_^ Coastal/Equatorial Westward
Kelvin waves ■< Rossby waves
Fig. 5.187 Sketch of the propagation of signals induced by deepwater formation in the world's oceans in the form of Kelvin waves and Rossby waves: the Indonesian Passage is blocked by an artificial bridge near the northwestern corner of Australia.
As Kelvin waves move poleward along the eastern boundaries of each basin, they send westward Rossby waves, as indicated by thin arrows (labeled A, B, C) in Figure 5.187; these Rossby waves carry the signals to the ocean interior.
Kelvin waves travel very fast: 3 m/s for the first baroclinic mode. Within one month the signals can reach the western equatorial Atlantic Ocean (Fig. 5.188a). From here the Kelvin waves travel along the equator. Reaching the eastern boundary, the signal propagates poleward along the coast into both hemispheres, generating Rossby waves that propagate westward.
The first signal will reach the equatorial Indian Ocean within a year, but it takes about 5 years for the amplitude there to become appreciable, as shown by the dashed line in Figure 5.188a. From there it takes another 5 years to generate a significant signal in the equatorial Pacific Ocean (dot-dashed line in Fig. 5.188a), although the first sign of change will reach the equatorial Pacific Ocean within a year.
It takes a much longer time for the signals to reach the ocean interior, because locations away from the equator can be reached only by the Rossby waves (indicated by the thin lines with arrows in Figure 5.187) generated along the eastern coast of the individual basin. The higher the latitude, the longer it takes for the signal to cross back to the western boundary. For example, signals are visible at a station in the South Atlantic Ocean (20° S, 30° W) at
year 3; they reach a station in the South Indian Ocean (20° S, 50° E) at year 5, and a station in the South Pacific Ocean (20° S, 170° E) at year 12.5 (Fig. 5.188b).
At 40° S the signals arrive with a much longer delay. They reach the corresponding longitude positions at years 10, 16, and 25 (Fig. 5.188c). The corresponding pathways of long Rossby waves are depicted by the thin lines with arrows X, Y, Z in Figure 5.187. It is very interesting to note that signals arrive at the station in the South Atlantic Ocean (40° S, 30° W) in two stages. For the first stage, a weak signal comes from the westward-propagating Rossby waves within the Atlantic Ocean. Much stronger signals arrive later when the Rossby waves in the Indian Ocean reach this location, but it takes 25 years for these signals to reach there.
Thus, the eastern coast of South America consists of three regimes (Fig. 5.185), controlled by Rossby waves generated along the southern coast of Africa (SA), along the coast of Australia Si (the shaded area), and along the western coast of South America (SP). Given the much longer arrival times of the Rossby waves at high latitudes and over longer distances, the response of the thermocline to changes in deepwater formation in the North Atlantic Ocean is much delayed at these locations.
The details of the global thermocline adjustment on time scales from months to decades by the baroclinic Kelvin waves and Rossby waves has been discussed by Johnson and Marshall (2002). As an example, assume that the ocean is at rest initially, and the thermocline has a constant depth of 500 m. At t = 0 a deepwater source of 10 Sv is switched on. The evolution of the thermocline depth on a time scale of months is shown in Figure 5.189. Since the first baroclinic Kelvin waves travel rather fast, it takes less than one month for them to travel from the northern boundary to the equator, and it takes less than a month to cross the equator.
Layer thickness along the meridional boundaries
The upper layer thickness along the eastern boundary is approximately constant, and it declines almost linearly with time (Fig. 5.190a).
• The constant layer thickness along the eastern boundary is due to the no-flux boundary condition along the eastern wall; thus, weak friction gives rise to geostrophy and a layer depth that is roughly independent of y.
• The non-constant layer depth along the western wall is due to friction associated with the western boundary current. There is also a potential contribution due to the inertial terms.
A time-delay equation predicting layer thickness along the eastern boundary
The adjustment in the basin interior is carried out through baroclinic Rossby waves dh c dh 8 g'H
Note that the speed of long Rossby waves depends on the latitude. Based on quasi-geostrophic theory, the speed of long Rossby waves can be readily calculated from a simple theoretical formula from the stratification (Chelton et al., 1998). However, satellite observations indicate that the speed diagnosed from satellite observations is different from the value predicted from the eigenvalue problem of the normal mode in quasi-geostrophic theory. This discrepancy was first reported by Chelton and Schlax (1996), shown as the black dots (satellite data analysis) and black lines (theory) in Figure 5.191b. As more refined satellite data are now available, this issue has been explored in detail. A recent study by Chelton et al. (2007) revealed a complicated picture for the propagation of nearly linear large-scale eddies and the strongly nonlinear relatively small-scale eddies (Fig. 5.191a). It is clear that eddy dynamics requires much deeper study.
A major source of the discrepancy between the theoretical value and that diagnosed from observations is due to the existence of strong currents and eddies in the oceans. Along this line there have been many studies devoted to wave-mean-current interaction in the oceans;
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