In order to interpret the behavior of the upper-layer thickness, we simplify governing equations to
where characteristic velocities, 
and 
are defined as
Two processes govern the temporal variation of the upper-layer thickness. One is expressed by the second and third terms on the left-hand side of Eq. (1), which are the eadvectionf of the upper-layer thickness due to the combination of the vertically averaged flow and westward propagation of the long baroclinic Rossby-wave [see Eq. (2)]. Another is expressed by the right-hand side of Eq. (1). This term generates the anomaly of the upper-layer thickness when the lower-layer flow impinges to the bottom slope (Isobe, 2000). When the lower-layer flow is heading to the shallow (deep) portion, the upwelling (downwelling) occurs through this term.
Figure 10 shows the distribution of the lower-layer
zonal velocity (upper panels) and impinging
term (lower panels) above the ridge (1440
km < x < 1940 km) every 60 days. It is found
that both westward and eastward flows with
the speed of several cm/s appear on the eastern
side of the ridge. The lower-layer flow remains
throughout the annual cycle because isostasy
is not accomplished for such short period
variation. Therefore, the impinging process
works mainly on the eastern side of the ridge
as shown in the lower panels. Hence, the
anomaly of the upper-layer thickness is generated
on the eastern side of the ridge.
Figure 11 shows the distribution of the characteristic velocities above the ridge every 60 days, representing the advection process of the upper-layer thickness. In general, the anomaly of the upper-layer thickness generated on the eastern side of the ridge is carried westward above the ridge. In the northern part, it is found that magnitudes of the characteristic velocities are small. This is because the characteristic velocities are composed of the vertically averaged flow and westward propagation of the long Rossby-wave, and in addition, directions of these two components are opposite in the northern part of the ridge. Namely, the propagation speed of the anomaly of the upper-layer thickness varies meridionally.
Thereafter, the anomaly of the upper-layer thickness reaches the western half of the ridge. Figure 12 shows the magnitude of the lower-layer flow above the ridge (1440 km < x < 1940 km) every 60 days. It is interesting to note that the lower-layer flow mostly vanishes in the western half of the ridge. This means that isostasy is accomplished with respect to each anomaly of the upper-layer thickness moving on the bottom topography. Thus, the anomaly of the upper-layer thickness generated above the ridge carries the information of the volume transport variation to the west of the ridge. As mentioned previously, the time when the anomaly reaches the western edge of the ridge varies meridionally because of the difference of the characteristic velocities. Hence, the phase of the annual variation of the volume transport is delayed northward as shown in Fig.8
