2940 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 37 NOTES AND CORRESPONDENCE On Sverdrup Discontinuities and Vortices in the Southwest Indian Ocean 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 Agulhas Current 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 Atlantic Ocean, 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 Unauthenticated | Downloaded 09/28/21 01:12 PM UTC JPO3154 DECEMBER 2007 NOTES AND CORRESPONDENCE 2941 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 boundary current 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- Unauthenticated | Downloaded 09/28/21 01:12 PM UTC 2942 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 37 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).