
(1989) for the nondimensional, equatorial wind-stress distribution:
'= -(1- x)
(6.6.19)
which is meant to correspond to the wind-stress distribution in the equatorial
Atlantic which increases in strength westward. The calculations have been done
for r = 1 which yield a dissipation time for the upper layer equal to LjU, i.e.,
the characteristic zonal advective time.
Panel a shows the streamfunction of the lower layer. Fluid enters the
undercurrent largely in the western basin, both from the western boundary
current and from the interior, and rises into the surface layer as it flows eastward. Panel b shows the streamfunction of the upper layer. The flow emerges
from the equatorial upwelling region and flows northwestward in a broader
pattern than the equatorward directed flow of the lower layer. Panel c presents
the isopleths of u2• The undercurrent speed is nearly constant along the equator
as the entrainment balances the acceleration due to the convergence of fluid
from the interior. The thinning and narrowing of the current, rather than its
deceleration, yields the necessary reduction in transport until, very near the
eastern boundary, there is a rapid reduction in the current speed as we ob-
Equatorial Dynamics of the Thermocline: The Equatorial Undercurrent
y;
1-x =-Ax= 2 ; .
(6.6.18)
Equation (6.6.18) can be thought of as determining the particular characteristic
(i.e., the value of Ye) which strikes the equator at this location. The value oft{! 1
is determined by integrating along the characteristic and in particular its value
on the equator at that longitude is then known. This determines the value of B2
at the equator from (6.6.16). Then the system (6.4.26) can be integrated in
latitude at this longitude which is one step in x west of the eastern boundary.
This determines hand ht along the latitude corresponding to the first zonal step
from the eastern boundary. With the layer thicknesses known on this meridian
the equation (6.6.14) can then be recalculated another step westward along the
characteristic and the process iterated until the western boundary is reached.
At each step the Bernoulli function is determined on the equator.
This method of determining the Bernoulli function on the equator appears
inconsistent with the suggestion of the previous section in which the Bernoulli
function on the equator is determined in the west by the value carried to the
equator by the western boundary current. The inconsistency really reflects the
overidealization of each partial attempt to deal with the dynamics. The previous specification of the Bernoulli function most likely overidealizes the
conservative nature of the dynamics which should have a limited range of
validity near the western boundary before the effect of cross-isopycnal flux
become significant. The linear dynamics of the upper layer discussed in this
section is probably more relevant to the eastern regime of the upper density
layers of the undercurrent. There does not currently exist an analytical model
which joins the two regimes.
Figure 6.6.4 shows the results of the calculation of Pedlosky and Samelson
(1989) for the nondimensional, equatorial wind-stress distribution:
'= -(1- x)
(6.6.19)
which is meant to correspond to the wind-stress distribution in the equatorial
Atlantic which increases in strength westward. The calculations have been done
for r = 1 which yield a dissipation time for the upper layer equal to LjU, i.e.,
the characteristic zonal advective time.
Panel a shows the streamfunction of the lower layer. Fluid enters the
undercurrent largely in the western basin, both from the western boundary
current and from the interior, and rises into the surface layer as it flows eastward. Panel b shows the streamfunction of the upper layer. The flow emerges
from the equatorial upwelling region and flows northwestward in a broader
pattern than the equatorward directed flow of the lower layer. Panel c presents
the isopleths of u2• The undercurrent speed is nearly constant along the equator
as the entrainment balances the acceleration due to the convergence of fluid
from the interior. The thinning and narrowing of the current, rather than its
deceleration, yields the necessary reduction in transport until, very near the
eastern boundary, there is a rapid reduction in the current speed as we ob-