The Nondissipative Model
351
models of the general circulation. McCreary and Lu (1994) present an alternative representation for the bifurcation latitude which in general somewhat
departs from the zero wind stress curl line. However, their determination is
valid only if the outcrop line occurs far enough south to lie in a region of
westward wind stress. Even then determination of the bifurcation point is
unfortunately only implicit.
Pedlosky (1987) rather arbitrarily chose a value of B0, and hence implicitly
a bifurcation latitude, and examined the nature of the equatorial solution of
the set (6.4.26a,b,c). Although the strength of the model's undercurrent depends on Bo the structure of the solution is not very sensitive to its value.
Section 6.5 considers the role of the shadow zone in determining he
structure of the solution. In the calculations of Pedlosky (1987) H 2 is taken
equal to zero. It is assumed that the equator is south of the shadow zone
boundary of the lowest thermocline layer and that layer 2 corresponds to an
upper layer whose thickness vanishes on the eastern boundary. As we saw in
Chapter 4, the presence of a variable mixed layer depth endows even shallow
layers in the thermocline with shadow zones, but these are relatively narrow. In
the solutions presented by Pedlosky (1987), H 2 in the boundary condition
(6.4.27) is set equal to zero.
Figure 6.4.2 shows that solution for the case in which r 12 = 1, y2 = 5 and
the matching with the midlatitude solution occurs at Yn = 2.5. Bo was chosen to
be equal to 1.265, which was equal to h(O,yn) for the case in which the wind
stress is taken to be independent of longitude and equal (in scaled units) to -1
corresponding to a stress of 1 dyn/cm 2 • The eastern boundary is placed at x = 1
and the western boundary at x = 0. The relation (6.4.16) is used to relate h1
to h.
In the figure panels the solid line represents the zonal velocity in the interval y;::: 0. The dashed line represents the shear, 8u2/8y, and the dotteddashed line is the depth h. The dotted curve is the depth of the base of layer 1;
note that it is flat, in accordance with (6.4.16).
The zonal velocity at large values of y is westward and is determined by the
solution. At x = 0.5, for example, which is shown in panel b, the zonal velocity
far from the equator is -0.05196. With the scaling velocity introduced earlier,
U = 130 cm/s, this corresponds to a westward flow of 6.7 cm/s. As opposed to
the Fofonoff and Montgomery solution the shear is nearly zero in the region
outside the undercurrent rather than growing linearly from the matching latitude. Indeed, the westward velocity actually increases in magnitude southward
from the starting latitude until at y ~ 1 the velocity changes sign and rapidly
increases to the east. The solution now has a boundary layer character in which
the eastward jet is limited to the domain determined by the internal, physical
scale f rather than by the matching latitude Yn· The maximum eastward velocity is attained on the equator and has a magnitude of order unity in nondimensional units. The current therefore has scales for velocity, width and
depth which are in accordance with our original scaling estimates (e.g., the
nondimensional variables are order one) and in accordance with observations.
351
models of the general circulation. McCreary and Lu (1994) present an alternative representation for the bifurcation latitude which in general somewhat
departs from the zero wind stress curl line. However, their determination is
valid only if the outcrop line occurs far enough south to lie in a region of
westward wind stress. Even then determination of the bifurcation point is
unfortunately only implicit.
Pedlosky (1987) rather arbitrarily chose a value of B0, and hence implicitly
a bifurcation latitude, and examined the nature of the equatorial solution of
the set (6.4.26a,b,c). Although the strength of the model's undercurrent depends on Bo the structure of the solution is not very sensitive to its value.
Section 6.5 considers the role of the shadow zone in determining he
structure of the solution. In the calculations of Pedlosky (1987) H 2 is taken
equal to zero. It is assumed that the equator is south of the shadow zone
boundary of the lowest thermocline layer and that layer 2 corresponds to an
upper layer whose thickness vanishes on the eastern boundary. As we saw in
Chapter 4, the presence of a variable mixed layer depth endows even shallow
layers in the thermocline with shadow zones, but these are relatively narrow. In
the solutions presented by Pedlosky (1987), H 2 in the boundary condition
(6.4.27) is set equal to zero.
Figure 6.4.2 shows that solution for the case in which r 12 = 1, y2 = 5 and
the matching with the midlatitude solution occurs at Yn = 2.5. Bo was chosen to
be equal to 1.265, which was equal to h(O,yn) for the case in which the wind
stress is taken to be independent of longitude and equal (in scaled units) to -1
corresponding to a stress of 1 dyn/cm 2 • The eastern boundary is placed at x = 1
and the western boundary at x = 0. The relation (6.4.16) is used to relate h1
to h.
In the figure panels the solid line represents the zonal velocity in the interval y;::: 0. The dashed line represents the shear, 8u2/8y, and the dotteddashed line is the depth h. The dotted curve is the depth of the base of layer 1;
note that it is flat, in accordance with (6.4.16).
The zonal velocity at large values of y is westward and is determined by the
solution. At x = 0.5, for example, which is shown in panel b, the zonal velocity
far from the equator is -0.05196. With the scaling velocity introduced earlier,
U = 130 cm/s, this corresponds to a westward flow of 6.7 cm/s. As opposed to
the Fofonoff and Montgomery solution the shear is nearly zero in the region
outside the undercurrent rather than growing linearly from the matching latitude. Indeed, the westward velocity actually increases in magnitude southward
from the starting latitude until at y ~ 1 the velocity changes sign and rapidly
increases to the east. The solution now has a boundary layer character in which
the eastward jet is limited to the domain determined by the internal, physical
scale f rather than by the matching latitude Yn· The maximum eastward velocity is attained on the equator and has a magnitude of order unity in nondimensional units. The current therefore has scales for velocity, width and
depth which are in accordance with our original scaling estimates (e.g., the
nondimensional variables are order one) and in accordance with observations.