The Nondissipative Model
349
interval (0, Yn) is given by:
{Yn hu dy) B6 - h2(0, Yn)
Jo
x=O
2y2
(6.4.34)
If B0 > h(O, Yn) there is a net eastward mass flux at x = 0. The situation is
shown schematically in Fig. 6.4.1. The flow entering the undercurrent from the
subtropical gyre enters on two distinct paths. The first is composed of interior
streamlines that directly reach the equator, such as the streamline marked l/1; in
the figure. It flows westward in the interior and turns eastward in the undercurrent producing no net eastward transport across the line (0, Yn). Other
streamlines, such as the one labeled 1/Jb, strike the western boundary before
hitting the equator. A critical point, y., exists in the boundary layer such that
south of y = y. the boundary layer transport is southward. If the streamline 1/Jb
strikes the western boundary south of y., it proceeds to the equator and adds to
the eastward mass flux of the undercurrent. If the matching position y = Yn is
south of the latitude y = y., there is a net eastward mass flux in the latitude
interval (0, Yn) equal to the southward transport of the western boundary layer
at y = Yn· Only if Bois equal to h(O, Yn) is the net zonal mass flux balance across
a latitude section. This occurs of course only if Yn coincides with the bifurcation
latitude y., for then (6.4.34) would yield the balance.
'l'o
Fig. 6.4.1. Connection of the western boundary current and the intitiation of the EUC. The critical
streamline t/1 = t/Jo intersects the stagnation point of the western boundary current at the latitude
y •. The value of the Bernoulli function on the equator is determined by the Bernoulli function on
this streamline. If Yn = y. the net zonal mass flux across the section (O,yn)is zero
349
interval (0, Yn) is given by:
{Yn hu dy) B6 - h2(0, Yn)
Jo
x=O
2y2
(6.4.34)
If B0 > h(O, Yn) there is a net eastward mass flux at x = 0. The situation is
shown schematically in Fig. 6.4.1. The flow entering the undercurrent from the
subtropical gyre enters on two distinct paths. The first is composed of interior
streamlines that directly reach the equator, such as the streamline marked l/1; in
the figure. It flows westward in the interior and turns eastward in the undercurrent producing no net eastward transport across the line (0, Yn). Other
streamlines, such as the one labeled 1/Jb, strike the western boundary before
hitting the equator. A critical point, y., exists in the boundary layer such that
south of y = y. the boundary layer transport is southward. If the streamline 1/Jb
strikes the western boundary south of y., it proceeds to the equator and adds to
the eastward mass flux of the undercurrent. If the matching position y = Yn is
south of the latitude y = y., there is a net eastward mass flux in the latitude
interval (0, Yn) equal to the southward transport of the western boundary layer
at y = Yn· Only if Bois equal to h(O, Yn) is the net zonal mass flux balance across
a latitude section. This occurs of course only if Yn coincides with the bifurcation
latitude y., for then (6.4.34) would yield the balance.
'l'o
Fig. 6.4.1. Connection of the western boundary current and the intitiation of the EUC. The critical
streamline t/1 = t/Jo intersects the stagnation point of the western boundary current at the latitude
y •. The value of the Bernoulli function on the equator is determined by the Bernoulli function on
this streamline. If Yn = y. the net zonal mass flux across the section (O,yn)is zero