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Inertially Induced Connections between Subgyres in the South

V. PALASTANGA,H.A.DIJKSTRA, AND W. P. M. DE RUIJTER Institute for Marine and Atmospheric Research, Utrecht, Utrecht, Netherlands

(Manuscript received 3 July 2007, in final form 18 August 2008)

ABSTRACT

A barotropic shallow-water model and continuation techniques are used to investigate steady solutions in an idealized South Indian Ocean basin containing . The aim is to study the role of inertia in a possible connection between two subgyres in the South Indian Ocean. By increasing inertial effects in the model, two different circulation regimes are found. In the weakly nonlinear regime, the subtropical gyre presents a recirculation cell in the southwestern basin, with two boundary currents flowing westward from the southern and northern tips of Madagascar toward Africa. In the highly nonlinear regime, the inertial recirculation of the subtropical gyre is found to the east of Madagascar, while the East overshoots the island’s southern boundary and connects through a southwestward jet with the current off .

1. Introduction (2003) calculated 20 Sv southward. The recirculation, the EMC, and the flow from the Channel form The presence of Madagascar in the South Indian the sources of the AC. A recent analysis of climatological Ocean presents unique characteristics to the subtropical data revealed a surface anticyclonic recirculation to the gyre circulation. This large-scale island blocks the wind- east of Madagascar that is composed of an eastward cur- driven circulation between 128 and 258S. As a conse- rent in the upper 300 m around 258S, the South Indian quence, the (SEC) bifurcates Ocean Countercurrent (SICC) and, between 108 and 208S, around 178S into the (NMC) the westward flow of the SEC (Palastanga et al. 2007). to the north and the (EMC) The signature of these currents can be seen in the to the south (Swallow et al. 1988). The fate of the EMC mean dynamic topography (Fig. 1) of the South Indian at its termination point is still not fully clear. It either Ocean as presented in Rio and Hernandez (2004). The undergoes an eastward retroflection with subsequent plot suggests that there may be two subgyres that are shedding (Lutjeharms 1988) or it continues west- connected in the region around south Madagascar. ward as a free jet toward the African coast (Quartly While the southwestern recirculation might be related to and Srokosz 2004). The main subtropical gyre western bottom topography (Stramma and Lutjeharms 1997), the , the (AC), originates dynamical connection between the subgyres has not been around 278S along the African coast. Hydrographic data addressed as far as we know. Quick inspection of the of the Indian Ocean subtropical gyre (integrated over the structure of the wind stress curl in the South Indian Ocean upper 1000 m) indicate a broad westward flow between suggests that the recirculation east of Madagascar is not 108 and 308S and a recirculation in the southwestern part caused by linear Sverdrup dynamics (Pedlosky et al. of the gyre (Stramma and Lutjeharms 1997). 1997), so inertia likely is important for this connection. Recent estimates of the trans- Nonlinear effects on the circulation around Madagascar port showed a highly variable flow, with an annual mean are expected to be important due to western bound- transportof14Sv(1Sv[ 106 m3 s21; Ridderinkhof and de ary current separation at the island tips and the signifi- Ruijter 2003), while for the EMC, Donohue and Toole cant local mesoscale eddy activity (e.g., Schouten et al. 2003). Hydrographic observations in the Mozambique Corresponding author address: H. A. Dijkstra, Princetonplein 5, Channel showed a flow dominated by the southward 3584 CC, Utrecht, Netherlands. propagation of anticyclonic eddies (de Ruijter et al. E-mail: [email protected] 2002), with a frequency of 4 times per year related to the

DOI: 10.1175/2008JPO3872.1

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FIG. 1. Mean dynamic topography of the South Indian Ocean computed from hydrographic data, surface drifters, and altimetry (Rio and Hernandez 2004). Units in m2 s2. It shows the anticyclonic subtropical gyre circulation at the surface between 128 and 408S, with two separate recirculations: one to the east of Madagascar and another east of South Africa. pinching off of anticyclonic eddies from the northern the Mozambique Channel. Therefore, we use a baro- Channel anticyclonic (see, e.g., Fig. 1). tropic shallow-water model (described in section 2) for Eddies from the Mozambique Channel and from the South Indian Ocean, including Madagascar, and around southern Madagascar have been traced with determine steady solutions for different degrees of satellite altimetry migrating south (-westward) into the nonlinearity using the wind stress amplitude as the main AC system (Schouten et al. 2002; Quartly and Srokosz control parameter. A comparison between the model 2004; de Ruijter et al. 2004). Ultimately, they may in- flows in the steady nonlinear regime with key charac- fluence the variability of the AC retroflection and/or the teristics of the observed flow in this region is made in formation of Agulhas rings (Schouten et al. 2002; de section 3. Section 4 offers a summary and discussion of Ruijter et al. 2004), constituting an important link in the the results. global ocean circulation. Only a few modeling studies were devoted to inves- 2. The model tigate the large-scale South Indian Ocean circulation. We use the same barotropic shallow-water model as Using a primitive equation model between 208 and 508S, in Dijkstra and de Ruijter (2001a), but here we will ig- Matano et al. (1999) reproduced the AC and the gyre’s nore bottom topography. The model consists of the southwestern recirculation in a baroclinic experiment, shallow-water equations in spherical coordinates f, u, whereas in a barotropic experiment, the mean circula- and z; and it has a single layer with constant density r tion was constrained to the central Indian Ocean due to and equilibrium thickness H. The flow is driven at the the blocking effect of bottom topography. Woodberry f u surface by a wind stress field, tðf; uÞ 5 t0ðt ; t Þ; where et al. (1989) used a 1.5-layer model to simulate the 22 f u t0 is the amplitude (Nm ) and (t , t ) provides the monsoonal changes in the tropical Indian Ocean cur- spatial pattern. Lateral Laplacian friction, with lateral rents. Because their model has a southern boundary at friction coefficient AH, is the only dissipative mecha- 258S, the flows in the Mozambique Channel and of the nism in the model. The model domain covers the South EMC were not fully analyzed. Other studies have used Indian Ocean from 208 to 908E and from 418 to 58S, with eddy-resolving numerical models but focused on the realistic geometry. In the south, a zonal channel of influence of Madagascar eddies on the AC system constant depth is present that extends from the southern (Biastoch and Krauss 1999; Penven et al. 2006). wall to 368S. The channel prevents nonlinearities asso- The main motivation for this work is to investigate ciated with the return of the western boundary current whether time-independent inertial processes can gen- into the ocean’s interior to dominate the solution for erate a connection between the two subgyres while large amplitudes of the wind stress (Dijkstra and de remaining consistent with the mean transport through Ruijter 2001a).

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The model equations are nondimensionalized using TABLE 1. Standard values of parameters used in the numerical calculations. In the value of a, we have taken a 5 1. typical scales r0, H, U, r0/U, and t0 for length, layer 0 depth, velocity, time, and wind stress amplitude, re- 24 21 6 2V51.46 3 10 (s ) r0 5 6.37 3 10 (m) 3 23 2 spectively, where r0 is the radius of the earth. The r0 5 1.0 3 10 (kg m ) H 5 5.0 3 10 (m) nondimensional equations are then U 5 1.0 3 1021 (m s21) G 5 9.8 (m s22) 3 2 21 21 AH 5 1.0 3 10 (m s ) t0 5 1.0 3 10 (Pa) E 5 1.0 3 1024 () E 5 1.6 3 1027 () ›u u ›u ›u 22 5 e 1 1 y uy tan u y sin u a 5 2.2 3 10 () F 5 5.9 3 10 () ›t cos u ›f ›u eF ›h u 2 sin u ›y tf 5 1 E =2u 1 a ; is varied by varying a from 1 to 5. Steady solutions cos u ›f cos2 u cos2 u ›f h 0 using the Ekman number E as a control parameter (i.e., ð1aÞ varying E one order of magnitude) are also computed. Standard values of all the parameters used in the model ›y u ›y ›y 2 e 1 1 y 1 u tan u 1 u sin u are listed in Table 1. ›t cos u ›f ›u The model has been forced by the momentum flux ›h y 2 sin u ›u tu 5 e 1 =2 1 1 a ; fields obtained from the National Centers for Environ- F E v 2 2 ›u cos u cos u ›f h mental Prediction (NCEP) reanalysis data for the pe- ð1bÞ riod 1948–2003 (Kalnay et al. 1996). The data, which are originally given on a Gaussian grid with approximately ›h 1 ›ðhuÞ ›ðhyÞ cos u 1 1 5 0; ð1cÞ 28 horizontal resolution, have been interpolated onto ›t cos u ›f ›u the model’s grid. In addition, the data have been mod- where (u, y) are the velocities in the eastward and ified over the southern domain to constrain the flow northward direction, h(f, u, t) is the free surface ele- amplitude in the open channel. Because the wind stress vation, (tf, tu) are the components of the wind stress, in the southern part of the domain was set to a constant and h is the thickness of the water column. Note that amplitude equal to 0.001 Pa, the region of positive curl 8 because of the flat bottom, changes in h are due only extends as far as 32 S, while in reality this limit is found to changes in the sea surface height; that is, h 5 H 1 around 458S. h(f, u, t). The nondimensional parameters in the momentum 3. Results equations are the Rossby number e, the inverse Froude We first consider the case of the annual-mean wind number F, the Ekman number E, and the wind stress stress. The Munk boundary layer thickness is estimated 1 a 3 coefficient . Expressions for these parameters are as dM 5 ðAH=bÞ ; which gives ;36 km along the eastern Madagascar coast, based on the parameters in Table 1. U gH AH a0t0 d d e5 ; 5 ; 5 ; a 5 ; A measurepffiffiffiffiffiffiffiffiffiffiffiffi of the nonlinearity is the ratio I/ M, where F 2 E 2 2Vr0 U 2Vr0 2VrHU dI 5 UI =b is the inertial boundary layer thickness ð2Þ and UI is a typical maximum interior velocity. For dM dI, the flow is dominated by linear dynamics; when the where V is the angular velocity of the earth. We have ratio dI/dM is close to unity, both inertia and friction are also introduced a so-called homotopy parameter a0 to important in the boundary layers; and when dI dM, be able to continuously change from no wind (a0 5 0) to the flow is strongly nonlinear. realistic wind stress (a0 5 1); as seen below, we there- For a0 5 1, the barotropic streamfunction (note that fore will use tm 5 a0t0 as the amplitude of the wind the steady depth-averaged flow is divergence free) is stress within the model. On the continental boundaries plotted in Fig. 2 with contour levels in Sverdrups. It we specify no-slip conditions, while in the southern displays a typical anticyclonic/cyclonic gyre circulation channel we specify periodic conditions. south/north of 208S. The westward interior flow is di- The model equations are discretized on a staggered verted north and south at the coast of Madagascar, Arakawa C grid using second-order central differences; forming island boundary currents that mimic the NMC the resolution of the model is taken as 20 km (1/58). A and EMC. South of the island, the EMC flows straight to continuation technique based on the pseudoarclength the African coast to join the gyre western boundary method (Keller 1977) is used to determine steady-state current (called the Agulhas Current). A recirculation solutions as the control parameter is continuously var- region appears to the east of the AC, with a maximum ied. In this study, the wind stress amplitude in the model transport of about 40 Sv. This simulates quite well the

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and EMC transport has changed to ;1, so they both exert an equal contribution to the AC flow (Fig. 4). The transport of the western boundary currents increases

linearly with tm up to a wind stress amplitude of ;0.8 Pa, whereas for winds larger than ;0.8 Pa, the channel transport starts to diverge from the linear estimation. At that point, a southwestward tilt in the free jet from south Madagascar to Africa starts to be seen (Fig. 3b). The southwestward tilt of the flow from south Madagascar increases with increasing winds, as well as the intensity of the recirculation southeast of the island, which is

expected to increase the EMC transport. For tm ;1 Pa, the transports of the AC at 308S and across a section off FIG. 2. Barotropic streamfunction for the parameters as in Table south Madagascar start to decrease (Fig. 4), whereas the 1anda0 5 1. The model was forced by annual mean winds (with maximum amplitude equal to 0.16 Pa). The contour interval is 5 Sv. inertial recirculation moves farther east into the basin (Fig. 3c). Finally, for winds 5 times larger than the real value, the flow pattern (Fig. 3d) shows a recirculation subtropical recirculation described by Stramma and region that is completely situated to the east of Mada- Lutjeharms (1997). gascar, with an overshooting western boundary current The flow in the southern open channel transports ;10 that connects through a southwestward-flowing free jet Sv toward the east. Along the northern wall, stationary with the AC flow along South Africa. The relocation of Rossby waves are formed at the outflow of the northern the inertial recirculation modifies the relation between western boundary current. The flow in the Mozambique the western boundary current transports: the EMC and Channel is weak, with a net southward transport of 2.5 Mozambique Channel reach 54 and 38 Sv, respectively, Sv. The transports of the EMC and NMC across sections while the AC around 338S and 200 km off the African of 100-km width off the eastern Madagascar coast are coast carries 56 Sv southward. Note that for tm larger about 10 Sv. The solution is not very sensitive to the than 1 0.3 Pa, all boundary currents seem to achieve a value of E over the range from the standard value E 5 quasi-constant transport. 1.6 3 1027 down to E 5 5.6 3 1028. The main qualitative In the most nonlinear regime (Fig. 3d), the western features of the circulation remain the same. The intensity boundary current along the Mozambique Channel of the southwestern recirculation and the overshoot of shows maximum southward velocities of 0.7 m s21 near the western boundary current around South Africa in- the channel narrows. These are of the same order as the crease slightly. There is also a slight shift of the re- strong current events (1.0 m s21 in the upper layer) circulation to the north and east with decreasing E. measured by Ridderinkhof and de Ruijter (2003). The The steady solution, however, is sensitive to the am- model also shows a northward return current along the plitude of the wind stress. An increase in wind stress channel with velocities up to 0.3 m s21 in the central happens, for example, during July when the amplitude part. Velocities near the separation point of the NMC 21 has a maximum of t0 5 0.33 Pa. In Fig. 3, we present and EMC from the coast are high (;2ms ), while patterns of the barotropic streamfunction for different along the free jet toward South Africa maximum ve- 21 values of a0 under a July wind stress pattern, such that locities of ;1.5 m s are detected. These are compa- tm ranges from 0.33 Pa up to 1.5 Pa; the ratio dI/dM rable to the speeds of the AC between 278 and 348Sas varies from 1 to 3. As can be seen, the extra input of reported by Pearce and Gru¨ ndligh (1982), that is, 1.4– anticyclonic vorticity to the east of Madagascar can 1.6 m s21, with peaks up to 2.6 m s21. Observed maxi- generate a highly nonlinear flow around the island. The mum speeds in the EMC are above 1 m s21 (Nauw et al. transports of the different currents are plotted versus tm 2008). in Fig. 4 (currents are labeled). For the cases of relatively small tm, the western For a realistic wind stress strength (Fig. 3a), the flow boundary current transports show a (quasi) linear in-

field is very similar to that obtained with the annual crease with tm, as is expected for the linear problem mean winds (Fig. 2). Due to the slight northward shift of of the island circulation. In particular, the transport the trades in July, there is a slight northward shift of the through the Mozambique Channel can be compared subtropical gyre, with the subtropical recirculation lo- with the linear estimate from the Island Rule (Godfrey cated around 308S in front of the African coast. Inter- 1989). The latter provides an analytical estimate of the estingly, the ratio between the Mozambique Channel transport through the channel based on the circulation

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FIG. 3. Barotropic streamfunction for the case where the wind stress forcing has the spatial structure of July winds and amplitudes tm equal to (a) 0.33 Pa, which is the maximum amplitude of the observed wind stress; (b) 0.8 Pa; (c) 1 Pa; and (d) 1.5 Pa. Contours every 10, 20, 25, and 35 units, respectively. Units in Sv. of the wind stress field along a path connecting the is- time-dependent nonlinear flows that the Island Rule pre- land’s western boundary and the basin’s eastern bound- dicts between 80% and 90% of the modeled transports. ary. In other words, the effect of inertial, frictional, and/ They argued that nonlinearity led to an increase of the or topographic terms on the circulation integral of the frictional boundary layers, while the net contribution of momentum equations along such a path is negligible. relative vorticity fluxes to the east of the island vanishes Based on NCEP data, the Island Rule gives a transport due to the use of nonslip boundary conditions. of 3.5 Sv using annual mean winds and of 11 Sv using July monthly means. For amplitudes of the wind stress 4. Summary and discussion between 0 and 0.8 Pa, the modeled Mozambique Channel transport lies within 80%–87% of the Island Using a barotropic shallow-water model, we explored Rule (Fig. 4). The circulation pattern with realistic the possible connection between the subgyres in the winds (Fig. 3a) indicates a transport in the channel and southwestern Indian Ocean (Fig. 1). Within the pa- EMC of about 10 Sv, while the AC carries 30 Sv rameter volume investigated, the model solutions show southward. If the flow nonlinearity is increased (Fig. 3b), different circulation regimes according to the amplitude the channel and EMC transport reach 22 Sv, suggesting of the wind stress that controls the flow’s nonlinearity. that this is a pattern for the circulation consistent with In the quasi-linear regime, the current from Madagascar observations, that is, this and the quasi-linear case fall in is directed westward toward the African coast and inertial the range of solutions expected from observations. effects appear concentrated in the southwestern re- The Island Rule remains a valid approximation for circulation of the subtropical gyre. Increasing nonlinearity the Mozambique Channel transport if inertia is further induces a northward shift of the gyre recirculation to- increased: even in the most nonlinear case (Fig. 3d), the ward the east of Madagascar, and eventually a large transport through the channel is about 70% of the linear overshoot of the EMC into the open ocean and the lack estimate. The latter is related to a cancellation among of the southwestern recirculation. nonlinear terms along the zonal sections to the east of the It is found that such a connection is established in a island. Pedlosky et al. (1997) also found in experiments of strongly nonlinear regime while simultaneously being

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dipolar vortices that originate in the EMC separation region at large EMC transports (de Ruijter et al. 2004). Increasing inertial effects considerably affect the be- havior of the EMC-free jet and the intensity of the recirculation to the east of this jet (cf. Fig. 3d). The nonlinear behavior of the EMC around south Madagascar is similar to the Agulhas Current inertial retroflection regime found in a small basin with high resolution and low Ekman number by Dijkstra and de Ruijter (2001a). In that configuration, the inertial overshoot bridges the gap between the western boundary current and the line of zero wind stress curl from where the flow can re- connect with the eastward interior. The results here suggest that an inertial regime south of Madagascar is possible if the winds were about 2 times larger than their real amplitude. The necessary degree of nonlinearity could also be reached for lower Ekman number, that is, one order of magnitude smaller. The observed speeds in the separation region of the EMC are around 1 m s21 (Nauw et al. 2008), comparable to those in the AC FIG. 4. Transport of the NMC (gray dashed), the EMC (black 21 dashed), the flow through the Mozambique Channel (solid gray), (1.5 m s ). the flow around South Madagascar (black dotted line), and the AC Although some of the characteristics of the highly flow (gray dotted) as a function of July wind stress of varying nonlinear regime, as the overshooting of the western amplitude. Also shown is the transport predicted by the linear boundary current south of Madagascar and the east- Island Rule (solid black). For the western boundary currents along ward flow around 258S, are comparable to the observed the eastern coast of Madagascar sections of 100-km width were considered, while the transports across the SMC and AC were large-scale surface flow in the South Indian Ocean (Fig. computed along sections of 200-km width. 1), there are many simplifications of the model that make a comparison with observations difficult. In ad- dition, with the continuation techniques used here, one consistent with estimates of the Mozambique Channel computes only steady solutions. In the real ocean, time- transport. The results also suggest that the transport dependent processes (i.e., eddies generated by the flow through the Mozambique Channel is largely explained instabilities) alter these steady states through rectifica- by the input of vorticity by the large-scale wind stress, tion. In an idealized configuration of the Agulhas ret- although in an unsteady state the flow may break up into roflection, Dijkstra and de Ruijter (2001b) found that eddies, as suggested by observations (de Ruijter et al. rectification due to barotropic instabilities modified the 2002). In the strongly nonlinear regime, however, the degree of retroflection, but overall, the time-mean model shows unrealistically high transports in the sub- states were not that different from the steady states. tropical gyre, suggesting that other processes must be This, however, depends on the degree of instability of involved in the development of a recirculation to the the steady state. In the case of Dijkstra and de Ruijter east of Madagascar. For instance, time-dependent eddy- (2001b), there is only one unstable mode; in the present mean flow interactions could be crucial for the mean problem, there might be several unstable modes, and an circulation east of Madagascar. The role of eddies in analysis of the rectification of the steady states requires this region is supported by altimetry data that showed that several transient integrations are performed to westward-propagating Rossby waves along the subtrop- study time-mean states as the wind stress strength is ical band 208–308S (Morrow and Birol 1998; Schouten changed. It would also be of interest to analyze whether et al. 2002), which, while converging in the region off a rectification of the Mozambique Channel flow could southeast Madagascar, create a high energy area and drive a nonlinear transport and to compare the unsta- may also interact with local instabilities of the SICC. ble modes with the observed variability with typical Furthermore, it is speculated that the degree of eddy frequencies of 7 times per year (Quadfasel and Swallow variability south(east) of Madagascar could modify in- 1986), and 4 to 5 times per year (Schouten et al. 2003). termittently the tilt of the western boundary current Another simplification of the present model is the continuation toward the African coast. This is sup- lack of bottom topography. Still, the model flow forced ported by the preferred southwestward path taken by with realistic winds compares well with simulations of

Unauthenticated | Downloaded 10/01/21 01:27 PM UTC FEBRUARY 2009 N O T E S A N D C O R R E S P O N D E N C E 471 the Agulhas system flow from GCMs (e.g., Biastoch and Keller, H. B., 1977: Numerical solution to bifurcation and non- Krauss 1999). Although the Agulhas retroflection and linear eigenvalue problems. Applications of Bifurcation The- the location of the recirculation in reality are probably ory, P. H. Rabinowitz, Ed., Academic Press, 359–384. Lutjeharms, J. R. E., 1988: Remote sensing corroboration of the influenced by the bathymetry (Matano et al. 1999), retroflection of the East Madagascar current. Deep-Sea Res., the connection of the flow from the east and south of 35, 2045–2050. Madagascar with the main western boundary current is Matano, R. P., C. G. Simionato, and P. T. Strub, 1999: Modeling well constrained in this simplified model. Snapshots the wind-driven variability of the South Indian Ocean. J. 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