potential vorticity in the Northern Hemisphere (Fig. 4.75a). The coexistence of potential vorticity with opposite signs indicates that symmetric instability may occur and thus modify the solution.

Furthermore, it is readily seen that the zonal velocity profile satisfies the necessary condition for barotropic instability. The barotropic instability is likely to smooth out the velocity cusp near the equator. Even for the hemispherical symmetric solution first obtained by Pedlosky (1987b), it can readily be seen that the zonal profile of the solution satisfies the necessary condition for barotropic instability.

The fact that symmetric instability may arise from the hemispheric asymmetric solution may also not be a significant deficiency. To some extent, it may be a realistic property. It was suggested recently by Hua et al. (1997) that the observed equatorial mean circulation may marginally satisfy the condition for symmetric instability. Using a numerical model, they further demonstrated that for a basic state flow with this kind of instability, the nonlinear equilibrated state of the equatorial ocean circulation exhibits some secondary flows which resemble the observed multiple equatorial jets underneath the Equatorial Undercurrent.

Application to the Pacific Ocean

Evidence of off-equator shift of the Equatorial Undercurrent core

Direct field measurements have also indicated the asymmetrical nature of the zonal velocity profile in the Equatorial Undercurrent. Hayes (1982) studied the zonal geostrophic velocity profile along two sections in the eastern equatorial Pacific. Geostrophic velocity calculated from hydrographic data is consistent with that obtained from the free-fall acoustically tracked velocimeter (TOPS). The geostrophic velocity south of the equator (at 0.5° S and

1° S) was clearly stronger than that north of the equator. Wyrtki and Kilonsky (1984) calculated the geostrophic zonal velocity from the data collected during the Hawaii to Tahiti Shuttle Experiment. Their results indicated that the center of the Equatorial Undercurrent is located at 0.5° S.

However, in the western part of the equatorial Pacific Ocean, the core of the undercurrent is located north of the equator. Tsuchiya et al. (1989) made a detailed analysis of the water mass properties collected during the Western Equatorial Pacific Ocean Circulation Study (WEPOCS). Their analysis clearly showed that the major portion of the water in the Equatorial Undercurrent at its beginning north of Papua New Guinea is supplied from the south by a narrow western boundary undercurrent (New Guinea Coastal Undercurrent). In fact, the water mass north of the equator can be traced back to its source in the south.

Gouriou and Toole (1993) analyzed the mean circulation in the western equatorial Pacific Ocean. As indicated in their Fig. 8B, there is a patch of negative potential vorticity north of the equator, adjacent to the positive potential vorticity in the environment. Such a patch of negative potential vorticity must come from the Southern Hemisphere.

Joyce (1988) argued that the wind stress on the equatorial ocean can force a cross-equatorial flow in the upper ocean. By applying a generalized Sverdrup relation to the equatorial oceans, he inferred that there is a southward cross-equatorial flow in the eastern equatorial Pacific Ocean, and a northward cross-equatorial flow in the western equatorial Pacific Ocean. His calculation, however, did not include the contribution due to the relative vorticity term, nor the connection with the western boundary currents.

The total volume flux going through the western boundary at the beginning of the undercurrent can be estimated from the streamfunction profile shown in Figure 4.75b. For example, the volume flux from the Southern and Northern Hemispheres is about 0.1 and 0.05 in nondimensional units. For the Pacific Ocean, the scale of the streamfunction is about 206 Sv; thus, the volume flux contribution from the western boundary currents is about 20 Sv and 10 Sv. The cross-equatorial flux, f 0, is about 0.03 nondimensional units, which corresponds to about 6 Sv in dimensional units. Tsuchiya et al. (1989) estimated that the volume flux of 5 Sv is fed to the eastward interior circulation between 3° S and the equator. If there were no Indonesian Throughflow, this would be the volume flux fed to the undercurrent. This flux rate is rather close to the 6 Sv estimated in the discussion above.

Determination of the cross-equatorial flow in the source regime of the undercurrent

The dynamical factor that controls the position of the separating streamline is the strength of the Bernoulli function at the latitude of the western boundary bifurcation. In reality, the bifurcation of the western boundary is a complicated three-dimensional phenomenon, which is determined by many dynamical factors, such as the large-scale forcing fields and the resulting pressure field, the shape of the coastline, bottom topography, and eddies. However, a barotropic bifurcation latitude may provide a simple and useful first step to this complicated problem.

The total poleward Ekman flux across a latitudinal section is fL TX

Jo f Po and the equatorward geostrophic flux is

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