Abstract
Introduction
Data & methods
Results
Conclusion
Acknowledgements
References
 

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The eddies in the buoy tracks

The eddies revealed in the overall buoy tracks are seen in Figure 2a. The figure presents the total of 126 eddies obtained from the trajectories in relation to their direction of rotation and bathymetry of the study area. The figure also demonstrates that there is no obvious relation between the direction of rotation and the position of the eddy, or the particular current from which the structures have been formed. The eddies in the western STF are the biggest. Except for the structures present in the vicinity of 30 ^oS, 38 ^oW (close to the Rio Grande Rise), the eddies do not seem to be associated with the bathymetry, but rather with the troughs of the BMC meanders.

The eddies in the BC/BCC front are smaller than the ones found in the SAC. Some of those found in the BCC, in water depths shallower than 100 m, are very elongated and reminiscent of tidal or inertial oscillations but are possibly related to current reversals caused by the passage of atmospheric frontal systems.

In fact, an animation made with the buoy trajectories has shown for time periods of 2-4 days in April to June 1993 (when two or three buoys were at the same time in the BCC), current reversals occurred during their advection to the north. It was a surprise to observe that, although the three buoys were being advected in the BCC in positions about 300-400 km apart one from another, they suffered the same reversals at the same time. That implies the same forcing mechanism was acting in the BCC at the SBCS over a length scale of several hundreds of kilometres. The periods and scales of these perturbations suggest the passage of cold atmospheric pressure systems over the SBCS. The signature of these reversals in the buoy trajectories are the elongated (cyclonic or anticyclonic) eddies along the Brazilian shelf seen in Figure 2a.

No relationship was found between the sea surface temperature (measured by the buoys) and the eddies’ sizes. Nevertheless, the temperatures around the eddies were very coherent, with standard deviations tending to be smaller than 1 ^oC. That confirms the expected efficiency of the drifters to follow a particular water mass (represented by a particular isotherm) and, in the case of the eddies, to delimit them from adjacent waters with distinct temperature signatures.

The simple statistics obtained for the rotational period, perimeter and diameter of the eddies in class 1 and class 2 are given in Table 1. As described before, the eddies’ diameters (D) were computed from the eddies’ perimeters (P) supposing that the structures had a circular shape using the relation D = P/p. The diameters can be compared to measurements taken subsequently from the eddies present in the AVHRR images.

The mean diameter of 11.5 km (+/- 10.1 km, 1 std. dev.) found here for the eddies in class 1 is very similar to the diameter of the kind of small scale eddy seen in Figure 3a. These eddies are probably generated at the shelfbreak by shear instabilities between the BC and the BCC. As described by Souza (2000), the shear instabilities are common all along the BC/BCC front. Instability waves or mushroom-like features, as the one seen in Figure 3b can cause detachment of eddies from the BC towards the BCC and vice-versa. Typical diameters of these eddies, as measured from satellite images, are in the order of 10 to 50 km.

Typical diameters of about 50 km for eddies in the SWA were recently reported by Willson and Rees (2000). By using a combination of satellite images and in situ data, the authors described eddies occurring in the SWA as far north as 32 ^oS.  They also point out that the surface waters of the eddies north of 36 ^oS are influenced by coastal waters.

The mean diameter found here for eddies in class 2 (140.7 km) is in close agreement to the diameters reported by Garzoli (1993) for the eddies in the BMC region. Warm core eddies from the BC were reported by Legeckis and Gordon (1982) to be elliptical with mean major and minor axis of 180 km and 120 km, respectively. An average of these axes result in a typical diameter of 150 km, a measurement very similar to the one presented by Garzoli (1993) and also very close to the mean diameter found here for the class 2 eddies. Vigan, Provost and Podestá (2000) have also described eddies in the BMC region with diameters of 160-170 km.

The diameters found for the eddies in the BC, BCC and SAC, divided into classes 1 and 2, were analysed with respect to the typical Rossby radius of deformation (Rd) computed for the eddies’ mean latitude. Eddies with length scales bigger than the Rossby radius of deformation tend to be generated by detachment from meanders in the main flow, generally caused by baroclinic instabilities, and tend to be in geostrophic balance. Small scale eddies, on the other hand, tend to follow a very unpredictable behaviour typical of turbulent flows. In the last case, D is several times smaller than Rd.

Class 1 eddies have diameters much smaller than Rd while the majority of class 2 eddies tend to be bigger than Rd. Although this result is expected since class 1 eddies are the smaller ones, it was also noticed that in both classes the relation D/Rd is very variable. In class 1, D/Rd ranges from about 0.5 to numbers in the order of 10-3.  In class 2, on the other hand, D/Rd varies from 0.5 to about 4.5. This last number is in agreement with those reported by Richards and Gould (1996) to dominate typical fully developed eddy flow in the ocean.

The relationship between the Rossby number (Ro) and the eddies’ diameter is presented in Figure 4. Apart from the mean Ro found for the eddies in class 2 (Ro = 0.24), all the other mean numbers indicate a very non-linear flow, where the acceleration forces predominate over the Coriolis force (Ro = 1 or greater). Minimum Rossby numbers for the particular currents, however, demonstrate that for some of the eddies quasi-geostrophy or geostrophy (where Ro ~ 0.1 or Ro ~ 0, respectively) can apply.

Figure 4 also includes the Ro/D relation found by Chassignet et al. (1990) for three eddies of the BMC region. Analysing the distribution of the pair (Ro, D) of Chassignet et al.’s (1990) eddies in relation to the distribution of the eddies described here, we can conclude that they are very similar, supporting the consistency of the methods used here to describe the eddy activity in the BMC and SBCS regions.

A relationship between the rotational period (TR), perimeter (P), diameter (D) and tangential velocity (VT) was obtained by linear regression between these variables for the eddies in classes 1 and 2 independently. The results are collated in Tables 2 and 3. Note that, since the eddies’ P and D are directly proportional, the linear regressions between these parameters and TR or VT are the same, apart from a factor of p in the slope.

Tables 2 and 3 show that the linear regressions were better adjusted when relating P or D with TR (r = 0.79 and r = 0.65 for classes 1 and 2, respectively) than when relating P or D with VT. The linear regressions were applied to the overall set of eddies independently of their direction of rotation because the eddies’ TR, VT, P and D did not present any relation with their direction of rotation.

As quoted before, there are very few measurements of VT or TR for eddies in the SWA. In order to ‘validate’ our empirical relations between P or D and VT or TR we compare estimations of these variables obtained from the empirical models presented in this chapter with actual measurements made by three different authors in the SWA. This comparison is seen in Table 4. 

The eddies in the satellite images

Figure 2b presents the distribution of the cold core and the warm core eddies found in AVHRR images for the study area between March 1993 and July 1994. The sizes of the eddies are represented by the proportional crosses.

No relation was obtained between the eddies’ core temperature and the position where the eddies were found. Although for the small eddies the temperature of the core does not imply a specific direction of rotation, it is generally true that the mesoscale warm core eddies are anticyclonic features, and cold core eddies are cyclonic ones. The overall positions of the eddies in Figure 2b agree with those observed for the eddies found in the buoys’ trajectories (Figure 2a), the smaller eddies being found in the BC/BCC front. Figure 2 also indicates that the buoy trajectories, although not attached to the waters coming from the MC, were good indicators of the eddy dynamics over the entire study region.

Unfortunately, it was not possible to statistically compare size measurements made in the same eddies by using buoy tracks and AVHRR images at the same time. Mainly owing to cloud coverage, very few were the images where one could superimpose buoy tracks and see fully developed eddies in both data sets. Moreover, most of the individual eddies identified in the AVHRR images were not the same as the already described ones of the buoy trajectories. Rather, the two data sets are complementary to each other.

The distribution of the eddies’ core temperatures (mean and standard deviation derived from temperature transects along the major and minor axes) revealed that they do not have relation with the eddies’ sizes. The temperature dynamical range (about 10 ^oC to 30 ^oC), though, was a little wider than the range of temperatures found for the eddies in the buoys’ trajectories. Temperature standard deviations were also broader in the AVHRR eddies. The explanation for it is that the temperature measurements for the eddies in the buoys’ trajectories were measured along their perimeters, while the measurements for the eddies in the images were from the eddies’ interior, where they tend to follow a gradient from the centre to the border.

The distribution of the AVHRR eddies sizes (perimeter, diameter) did not follow that of the eddies found in the buoy trajectories, where small-scale eddies of TR lower than 5 days and P lower than 100 km dominate the spectrum of eddies sampled by the buoys (about 65 % of the frequency). Because of it, instead of analysing the eddies properties in class 1 or 2, as was done with the buoy trajectories, the AVHRR eddies are described in relation to their core temperatures: warm or cold. The majority (85 %) of the AVHRR eddies had P (D) bigger than 100 km (31.8 km). Following that, if any comparison is to be made between the AVHRR eddies and those revealed by the buoy trajectories, we have to consider the buoy eddies of class 2.

Table 5 shows the simple size statistics for the eddies found in the AVHRR images. All the parameters analysed in Table 5 (apart from the diameter std.) indicated that, for the area and period studied, cold core eddies were bigger than warm core ones. Moreover, the mean diameters (perimeters) found for both warm and cold core AVHRR eddies are distinct from the ones found for the class 2 (D > 31.8 km) eddies of the buoys’ trajectories (Table 1). The mean diameters of the AVHRR cold and warm core eddies were 82 km and 65 km, respectively, while the mean diameter of the class 2 eddies in the trajectories was 140.7 km. Maximum values for the AVHRR eddies’ diameters reached values of 262 km and 182 km (cold and warm core eddies, respectively), while in the trajectories the maximum eddy diameter was 346.2 km. The measurements obtained here for the AVHRR eddies are also distinct from the ones presented by Legeckis and Gordon (1982) and Garzoli (1993) for the BMC region.

When analysing Table 5 one must remember, however, that the observations described in this paper for the 1993 and 1994 SST images included the anticyclonic eddy generally present at the location of the BC return flow at about 37 ^oS, 50 ^oW, but missed the eddies which were possibly ejected by the BC southwards of this extreme location. That is because the AVHRR images used here were restricted to the latitudes lower than 42 ^oS. Both Legeckis and Gordon (1982) and Olson et al. (1988) indicate the presence of anticyclonic eddies formed by detachment from the BC extremes in the region south of 42 ^oS. These eddies formed at the BC extremes generally have dimensions larger than the mean found here for the warm core eddies and have contributed to the typical mean diameters of 100 km to 150 km described for them by Legeckis and Gordon (1982) and Garzoli (1993).

The relationship between the eddy diameters (D) and the typical internal Rossby radius of deformation (Rd) of the AVHRR eddies is almost identical to the one found for the class 2 eddies of the buoy trajectories. Values of the ratio D/Rd ranged from about 0.1 to about 5, the first representing small-scale eddies mainly formed in the BCC/BC front and the last being characteristic of a fully developed eddy field (Richards and Gould, 1996) at the BMC region.

Figure 5 displays AVHRR SST images showing some examples of the eddies generated in the western STF, or the BMC region, since Figure 2 already presented examples of eddy formation at the BC/BCC front or SBCS region. Figure 5a is a very good example of the cold core eddy formation in the BMC by the detachment from meanders of the SAC. The figure shows three eddies being expelled from the main current by the breaking off from high amplitude meanders. These structures travel towards the warm part of the BMC region. They are a source of eutrophic water from subantarctic origin to the tropical domain of the BMC region, and possibly have direct association with high primary production and fish. Their fate is unknown in the BMC region, and the data set available for this work, although suggesting time scales of a month for these eddies lifetime, was unfortunately not enough to verify their complete evolution or coalescence. That limitation was mainly caused by cloud coverage.

Legeckis and Gordon (1982) have reported that the formation of cold core eddies in the BMC region is less frequent than that of the warm core eddies. The latter were reported to be formed as a detachment from the BC extremes. Garzoli and Garraffo (1989) studied 17 months worth of echo sounders records in the BMC region from November 1984 to March 1986. They have reported that during this period of time cold intrusions were present in the records with no apparent periodicity. Three of these intrusions were associated with cold core eddies which were present in the records for periods of time between 20 days and 60 days.

Garzoli and Garraffo (1989) also computed the potential energy associated with the cold core eddies (6.5 x 10¹⁵ J), adding that it is of the same order of magnitude as the Gulf Stream eddies. The AVHRR data set analysed here, although suggesting that the periods of about a month or two can reflect the time scales for the cold core eddies lifetime in the BMC region in agreement with Garzoli and Garraffo (1989), disagrees with the suggestion made by Legeckis and Gordon (1982) that the cold core eddies are less frequent than their warm counterparts in the BMC region.

Figure 5b exemplifies the presence of warm core eddies which tend to be formed in the warm part of the BMC between two consecutive cold meanders in the SAC. The eddies are circular, have diameters close to 100 km, and are very typical. However, previous descriptions of the warm core eddies in the BMC generally reported the eddies formed to the west of the first SAC meander (seen in Figure 5b at 39 ^oS, 52 ^oW) or at the south of the BC extreme location, below 42 ^oS. We have indications from the images that this sort of eddy is formed regularly at the meander’s trough in the warm part of the confluence. It is unlikely that they can break through the front and travel southwards, although we did not have enough material to confirm that. If travelling towards the cold part of the front, these eddies could add a huge amount of heat, salt and momentum from the tropical to the subantarctic domain of the BMC region.

Figure 2 show examples of eddies or frontal instabilities of the BC/BCC front and SBCS region. In the case of Figure 2a, the features are only about 10 km in diameter, but Figure 2b shows that the scales can reach 50-60 km.

Typical diameters of 40 km were reported to characterise the shelfbreak eddies of the Middle Atlantic Bight in the United States coast (Garvine, Wong, Gawarkiewicz, McCarthy, Houghton and Aikman, 1988). The structures were described to be about 4 times smaller than the eddies of the Gulf Stream. The authors also described that the front in which the eddies were formed separates cooler, fresher waters in the shelf from warmer, saltier water from the slope. Prominent features of the eddy groups, following Garvine et al. (1988), were described to be the (1) plumes of lighter shelf water that protruded into slope water curling backwards in opposite direction of the shelf flow and (2) neighbouring cyclones with slope water partially or wholly surrounded by the plumes.

The characteristics of the BC/BCC front are very similar to those from the shelf/slope front off the American Middle Atlantic Bight. By analogy, some of the eddies formed in the BC/BCC front are considered here to be shelfbreak eddies. Together with frontal instabilities of the BC and BCC in the form of waves with crests protruding in direction opposite to that of the current, mushroom-like features are quite common at the BC/BCC front. These features would liberate warm core eddies from BC into BCC or cold core eddies from BCC into BC. Several structures like that are likely to be formed all along the BC/BCC front. The exchange of heat, salt and momentum between the BC and the BCC through the detachment of small-scale eddies is a process which demands further investigation.
 

rbds@soc.soton.ac.uk (c) April 2001, all rights reserved.