Inertially Induced Connections between Subgyres in the South Indian Ocean

V. Palastanga Institute for Marine and Atmospheric Research, Utrecht, Utrecht, Netherlands

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H. A. Dijkstra Institute for Marine and Atmospheric Research, Utrecht, Utrecht, Netherlands

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W. P. M. de Ruijter Institute for Marine and Atmospheric Research, Utrecht, Utrecht, Netherlands

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Abstract

A barotropic shallow-water model and continuation techniques are used to investigate steady solutions in an idealized South Indian Ocean basin containing Madagascar. 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 Madagascar Current overshoots the island’s southern boundary and connects through a southwestward jet with the current off South Africa.

Corresponding author address: H. A. Dijkstra, Princetonplein 5, 3584 CC, Utrecht, Netherlands. Email: dijkstra@phys.uu.nl

Abstract

A barotropic shallow-water model and continuation techniques are used to investigate steady solutions in an idealized South Indian Ocean basin containing Madagascar. 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 Madagascar Current overshoots the island’s southern boundary and connects through a southwestward jet with the current off South Africa.

Corresponding author address: H. A. Dijkstra, Princetonplein 5, 3584 CC, Utrecht, Netherlands. Email: dijkstra@phys.uu.nl

1. Introduction

The presence of Madagascar in the South Indian Ocean presents unique characteristics to the subtropical gyre circulation. This large-scale island blocks the wind-driven circulation between 12° and 25°S. As a consequence, the South Equatorial Current (SEC) bifurcates around 17°S into the North Madagascar Current (NMC) to the north and the East Madagascar Current (EMC) to the south (Swallow et al. 1988). The fate of the EMC at its termination point is still not fully clear. It either undergoes an eastward retroflection with subsequent eddy shedding (Lutjeharms 1988) or it continues westward as a free jet toward the African coast (Quartly and Srokosz 2004). The main subtropical gyre western boundary current, the Agulhas Current (AC), originates around 27°S along the African coast. Hydrographic data of the Indian Ocean subtropical gyre (integrated over the upper 1000 m) indicate a broad westward flow between 10° and 30°S and a recirculation in the southwestern part of the gyre (Stramma and Lutjeharms 1997).

Recent estimates of the Mozambique Channel transport showed a highly variable flow, with an annual mean transport of 14 Sv (1 Sv ≡ 106 m3 s−1; Ridderinkhof and de Ruijter 2003), while for the EMC, Donohue and Toole (2003) calculated 20 Sv southward. The recirculation, the EMC, and the flow from the Mozambique Channel form the sources of the AC. A recent analysis of climatological data revealed a surface anticyclonic recirculation to the east of Madagascar that is composed of an eastward current in the upper 300 m around 25°S, the South Indian Ocean Countercurrent (SICC) and, between 10° and 20°S, the westward flow of the SEC (Palastanga et al. 2007).

The signature of these currents can be seen in the mean dynamic topography (Fig. 1) of the South Indian Ocean as presented in Rio and Hernandez (2004). The plot suggests that there may be two subgyres that are connected in the region around south Madagascar. While the southwestern recirculation might be related to bottom topography (Stramma and Lutjeharms 1997), the dynamical connection between the subgyres has not been addressed as far as we know. Quick inspection of the structure of the wind stress curl in the South Indian Ocean suggests that the recirculation east of Madagascar is not caused by linear Sverdrup dynamics (Pedlosky et al. 1997), so inertia likely is important for this connection.

Nonlinear effects on the circulation around Madagascar are expected to be important due to western boundary current separation at the island tips and the significant local mesoscale eddy activity (e.g., Schouten et al. 2003). Hydrographic observations in the Mozambique Channel showed a flow dominated by the southward propagation of anticyclonic eddies (de Ruijter et al. 2002), with a frequency of 4 times per year related to the pinching off of anticyclonic eddies from the northern Channel anticyclonic loop current (see, e.g., Fig. 1). Eddies from the Mozambique Channel and from around southern Madagascar have been traced with satellite altimetry migrating south (-westward) into the AC system (Schouten et al. 2002; Quartly and Srokosz 2004; de Ruijter et al. 2004). Ultimately, they may influence the variability of the AC retroflection and/or the formation of Agulhas rings (Schouten et al. 2002; de Ruijter et al. 2004), constituting an important link in the global ocean circulation.

Only a few modeling studies were devoted to investigate the large-scale South Indian Ocean circulation. Using a primitive equation model between 20° and 50°S, Matano et al. (1999) reproduced the AC and the gyre’s southwestern recirculation in a baroclinic experiment, whereas in a barotropic experiment, the mean circulation was constrained to the central Indian Ocean due to the blocking effect of bottom topography. Woodberry et al. (1989) used a 1.5-layer model to simulate the monsoonal changes in the tropical Indian Ocean currents. Because their model has a southern boundary at 25°S, the flows in the Mozambique Channel and of the EMC were not fully analyzed. Other studies have used eddy-resolving numerical models but focused on the influence of Madagascar eddies on the AC system (Biastoch and Krauss 1999; Penven et al. 2006).

The main motivation for this work is to investigate whether time-independent inertial processes can generate a connection between the two subgyres while remaining consistent with the mean transport through the Mozambique Channel. Therefore, we use a barotropic shallow-water model (described in section 2) for the South Indian Ocean, including Madagascar, and determine steady solutions for different degrees of nonlinearity using the wind stress amplitude as the main control parameter. A comparison between the model flows in the steady nonlinear regime with key characteristics of the observed flow in this region is made in section 3. Section 4 offers a summary and discussion of the results.

2. The model

We use the same barotropic shallow-water model as in Dijkstra and de Ruijter (2001a), but here we will ignore bottom topography. The model consists of the shallow-water equations in spherical coordinates ϕ, θ, and z; and it has a single layer with constant density ρ and equilibrium thickness H. The flow is driven at the surface by a wind stress field, τ(ϕ, θ) = τ0(τϕ, τθ), where τ0 is the amplitude (Nm−2) and (τϕ, τθ) provides the spatial pattern. Lateral Laplacian friction, with lateral friction coefficient AH, is the only dissipative mechanism in the model. The model domain covers the South Indian Ocean from 20° to 90°E and from 41° to 5°S, with realistic geometry. In the south, a zonal channel of constant depth is present that extends from the southern wall to 36°S. The channel prevents nonlinearities associated with the return of the western boundary current into the ocean’s interior to dominate the solution for large amplitudes of the wind stress (Dijkstra and de Ruijter 2001a).

The model equations are nondimensionalized using typical scales r0, H, U, r0/U, and τ0 for length, layer depth, velocity, time, and wind stress amplitude, respectively, where r0 is the radius of the earth. The nondimensional equations are then
i1520-0485-39-2-465-e1a
i1520-0485-39-2-465-e1b
i1520-0485-39-2-465-e1c
where (u, υ) are the velocities in the eastward and northward direction, η(ϕ, θ, t) is the free surface elevation, (τϕ, τθ) are the components of the wind stress, and h is the thickness of the water column. Note that because of the flat bottom, changes in h are due only to changes in the sea surface height; that is, h = H + η(ϕ, θ, t).
The nondimensional parameters in the momentum equations are the Rossby number ϵ, the inverse Froude number F, the Ekman number E, and the wind stress coefficient α. Expressions for these parameters are
i1520-0485-39-2-465-e2
where Ω is the angular velocity of the earth. We have also introduced a so-called homotopy parameter α0 to be able to continuously change from no wind (α0 = 0) to realistic wind stress (α0 = 1); as seen below, we therefore will use τm = α0τ0 as the amplitude of the wind stress within the model. On the continental boundaries we specify no-slip conditions, while in the southern channel we specify periodic conditions.

The model equations are discretized on a staggered Arakawa C grid using second-order central differences; the resolution of the model is taken as 20 km (1/5°). A continuation technique based on the pseudoarclength method (Keller 1977) is used to determine steady-state solutions as the control parameter is continuously varied. In this study, the wind stress amplitude in the model is varied by varying α0 from 1 to 5. Steady solutions using the Ekman number E as a control parameter (i.e., varying E one order of magnitude) are also computed. Standard values of all the parameters used in the model are listed in Table 1.

The model has been forced by the momentum flux fields obtained from the National Centers for Environmental Prediction (NCEP) reanalysis data for the period 1948–2003 (Kalnay et al. 1996). The data, which are originally given on a Gaussian grid with approximately 2° horizontal resolution, have been interpolated onto the model’s grid. In addition, the data have been modified over the southern domain to constrain the flow amplitude in the open channel. Because the wind stress in the southern part of the domain was set to a constant amplitude equal to 0.001 Pa, the region of positive curl extends as far as 32°S, while in reality this limit is found around 45°S.

3. Results

We first consider the case of the annual-mean wind stress. The Munk boundary layer thickness is estimated as δM = , which gives ∼36 km along the eastern Madagascar coast, based on the parameters in Table 1. A measure of the nonlinearity is the ratio δI/δM, where δI = UI/β is the inertial boundary layer thickness and UI is a typical maximum interior velocity. For δMδI, the flow is dominated by linear dynamics; when the ratio δI/δM is close to unity, both inertia and friction are important in the boundary layers; and when δIδM, the flow is strongly nonlinear.

For α0 = 1, the barotropic streamfunction (note that the steady depth-averaged flow is divergence free) is plotted in Fig. 2 with contour levels in Sverdrups. It displays a typical anticyclonic/cyclonic gyre circulation south/north of 20°S. The westward interior flow is diverted north and south at the coast of Madagascar, forming island boundary currents that mimic the NMC and EMC. South of the island, the EMC flows straight to the African coast to join the gyre western boundary current (called the Agulhas Current). A recirculation region appears to the east of the AC, with a maximum transport of about 40 Sv. This simulates quite well the subtropical recirculation described by Stramma and Lutjeharms (1997).

The flow in the southern open channel transports ∼10 Sv toward the east. Along the northern wall, stationary Rossby waves are formed at the outflow of the northern western boundary current. The flow in the Mozambique Channel is weak, with a net southward transport of 2.5 Sv. The transports of the EMC and NMC across sections of 100-km width off the eastern Madagascar coast are about 10 Sv. The solution is not very sensitive to the value of E over the range from the standard value E = 1.6 × 10−7 down to E = 5.6 × 10−8. The main qualitative features of the circulation remain the same. The intensity of the southwestern recirculation and the overshoot of the western boundary current around South Africa increase slightly. There is also a slight shift of the recirculation to the north and east with decreasing E.

The steady solution, however, is sensitive to the amplitude of the wind stress. An increase in wind stress happens, for example, during July when the amplitude has a maximum of τ0 = 0.33 Pa. In Fig. 3, we present patterns of the barotropic streamfunction for different values of α0 under a July wind stress pattern, such that τm ranges from 0.33 Pa up to 1.5 Pa; the ratio δI/δM varies from 1 to 3. As can be seen, the extra input of anticyclonic vorticity to the east of Madagascar can generate a highly nonlinear flow around the island. The transports of the different currents are plotted versus τm in Fig. 4 (currents are labeled).

For a realistic wind stress strength (Fig. 3a), the flow field is very similar to that obtained with the annual mean winds (Fig. 2). Due to the slight northward shift of the trades in July, there is a slight northward shift of the subtropical gyre, with the subtropical recirculation located around 30°S in front of the African coast. Interestingly, the ratio between the Mozambique Channel 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 τm 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 τm ∼1 Pa, the transports of the AC at 30°S and across a section off south Madagascar start to decrease (Fig. 4), whereas the 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 region that is completely situated to the east of Madagascar, with an overshooting western boundary current that connects through a southwestward-flowing free jet with the AC flow along South Africa. The relocation of the inertial recirculation modifies the relation between the western boundary current transports: the EMC and Mozambique Channel reach 54 and 38 Sv, respectively, while the AC around 33°S and 200 km off the African coast carries 56 Sv southward. Note that for τm larger than 1 0.3 Pa, all boundary currents seem to achieve a quasi-constant transport.

In the most nonlinear regime (Fig. 3d), the western boundary current along the Mozambique Channel shows maximum southward velocities of 0.7 m s−1 near the channel narrows. These are of the same order as the strong current events (1.0 m s−1 in the upper layer) measured by Ridderinkhof and de Ruijter (2003). The model also shows a northward return current along the channel with velocities up to 0.3 m s−1 in the central part. Velocities near the separation point of the NMC and EMC from the coast are high (∼2 m s−1), while along the free jet toward South Africa maximum velocities of ∼1.5 m s−1 are detected. These are comparable to the speeds of the AC between 27° and 34°S as reported by Pearce and Gründligh (1982), that is, 1.4–1.6 m s−1, with peaks up to 2.6 m s−1. Observed maximum speeds in the EMC are above 1 m s−1 (Nauw et al. 2008).

For the cases of relatively small τm, the western boundary current transports show a (quasi) linear increase with τm, as is expected for the linear problem of the island circulation. In particular, the transport through the Mozambique Channel can be compared with the linear estimate from the Island Rule (Godfrey 1989). The latter provides an analytical estimate of the transport through the channel based on the circulation of the wind stress field along a path connecting the island’s western boundary and the basin’s eastern boundary. In other words, the effect of inertial, frictional, and/or topographic terms on the circulation integral of the momentum equations along such a path is negligible. Based on NCEP data, the Island Rule gives a transport of 3.5 Sv using annual mean winds and of 11 Sv using July monthly means. For amplitudes of the wind stress between 0 and 0.8 Pa, the modeled Mozambique Channel transport lies within 80%–87% of the Island Rule (Fig. 4). The circulation pattern with realistic winds (Fig. 3a) indicates a transport in the channel and EMC of about 10 Sv, while the AC carries 30 Sv southward. If the flow nonlinearity is increased (Fig. 3b), the channel and EMC transport reach 22 Sv, suggesting that this is a pattern for the circulation consistent with observations, that is, this and the quasi-linear case fall in the range of solutions expected from observations.

The Island Rule remains a valid approximation for the Mozambique Channel transport if inertia is further increased: even in the most nonlinear case (Fig. 3d), the transport through the channel is about 70% of the linear estimate. The latter is related to a cancellation among nonlinear terms along the zonal sections to the east of the island. Pedlosky et al. (1997) also found in experiments of time-dependent nonlinear flows that the Island Rule predicts between 80% and 90% of the modeled transports. They argued that nonlinearity led to an increase of the frictional boundary layers, while the net contribution of relative vorticity fluxes to the east of the island vanishes due to the use of nonslip boundary conditions.

4. Summary and discussion

Using a barotropic shallow-water model, we explored the possible connection between the subgyres in the southwestern Indian Ocean (Fig. 1). Within the parameter volume investigated, the model solutions show different circulation regimes according to the amplitude of the wind stress that controls the flow’s nonlinearity. In the quasi-linear regime, the current from Madagascar is directed westward toward the African coast and inertial effects appear concentrated in the southwestern recirculation of the subtropical gyre. Increasing nonlinearity induces a northward shift of the gyre recirculation toward the east of Madagascar, and eventually a large overshoot of the EMC into the open ocean and the lack of the southwestern recirculation.

It is found that such a connection is established in a strongly nonlinear regime while simultaneously being consistent with estimates of the Mozambique Channel transport. The results also suggest that the transport through the Mozambique Channel is largely explained by the input of vorticity by the large-scale wind stress, although in an unsteady state the flow may break up into eddies, as suggested by observations (de Ruijter et al. 2002). In the strongly nonlinear regime, however, the model shows unrealistically high transports in the subtropical gyre, suggesting that other processes must be involved in the development of a recirculation to the east of Madagascar. For instance, time-dependent eddy-mean flow interactions could be crucial for the mean circulation east of Madagascar. The role of eddies in this region is supported by altimetry data that showed westward-propagating Rossby waves along the subtropical band 20°–30°S (Morrow and Birol 1998; Schouten et al. 2002), which, while converging in the region off southeast Madagascar, create a high energy area and may also interact with local instabilities of the SICC. Furthermore, it is speculated that the degree of eddy variability south(east) of Madagascar could modify intermittently the tilt of the western boundary current continuation toward the African coast. This is supported by the preferred southwestward path taken by dipolar vortices that originate in the EMC separation region at large EMC transports (de Ruijter et al. 2004).

Increasing inertial effects considerably affect the behavior 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 reconnect 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 s−1 (Nauw et al. 2008), comparable to those in the AC (1.5 m s−1).

Although some of the characteristics of the highly nonlinear regime, as the overshooting of the western boundary current south of Madagascar and the eastward flow around 25°S, are comparable to the observed large-scale surface flow in the South Indian Ocean (Fig. 1), there are many simplifications of the model that make a comparison with observations difficult. In addition, with the continuation techniques used here, one computes only steady solutions. In the real ocean, time-dependent processes (i.e., eddies generated by the flow instabilities) alter these steady states through rectification. In an idealized configuration of the Agulhas retroflection, Dijkstra and de Ruijter (2001b) found that rectification due to barotropic instabilities modified the degree of retroflection, but overall, the time-mean states were not that different from the steady states. This, however, depends on the degree of instability of the steady state. In the case of Dijkstra and de Ruijter (2001b), there is only one unstable mode; in the present problem, there might be several unstable modes, and an analysis of the rectification of the steady states requires that several transient integrations are performed to study time-mean states as the wind stress strength is changed. It would also be of interest to analyze whether a rectification of the Mozambique Channel flow could drive a nonlinear transport and to compare the unstable modes with the observed variability with typical frequencies of 7 times per year (Quadfasel and Swallow 1986), and 4 to 5 times per year (Schouten et al. 2003).

Another simplification of the present model is the lack of bottom topography. Still, the model flow forced with realistic winds compares well with simulations of the Agulhas system flow from GCMs (e.g., Biastoch and Krauss 1999). Although the Agulhas retroflection and the location of the recirculation in reality are probably influenced by the bathymetry (Matano et al. 1999), the connection of the flow from the east and south of Madagascar with the main western boundary current is well constrained in this simplified model. Snapshots from the high-resolution (0.03°) Naval Layer Ocean Model (NLOM) indicate that the flow south of Madagascar (EMC) varies intermittently in speed and direction, from westward to southwestward sometimes terminating in the open ocean (Shriver et al. 2007).

With all its limitations, however, the model results here indicate an inertial behavior of the southeast Madagascar jet that may help to interpret results from more sophisticated models of the circulation in the southwest Indian Ocean. In this way, they can help to improve our understanding of the processes controlling the interocean exchange between the Indian Ocean and the Atlantic.

Acknowledgments

We thank Arjen Terwisscha van Scheltinga (IMAU) for making the fully implicit multilayer shallow-water model used in this study and his help in using it, and Peter Jan van Leeuwen (IMAU) for useful discussions on the results.

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Fig. 1.
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 12° and 40°S, with two separate recirculations: one to the east of Madagascar and another east of South Africa.

Citation: Journal of Physical Oceanography 39, 2; 10.1175/2008JPO3872.1

Fig. 2.
Fig. 2.

Barotropic streamfunction for the parameters as in Table 1 and α0 = 1. The model was forced by annual mean winds (with maximum amplitude equal to 0.16 Pa). The contour interval is 5 Sv.

Citation: Journal of Physical Oceanography 39, 2; 10.1175/2008JPO3872.1

Fig. 3.
Fig. 3.

Barotropic streamfunction for the case where the wind stress forcing has the spatial structure of July winds and amplitudes τm 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.

Citation: Journal of Physical Oceanography 39, 2; 10.1175/2008JPO3872.1

Fig. 4.
Fig. 4.

Transport of the NMC (gray dashed), the EMC (black dashed), the flow through the Mozambique Channel (solid gray), the flow around South Madagascar (black dotted line), and the AC flow (gray dotted) as a function of July wind stress of varying amplitude. Also shown is the transport predicted by the linear Island Rule (solid black). For the western boundary currents along the eastern coast of Madagascar sections of 100-km width were considered, while the transports across the SMC and AC were computed along sections of 200-km width.

Citation: Journal of Physical Oceanography 39, 2; 10.1175/2008JPO3872.1

Table 1.

Standard values of parameters used in the numerical calculations. In the value of α, we have taken α0 = 1.

Table 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 12° and 40°S, with two separate recirculations: one to the east of Madagascar and another east of South Africa.

  • Fig. 2.

    Barotropic streamfunction for the parameters as in Table 1 and α0 = 1. The model was forced by annual mean winds (with maximum amplitude equal to 0.16 Pa). The contour interval is 5 Sv.

  • Fig. 3.

    Barotropic streamfunction for the case where the wind stress forcing has the spatial structure of July winds and amplitudes τm 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.

  • Fig. 4.

    Transport of the NMC (gray dashed), the EMC (black dashed), the flow through the Mozambique Channel (solid gray), the flow around South Madagascar (black dotted line), and the AC flow (gray dotted) as a function of July wind stress of varying amplitude. Also shown is the transport predicted by the linear Island Rule (solid black). For the western boundary currents along the eastern coast of Madagascar sections of 100-km width were considered, while the transports across the SMC and AC were computed along sections of 200-km width.

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