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NOTES AND CORRESPONDENCE

On Sverdrup Discontinuities and Vortices in the Southwest

J. H. LACASCE Institute for Geophysics, University of Oslo, Oslo, Norway

P. E. ISACHSEN Norwegian Institute for Water Research, Oslo, Norway

(Manuscript received 28 June 2006, in final form 15 March 2007)

ABSTRACT

The southwest Indian Ocean is distinguished by discontinuities in the wind-driven Sverdrup circulation. These connect the northern and southern tips of Madagascar with Africa and the southern tip of Africa with South America. In an analytical barotropic model with a flat bottom, the discontinuities produce intense westward jets. Those off the northern tip of Madagascar and the southern tip of Africa are always present, while the strength of that off southern Madagascar depends on the position of the zero curl line in the Indian Ocean (the jet is strong if the line intersects Madagascar but weak if the line is north of the island). All three jets are barotropically unstable by the Rayleigh–Kuo criterion. The authors studied the development of the instability using a primitive equation model, with a flat bottom and realistic coastlines. The model produced westward jets at the three sites and these became unstable after several weeks, generating 200–300-km scale eddies. The eddies generated west of Madagascar are in accord with observations and with previous numerical studies. The model’s Agulhas eddies are similar in size to the observed eddies, both the anticy- clonic rings and the cyclones that form to the west of the tip of South Africa. However, the model’s Agulhas does not retroflect, most likely because of its lack of stratification and topography, and so cannot capture pinching-off events. It is noteworthy nevertheless that a retroflection is not required to produce eddies here.

1. Introduction Lutjeharms et al. 2003; Matano and Beier 2003). The cyclones are somewhat smaller than the rings and sub- The separates from the African sequently drift west–southwest into the South Atlantic coast and retroflects, continuing eastward into the In- (Boebel et al. 2003). dian Ocean. Roughly six times per year the current The situation off southern Madagascar is similar, pinches off an energetic anticyclonic (counterclock- with the southward-flowing Southeast Madagascar Cur- wise) ring. These are typically 100–300 km wide and rent leaving the coast (Stramma and Lutjeharms 1997; extend deep into the water column (Lutjeharms and Schott and McCreary 2001) and generating large (order Gordon 1987; Olson and Evans 1986; Gordon and of 100–200 km) eddies. Satellite images suggest that Haxby 1990; Van Aken et al. 2003). The rings drift both signs of vortex form here (Quartly and Srokosz west-northwest into the South , decay- 2002; De Ruijter et al. 2004; Quartly et al. 2006) and ing as they go (Byrne et al. 1995; Grundlingh 1995). many of these eddies subsequently drift westward to- Cyclones also form in the region, typically to the west of ward Africa. A significant fraction later merge with the the retroflection (Penven et al. 2001; Boebel et al. 2003; Agulhas Current (Grundlingh 1995; Schouten et al. 2002a). Eddies also form west of the northern tip of Mada- Corresponding author address: J. H. LaCasce, Institute for Geo- physics, University of Oslo, P.O. Box 1022, Blindern, 0315 Oslo, gascar. The Northeast Madagascar Current leaves the Norway. northern tip and flows westward to join the East Afri- E-mail: [email protected] can Coastal Current (Stramma and Lutjeharms 1997;

DOI: 10.1175/2007JPO3652.1

© 2007 American Meteorological Society

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Schott and McCreary 2001). Current fluctuations with a energetics analysis of a numerical simulation of the re- period of 50 days and scales of several hundred kilo- gion. meters were identified in the region by Quadfasel and Hereinafter we consider a possible origin for the ed- Swallow (1986). These fluctuations were probably re- dies in the region. We point out that the southwest lated to the 200-km scale anticyclones that form here, Indian Ocean and the South Atlantic exhibit several some or all of which drift south into the Mozambique discontinuities in the wind-driven Sverdrup function. Channel (De Ruijter et al. 2002; Ridderinkhof and De These discontinuities, which are a consequence of the Ruijter 2003; Schouten et al. 2002b; Quartly and Sro- basin geometry, join the northern and southern tips of kosz 2004). These “Mozambique eddies” account for a Madagascar with Africa and the southern tip of Africa large portion of the highly variable transport in the with South America. Using a barotropic analytical Mozambique Channel (Ridderinkhof and De Ruijter model, we find that the discontinuities produce intense 2003). westward jets that are barotropically unstable. Simula- The southwest Indian Ocean is thus a region of sub- tions using a barotropic primitive equation model con- stantial variability. A number of authors have modeled firm this, displaying 200–300-km scale vortices at all the currents here, both analytically and numerically. three sites. The focus has been mostly on the retroflection of the Agulhas Current. In his seminal study of the linear, 2. Analytical model wind-driven circulation in the southern Indian/Atlantic We illustrate the idea by using an idealized model of basins, De Ruijter (1982) showed that a linear Agulhas the Indian–South Atlantic basins, extending from Current does not retroflect but, instead, proceeds west- South American to Australia (e.g., Fig. 1). Our model ward from the tip of South Africa into the South At- closely resembles that of De Ruijter (1982) except that lantic. He suggested that inertia is required for the we include a surrogate Madagascar island and use Car- Agulhas to join the eastward wind-driven flow farther tesian coordinates (the solution in spherical coordinates south. Subsequent analytical and numerical studies, is similar). The flow obeys the linear shallow water however, showed that topography, stratification, cur- equations on the ␤ plane, is driven by a zonal wind rent volume, and coastal orientation may also be im- stress that varies only in y, and is damped by linear portant for retroflection (Boudra and De Ruijter 1986; bottom (Ekman) drag. The flow thus obeys the baro- Ou and De Ruijter 1986; Boudra and Chassignet 1988; tropic vorticity equation (e.g., Pedlosky 1987): Ѩ ץ Matano 1996; Biastoch and Krauss 1999). It is accepted Ѩ .ϫ ␶ Ϫ ␦ٌ2␺ ϭϪ ␶ x͑y͒ Ϫ ␦ٌ2␺ ١ nevertheless that the retroflection is responsible for ٌ2␺ ϩ ␤ ␺ ϭ x Ѩyץ Ѩt Agulhas ring formation. Numerous questions remain, however, about the for- ͑1͒ mation of the many other vortices observed in the re- We have nondimensionalized the variables using the gion. For instance, the dynamical origin of the cyclones north–south basin length and an advective time scale that form northwest of the retroflection is not under- and imposed a rigid lid and flat bottom. Here ␺ is the stood, nor do we know precisely why vortices form velocity streamfunction, ␤ is the scaled meridional de- south of Madagascar. Lutjeharms (1988) suggested rivative of the Coriolis parameter, ␶ ϭ ␶xi is the wind that the Southeast Madagascar Current retroflects on stress, and ␦ is the scaled bottom drag. The boundary leaving the island and thus can pinch off anticyclones, conditions are ␺ ϭ 0 at the lateral walls and on the like the Agulhas. However, it remains controversial African continent. The streamfunction on Madagascar whether the current does, in fact, retroflect (De Ruijter is also constant but is not necessarily zero. We deter- et al. 2004; Quartly et al. 2006; Palastanga et al. 2006), mine the constant from Godfrey’s (1989) “island rule,” and cyclones are also found here (Grundlingh 1995; De which, assuming a wind stress that varies only in y, can Ruijter et al. 2004). be written The Northeast Madagascar Current on the other ␶͑y ͒ Ϫ ␶͑y ͒ hand does not retroflect, flowing westward after sepa- ␺ ϭ N S ͑ Ϫ ͒ ͑ ͒ I Ϫ xE xM 2 ration and generating large anticyclones. Quadfasel and yN yS

Swallow (1986) and Schott et al. (1988) suggested that in nondimensional form. Here yS and yN are the south- the eddy formation here resulted from barotropic in- ern and northern latitudes of Madagascar and xE and xM stability of the separated because the are the positions of the eastern (Australian) boundary observed 50-day oscillations could not be linked to the and of Madagascar. winds. Biastoch and Krauss (1999) also concluded that With weak bottom drag (␦ K 1), the solution method barotropic instability is important here, based on an follows Stommel (1948) for a wind-driven basin. As-

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FIG. 1. The (left) Sverdrup streamfunction in the analytical model, derived from the (right) wind stress curl. The contour spacing is 0.25, the solid lines indicate positive values (counter- clockwise circulation), and the dashed lines indicate negative values (clockwise circulation). The curl is assumed to be invariant in longitude. suming a steady flow and neglecting friction in (1) ever, is that there are discontinuities in the streamfunc- leaves the Sverdrup relation. We integrate this west- tion between the northern and southern tips of Mada- ward from the eastern boundaries until striking a west- gascar and Africa and between the southern tip of Af- ern boundary; the boundary condition is then satisfied rica and South America. The discontinuity west of in a frictional layer of thickness ␦. The currents that Africa has long been known (Welander 1959; Evenson occur in these western boundary layers represent the and Veronis 1975; Godfrey 1989). Those off Madagas- model’s Agulhas, East Madagascar, and Brazil Cur- car have not been discussed but are visible, for ex- rents. For forcing we use the wind stress curl shown at ample, in Godfrey (1989, Figs. 4 and 5). The disconti- the right in Fig. 2, which mimics the actual distribution nuities are the result of the streamfunction being “re- here (e.g., Trenberth et al. 1989). The curl is negative in set” at the African continent and the island. For the south, positive at midlatitudes, and weakly positive instance, the streamfunction increases in the Indian in the north. Ocean westward from the eastern boundary but is reset The resulting Sverdrup streamfunction is contoured to zero at Africa; it increases again in the South Atlan- in Fig. 1. The large-scale flow broadly resembles the tic. But south of Africa the streamfunction is not reset currents in the region [as also noted by Godfrey (1989) and continues to increase. So, there is a north–south and Schott and McCreary (2001)]. There are two and discontinuity in the South Atlantic at the latitude of the one-half gyres, with northward flow into the southern African tip. Similar comments apply to the northern Indian Ocean and southward flow in the northern In- and southern tips of Madagascar, although the stream- dian Ocean. The flow in the mid Indian is westward function is reset to the island constant rather than zero. toward Madagascar (as indicated in Fig. 2), and this is In the analytical model the discontinuities are the model’s South Equatorial Current. South of the smoothed out by bottom friction, which permits meridi- Indian Ocean the flow is eastward, originating where onal boundary layers of thickness ␦1/2. For example, the the Falklands Current leaves the South American streamfunction correction to the west of the African tip coast. This corresponds to the northern portion of the can be shown to be Antarctic Circumpolar Current (ACC), which is purely Sverdrupian owing to the closed boundary south of 1 Ѩ␶ x͑g͒ y Ϫ g Australia. ␺ˆ ϭϮ ͑x Ϫ x ͒ erfcͫϮ ͬ, ͑3͒ 2 E M Ѩy ͌␦͑ Ϫ ͒ The central point for the present discussion, how- 2 xM x

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Ϫ FIG. 2. The full solution to the steady version of (1), with ␦ ϭ 5 ϫ 10 4. Velocity vectors have been superimposed. The western boundary layers are very narrow and difficult to see in the figure. where the positive (negative) solution applies where y strength and the position of the wind stress curl. In the is greater (less) than the latitude of the African tip, y ϭ case shown in Fig. 2, the model’s South Equatorial Cur- g. Similar solutions are found west of the northern and rent splits into northward and southward branches on southern tips of Madagascar (while also taking into ac- the western side of Madagascar. The two jets from is- count the nonzero island streamfunction). The layers land tips are accordingly of similar strength. As such, spread out, as in a diffusive layer,1 in the westward the circulation around the island is weak and the island direction (Fig. 2). The greater the bottom friction, the constant is near zero; indeed, one obtains a flow nearly more pronounced the westward spreading. Using a dif- identical to that in Fig. 2 if one sets the island constant ferent type of friction, like momentum diffusion, alters to zero. the boundary layer width but not its character. The The situation changes though if the zero curl lines boundary layer from the African tip in Fig. 2 is similar shift north or south, as in Fig. 3 where the zero curl line to that of De Ruijter (1982), despite his having used lies to the north of the island. Now there is a strong 2 momentum diffusion. cyclonic circulation around the island, and this weakens Associated with the zonal discontinuities are intense the southern jet and strengthens the northern one. We jets that link the western boundary currents. The north- recover the southern jet if we set the island streamfunc- ward Sverdrup flow entering the Indian Ocean to the tion to zero, showing that the island circulation is im- east of Africa is carried in the jet connecting South portant here. The actual South Equatorial Current Africa to South America whence it continues south- spans a range of latitudes, so such a weakening of the ward. The intensity of the jets depends both on the southern current is conceivable. In addition, the flow from the southern tip is eastward in Fig. 3, producing an 1 The boundary layer equation can be converted to a diffusion apparent retroflection of the Southeast Madagascar equation by converting the x derivative to a time derivative. The Current (e.g., Lutjeharms 1988). same type of layer is found in Gill’s (1968) model of the ACC and Note too that the jet from South Africa in Fig. 3 is at the meridional boundaries in solutions of wind- or thermally substantially weaker than that in Fig. 2. This is because forced flows in a basin (e.g., Pedlosky 1969). the zero curl line in the Southern Ocean has shifted 2 There are, in addition, narrow boundary layers of thickness ␦ at the tips of Africa and Madagascar (e.g., Gill 1968; De Ruijter northward so that there is less inflow into the Indian 1982). These affect the flow very near the tips but do not alter the Ocean. The eastward flow south of the continent has transport in the zonal currents. also shifted northward, toward Africa, causing a partial

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FIG. 3. The solution to (1) in the case that the zero wind stress curl line in the Indian Ocean lies to the north of Madagascar. Note that the westward jet from the southern tip of the island has essentially vanished. retroflection of the model Agulhas. However, the develop to finite amplitude and will also allow realistic model Agulhas lacks a full retroflection, and this is its coastlines, something that influences the character of primary deficiency (as noted previously by De Ruijter the separating flow (Ou and De Ruijter 1986; Matano 1982). 1996; Dijkstra and De Ruijter 2001). Because the separated boundary currents are mostly zonal, we can evaluate their stability using the Ray- 3. Numerical simulations leigh–Kuo criterion. This requires that the meridional The model is the Regional Oceanic Modeling System ␤ Ϫ gradient of the mean potential vorticity, Uyy, (ROMS; e.g., Shchepetkin and McWilliams 2005). We change sign for instability (e.g., Pedlosky 1987). We use the model’s zonal velocities to calculate this directly and plot the results in Fig. 4. All three zonal currents ␤ Ϫ are sites of rapid variation in Uyy, with the largest changes occurring just to the west of the island and peninsula tips. With stronger friction, the variations are more confined to the tip regions because the fanning out of the currents decreases the meridional shear far- ther to the west. This suggests that the tip regions will be the most unstable, so eddies should form soon after the currents have detached from the boundaries. The Rayleigh–Kuo criterion is a necessary rather than a sufficient condition for instability; therefore, this does not guarantee eddy formation. The flow, more- over, is not purely zonal. A more detailed stability analysis is of course possible, but it would be compli- cated because of the westward spreading of the jets and ␤ Ϫ FIG. 4. The Rayleigh–Kuo quantity, Uyy, for the solution in moreover would depend on the choice of bottom fric- Fig. 2. The solid contours are positive and the dashed negative. tion. So we chose instead to examine numerical solu- ␤ Ϫ Regions where Uyy changes sign satisfy the necessary condi- tions. These will permit us to observe the instabilities tion for barotropic instability.

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FIG. 5. The ROMS model domain. The contours indicate the SSH from a linear run, at day 200. The ripples in the South Atlantic are residual Rossby waves, propagating westward. The color scale is Ϯ1m. configured this in a wedge-shaped basin (Fig. 5), with additional experiments with different depths and ob- walls at the equator, 60°S, 60°W, and 120°E and with tained essentially the same results as described hereaf- realistic Africa and Madagascar coastlines. The domain ter. closely resembles those used by Matano (1996) and Bi- For forcing, we used the annual-mean Trenberth astoch and Krauss (1999). The maximum resolution wind stress (Trenberth et al. 1989). The bottom friction was 0.12°, somewhat finer than that of Biastoch and coefficient was 10Ϫ4 msϪ1, which with a depth of Krauss and sufficient to resolve the 100-km eddies. 1000 m implies a spinup time O(100 days). We used We simulated only the barotropic mode, with a free both Laplacian and biharmonic friction, to prevent surface and a flat bottom. The depth was set at 1000 m; small-scale instabilities, with relatively small viscosities this is obviously shallower than the actual ocean, but (10 m2 sϪ1 and 106 m4 sϪ1, respectively). hastens the model spinup. Using a shallower ocean has two effects: First it alters the barotropic deformation a. Linear calculation radius, which in turn changes the speed of gravity waves We first ran the model without advection, for com- generated during spinup. Second, the velocity in the parison with the analytical model. The sea surface shallow-water equations is inversely proportional to the height (SSH) from a representative run is shown in Fig. fluid depth (Gill 1982), so decreasing the depth by a 5. The ocean spins up from rest and Rossby waves, factor of 5 magnifies the effective wind stress by the radiating from the eastern boundaries, propagate west- same amount (of course the fluid transport is indepen- ward through the domain. The wave activity gradually dent of the total depth).3 In any case, we conducted decreases, as the waves are damped by bottom drag and small-scale dissipation at the western boundaries, and the model settles into an approximate steady state. The 3 In idealized geometries, such an increase can favor an Agulhas retroflection, even with a flat bottom (e.g., Dijkstra and De flow then resembles that seen in the analytical model. Ruijter 2001), but this effect is less pronounced with realistic The southernmost gyre is the strongest (because of the coastlines (Matano 1996; Dijkstra and De Ruijter 2001). greater longitudinal extent of the basin and the strength

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FIG. 6. A close-up view of the Agulhas region from a nonlinear run, after the separated current goes unstable. Note the formation of a large anticyclone and an accompanying, smaller cyclone. The color scale is Ϯ1m.

of the winds) while the gyre in the northern Indian is Both types of vortex subsequently drift westward into fairly weak. the South Atlantic.4 There are strong meridional gradients in SSH west of The Madagascar region at the same time is shown in Africa and Madagascar, as expected. Although not in- Fig. 7. There are zonal currents flowing westward from dicated in the figure, the flow is westward both off the both the northern and southern tips, and both are un- tips of Madagascar and South Africa. So, the linear run stable. In the north, there is an anticyclone to the west conforms well to the analytical model, suggesting that of the island tip, and comparably sized cyclones form- the model setup is adequate for testing the stability of ing to the north of the jet. All of the vortices drift the boundary currents. westward toward Africa. Upon reaching Africa, the an- ticyclones proceed southward into the Mozambique Channel. Anticyclones are visible off the African coast, b. Nonlinear calculation although they are decaying. The gyres spin up in a similar fashion in the nonlinear To gauge the size of the emerging vortices, we used runs. The difference is that the three zonal jets become the wavelet transform to calculate spatial spectra along unstable, with the instabilities manifesting themselves the axes of the three jets. For this we used the meridi- first as meanders in the currents and then as distinct onal velocity, which is a more sensitive indicator of vortices. Both cyclonic and anticyclonic eddies form in all three currents near the tips of Madagascar and Af- rica (Figs. 6, 7). 4 Isolated anticyclonic vortices in the Southern Hemisphere ␤ The Agulhas region after the onset of instability is drift northwest due to self-advection on the plane, and cyclones similarly drift southwest (e.g., Sutyrin and Flierl 1994). Such mo- shown in Fig. 6. A large anticyclone has pinched off tion is observed in the South Atlantic (Boebel et al. 2003). The from the tip of South Africa and accompanying it is a vortices are prevented from crossing each other in the model smaller cyclone, which forms in the lee of the continent. because of the westward zonal flow.

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FIG. 7. A close-up view of the Madagascar region during the same nonlinear run shown in Fig. 6. The separated zonal currents off the north and south tips of the island are forming vortices. The color scale is Ϯ0.5 m. vortex motion than, say, the height. We calculated the particularly larger. The energy at 300 km, which occurs transform over a range of latitudes and longitudes in near day 140 in the north Madagascar case, reflects a the core of the jet and then averaged the result to ob- large anticyclone that has pinched off the island. Nev- tain a longitudinal spectrum.5 We did this at each time, ertheless, the instability proceeds similarly in the three and contour the result in Fig. 8. The contours for the jets, albeit with consistently larger scales in the Agulhas north Madagascar jet are on the left, those for the south case. jet in the middle, and those for the Agulhas jet on the There is nevertheless a difference in the way the vor- right. The contours are normalized so that they have tices form here. The north Madagascar and Agulhas comparable amplitudes (otherwise the spectra from the jets generate anticyclones soon after separation but the more energetic Agulhas would have the largest ampli- south Madagascar jet has a more meandering appear- tudes). ance. These differences stem from inertia and are thus In all cases, the instabilities appear after roughly 60 affected by coastal orientations and boundary current days. The emerging eddies are roughly 200 km in size in transport. The largest transport is in the Agulhas Cur- the two Madagascar jets and nearer to 300 km in the rent, which carries the entire inflow to the Indian basin. Agulhas jet. The scales remain roughly constant while Its energetic southwesterly separation from the African the eddies intensify, at least over the period shown. coast favors anticyclone formation. The northwestern There are also indications of energy at other scales, coast of Madagascar has a more north–south orienta- tion, causing the model’s northeast Madagascar Cur- rent to flow nearly northward as it detaches. It turns to 5 We used the Morlet wave in the Matlab software package. the west and then south before proceeding westward The scale shown is one-half of the wavelength produced by the and this also favors anticyclone formation. The south- wavelet routine, which yields a reasonable estimate of the scale of the emerging vortices. The meridional velocity is preferable to the eastern coast is instead oriented west-southwest, which SSH because it is a better indicator of the growing instability (␷ is allows the model’s southeast Madagascar Current to small in the unperturbed jet). join smoothly with the westward flow. So, the instability

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FIG. 8. Longitudinal spectra as a function of time, calculated from the wavelet routine in Matlab from the meridional velocities in the core regions of the three jets: (left) north Mada- gascar jet, (middle) south Madagascar jet, and (right) Agulhas jet. The spectra have been normalized individually. proceeds more gradually here. Note that, if the currents 4. Summary and discussion were made to follow the shelf break rather than the coast, the separation details could be altered further. We have considered the wind-driven, barotropic cir- As mentioned above, the spinup period is marked by culation in the southern Indian and Atlantic Oceans, Rossby wave propagation through the domain (Fig. 5). neglecting topography. The Sverdrup streamfunction Additional Rossby waves appear later on in the simu- here has three zonally oriented discontinuities, emanat- lations. These are excited in part by the local variability ing from the northern and southern tips of Madagascar from the zonal jets and also by perturbations that and the southern tip of Africa. An analytical calculation propagate along the boundaries. The waves perturb the suggests that these discontinuities generate westward zonal currents and cause the generation of even larger jets that are barotropically unstable. We confirmed this eddies by introducing larger-scale disturbances on the using a primitive-equation model with a single layer jets. Similar perturbations may occur in the ocean, how- and a flat bottom. The model produced 200–300-km ever, because the Indian Ocean lacks southern and east- scale eddies, of both signs, at all three locations. ern walls and, because the bottom is not flat, its large- The southwest Indian Ocean is stratified and has scale waves are likely to be quite different. It is for this complex bottom topography, so it is not obvious that a reason that we chose to focus on the earlier development. barotropic, flat bottom model is applicable here. Nev- The numerical simulations thus support the conclu- ertheless, there are similarities between the present re- sions from the analytical model: that the wind generates sults and observations. The Northwest Madagascar three zonal currents and these are regions of significant Current does separate from the northern tip of Mada- eddy generation. The principal shortcoming is that the gascar and proceed westward toward Africa, and anti- model’s Agulhas Current exhibits at best a weak ret- cyclonic eddies form in the area and drift southward roflection; there is eastward flow to the south, in the into the Mozambique Channel (e.g., De Ruijter et al. model’s ACC, but only a fraction of the detached Agul- 2002; Ridderinkhof and De Ruijter 2003). As noted, has joins that flow. Perhaps as a result of this difference, several previous authors have suggested that barotropic the model forms Agulhas eddies too frequently (at a instability is the likely cause of the eddy formation here, rate of roughly 15–20 per year). from observations (Quadfasel and Swallow 1986;

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Schott et al. 1988) and from analyses of model energet- Agulhas rings pinch off from the retroflection, and ics (Biastoch and Krauss 1999). So, the present model is modeling studies (e.g., Boudra and Chassignet 1988; in accord with those findings. Biastoch and Krauss 1999; Matano and Beier 2003) sug- The situation south of Madagascar is more contro- gest that baroclinic instability is important in this. This versial. Lutjeharms (1988) suggested the Southeast may, in turn, explain why the formation rate is slower Madagascar Current retroflects south of the island and than observed here if the baroclinic growth rate is proceeds eastward. Others (e.g., Quartly et al. 2006) slower than the barotropic one. maintain that the current actually flows westward but Nevertheless, there are two points worth emphasiz- that anticyclone formation yields a false impression of a ing. First, the present model may help explain the for- retroflection. It is also possible that a portion of the mation of the secondary vortices, particularly the cy- current retroflects, as suggested by Schott and Mc- clonic vortices seen to the west of South Africa (Penven Creary (2001). Nevertheless, the satellite-derived ob- et al. 2001; Boebel et al. 2003; Lutjeharms et al. 2003; servations of De Ruijter et al. (2004) reveal a “dipole Matano and Beier 2003). Second, the model demon- street” of vortices extending from south Madagascar to strates that eddies will form south of Africa even with- Africa, and this closely resembles the situation shown out a retroflection (at odds with Pichevin et al. 1999). in Fig. 7. The numerical simulations of Biastoch and Eddies are therefore an inevitable consequence of the Krauss (1999) exhibited vortex formation along the wind-driven circulation in this geometry. Madagascar coast, before the current even separated. However, our analytical model suggested that the in- Acknowledgments. Thanks are given to Will De stability should be greatest near the island tip, so this is Ruijter, Peter Jan van Leeuwen, and two anonymous also possibly consistent. In addition, we found that the reviewers for comments on the manuscript. The work southern jet can vanish if the zero wind stress curl line was supported by grants from the Norwegian Research shifts north of the island (Fig. 3); therefore, the current Council. may not be present at all times. This may account for REFERENCES some of the disagreement with regard to the observations. Biastoch, A., and W. Krauss, 1999: The role of mesoscale eddies On the other hand, the retroflection of the actual in the source regions of the Agulhas Current. J. Phys. Ocean- Agulhas Current is undisputed. We might have ex- ogr., 29, 2303–2317. pected a retroflection in our numerical model, given the Boebel, O., T. Rossby, J. Lutjeharms, W. Zenk, and C. Barron, results of Dijkstra and De Ruijter (2001), who suggest 2003: Path and variability of the Agulhas return current. that inertia alone can produce a retroflection.6 We Deep-Sea Res. II, 50, 35–56. Boudra, D. B., and W. P. M. De Ruijter, 1986: The wind-driven found, instead, that most of the flow proceeded west- circulation of the South Atlantic-Indian Ocean—II. Experi- ward. A similar result was obtained by Matano (1996), ments using a multi-layer numerical model. Deep-Sea Res., who showed that the southwest orientation of the South 33, 447–482. African coast favors a smoother connection to the zonal ——, and E. P. Chassignet, 1988: Dynamics of Agulhas Retro- flow than does a meridional wall (see also Ou and De flection and ring formation in a numerical model. Part I: The vorticity balance. J. Phys. Oceanogr., 18, 280–303. Ruijter 1986; Chassignet and Boudra 1988; Dijkstra and Byrne, D. A., A. L. Gordon, and W. F. Haxby, 1995: Agulhas De Ruijter 2001). 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