The Nondissipative Model
353
Fig. 6.4.3. Base of the moving layer
0
.2
4
.6
.8
1.0
representing the core of the under0 -t---'----J'-----'--------'-------'--.._____.____.__..___.__ x/xe
current shown as a solid line at the
equator and as a dashed line in the
matching region at y = Yn· (From .2
Pedlosky 1987)
4
.6
.8
1.0
/,,.-"'""
/
1.2
/ /
/
/
/
/
/
/
/
/
/
/
/
/
/
/
Only the half-plane y ~ 0 is shown in Fig. 6.4.2. The lower half-plane,
representing the southern hemisphere, is obtained by reflection. Since i1u2/i1y is
not zero on the equator, the velocity profile has a cusp. This is an inevitable
consequence of the adiabatic model, which preserves potential vorticity. On
the equator where y = 0 (6.4.26a) implies that:
OU2 (O) = -y 2 h2(0).
8y
Bo
(6.4.37)
Thus a cusp is present at the equator as long as the thickness of the layer
containing the undercurrent differs from zero. Small lateral friction, negligible
for determining the overall structure of the current, can smooth away the cusp.
Figure 6.4.4 shows the same profiles of the solution at x = 0.5 for the case
in which the relation between h and h1 has been chosen to be (6.4.19). The
dotted curve is the base of the upper layer, and it is seen to be a reflection of the
displacement of the base of the lower layer shown as a solid curve on the right
of the figure. The effect of the compensation of the upper layer on the velocity
of the undercurrent core is minor. There is a small reduction in the maximum
velocity from 1.004 in the example shown in Fig. 6.4.2 to 0.910 in Fig. 6.4.4.
Otherwise the qualitative nature of the current is unchanged. Note that the
bowing of the isopycnal surfaces, which is also evident in the observations, is
due entirely to the tilting of the isopycnal surface required by the thermal wind
balance of the zonal velocity. It is not forced by cross-isopycnal motion (there
is none in this model) dragging apart the isopycnals.
The isolines of Bernoulli function, B2, are streamlines of the flow, and
Fig. 6.4.5 shows some selected streamlines labeled with the value of B2• Along
the equator B2 is 1.265, and this is the streamline which emanates from the
353
Fig. 6.4.3. Base of the moving layer
0
.2
4
.6
.8
1.0
representing the core of the under0 -t---'----J'-----'--------'-------'--.._____.____.__..___.__ x/xe
current shown as a solid line at the
equator and as a dashed line in the
matching region at y = Yn· (From .2
Pedlosky 1987)
4
.6
.8
1.0
/,,.-"'""
/
1.2
/ /
/
/
/
/
/
/
/
/
/
/
/
/
/
/
Only the half-plane y ~ 0 is shown in Fig. 6.4.2. The lower half-plane,
representing the southern hemisphere, is obtained by reflection. Since i1u2/i1y is
not zero on the equator, the velocity profile has a cusp. This is an inevitable
consequence of the adiabatic model, which preserves potential vorticity. On
the equator where y = 0 (6.4.26a) implies that:
OU2 (O) = -y 2 h2(0).
8y
Bo
(6.4.37)
Thus a cusp is present at the equator as long as the thickness of the layer
containing the undercurrent differs from zero. Small lateral friction, negligible
for determining the overall structure of the current, can smooth away the cusp.
Figure 6.4.4 shows the same profiles of the solution at x = 0.5 for the case
in which the relation between h and h1 has been chosen to be (6.4.19). The
dotted curve is the base of the upper layer, and it is seen to be a reflection of the
displacement of the base of the lower layer shown as a solid curve on the right
of the figure. The effect of the compensation of the upper layer on the velocity
of the undercurrent core is minor. There is a small reduction in the maximum
velocity from 1.004 in the example shown in Fig. 6.4.2 to 0.910 in Fig. 6.4.4.
Otherwise the qualitative nature of the current is unchanged. Note that the
bowing of the isopycnal surfaces, which is also evident in the observations, is
due entirely to the tilting of the isopycnal surface required by the thermal wind
balance of the zonal velocity. It is not forced by cross-isopycnal motion (there
is none in this model) dragging apart the isopycnals.
The isolines of Bernoulli function, B2, are streamlines of the flow, and
Fig. 6.4.5 shows some selected streamlines labeled with the value of B2• Along
the equator B2 is 1.265, and this is the streamline which emanates from the