Research papers

The roles of vertical shear and topography on the eddy formation nearthe site of origin of the Brazil Current

R.G. Soutelino a,b,n, A. Gangopadhyay b, I.C.A. da Silveira a

a Departamento de Oceanografia Física, Química e Geológica do Instituto Oceanográfico, Universidade de São Paulo - IO-USP. Praça do Oceanográfico, 191,Cidade Universitária,São Paulo, SP, Brazilb School for Marine Science and Technology, University of Massachusetts at Dartmouth - SMAST-UMassD. 200 Mill Road, Suite 325, Fairhaven, MA, USA

a r t i c l e i n f o

Available online 23 October 2013

Keywords:Brazil CurrentMesoscale activityAbrolhos bankNumerical modeling

a b s t r a c t

The site of origin of the Brazil Current (BC) is currently one of the less explored aspects of regionalcirculation and mesoscale activity in the west side of the South Atlantic Subtropical gyre. The few studiesthat are available, based either on in situ data or on numerical modeling, seems to agree that the region ischaracterized by relatively weak baroclinic flow, with substantial mesoscale activity, which is quitedifferent from other western boundary current systems (e.g. Florida Current, in the North Atlantic). Wepresent numerical simulations that show that the main realistic mesoscale features in the eddy-richvicinities of the BC site of origin can be successfully modeled through the dynamical interaction betweenparameterized versions of two opposing mean western boundary currents (BC and North BrazilUndercurrent—NBUC) and local topography, with no influence of remote dynamics or atmosphericforcing. Large BC-related anticyclones observed in previous work were reproduced and recurrentlyformed during the model run. Two additional sensitivity experiments were performed. When NBUC isremoved from the physical setting, the BC interaction with topography is not sufficient to generate eddiessimilar to observations. When an idealized flat-bottom and a physiographic configuration with noAbrolhos and Royal Charlotte Banks are considered, the BC–NBUC interaction is also not capable ofdeveloping realistic mesoscale structures. Our geophysical instability analyses suggest that BC–NBUCvertical shear is promoting baroclinic energy fluxes from the mean flow to the perturbations, resulting ineddy formation and growth in the region.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

The Brazil Current System is a vertically heterogeneous com-posite of layered set of western boundary currents (WBC) alongthe western periphery of the South Atlantic Subtropical Gyre. Thesurface layer, generally called the Brazil Current (BC), follows thecontinental shelf along eastern and southern Brazil. It's pathpasses over the continental shelf and slopes of several majorbasins – the Espírito Santo, Campos and Santos Basins – where thesearch for recoverable hydrocarbons is concentrated (Fig. 1).

The vertical structure of the BC is unique among subtropicalwestern boundary currents, in that it gets modified as the currentflows southward (Stramma and England, 1999; Silveira et al.,2004). It is generally thought that between its site of origin

(151S) and 201S the BC is only about 200 m deep and transportsonly Tropical Water (TW). South of 201S, where the pycnocline-level South Atlantic Central Water (SACW) feeds the BC, it reachesdepths of 400–500 m. At latitudes further to the south of 281S,where Antarctic Intermediate Water (AAIW) is transported by theBC, the vertical extension of the current is about 1200 m (Böebelet al., 1999; Schmid et al., 2000) (Fig. 1).

The intricate pattern of bifurcations of the currents in thenorthern limb of the subtropical South Atlantic gyre is sketched inFig. 1. The thickening process that the BC goes through as it flowspoleward is apparent. Also evident is the fact that south of 301S,the BC and Deep Western Boundary Current (DWBC), whichtransports North Atlantic Deep Water (NADW), merge, and a watercolumn of more than 3000 m flows towards the confluence regionwith the Malvinas Current (Zemba, 1991).

The annual climatological mean latitudinal position for thenear-surface South Equatorial Current Bifurcation (BiSEC) isbetween 14.51S and 161S; recognized as the site of origin of theBC (Stramma and England, 1999; Rodrigues et al., 2007). North ofthe AAIW flow bifurcation (281S), an Intermediate WesternBoundary Current (IWBC) opposing the BC direction is set up.

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Continental Shelf Research

0278-4343/$ - see front matter & 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.csr.2013.10.001

n Corresponding author at: Departamento de Oceanografia Física, Química eGeológica do Instituto Oceanográfico, Universidade de São Paulo - IO-USP. Praça doOceanográfico, 191, Cidade Universitária, São Paulo, SP, Brazil.Tel.: þ55 2226229069.

E-mail addresses: rsoutelino@gmail.com, rsoutelino@ieapm.mar.mil.br,rsoutelino@usp.br (R.G. Soutelino).

Continental Shelf Research 70 (2013) 46–60

The Vitória-Trindade Ridge (VTR), a quasi-zonal seamount chain at211S, marks the latitude of bifurcation of the westward SACW flow(Stramma and England, 1999). Therefore, north of this latitude, theSACW flows north, adding transport to the IWBC and starting aflow which becomes the North Brazil Undercurrent (NBUC) northof the SEC bifurcation. The NBUC vertical extension is of about1200 m (Silveira et al., 1994; Stramma et al., 1995).

The climatological description of the southward BC near its siteof origin is a weak, shallow flow transporting largely TropicalWater (TW) southward. Peterson and Stramma (1991) proposedan explanation for the BC low-volume transport (of about 4 Sv;1 Sv¼106 m3 s�1), namely, that the bulk of the impinging south-ern SEC branch enters the NBUC and not the BC.

There are few studies about the BC organization and mesoscaleactivity within the 141S–201S latitude range. Miranda and Castro(1981) used a quasi-synoptic hydrographic section at 191S todescribe the BC, employing the classical geostrophic method(relative to an average reference depth of 500 m). Maximumvelocities of 0.72 m s�1 were estimated at the surface.

Stramma et al. (1990) also computed quasi-synoptic geos-trophic velocity distributions, in this case from several historicalhydrographic transects off the eastern Brazilian coast between 71Sand 201S. A section sampled in austral summer (February–March)revealed a southward-flowing BC. The authors also stated that theBC does not seem to strengthen appreciably from its site of originto 201S. They also constructed a horizontal pattern for the BC siteof origin, with the only feeding source being the bifurcated SEC.A large cyclonic feature extending from 141S to nearly 201S andcentered at 341W was presented, and apparently is not connectedto the BC.

Regarding mesoscale activity and eddy features present in thisarea, the first study, based on modeling efforts, was carried byCampos (2006). The authors simulated an equatorward propaga-tion of a cyclonic eddy feature known by the Vitória Eddy (VE). TheVE was first described by Schmid et al. (1995) through multiplesources of observations at the lee of Abrolhos Bank (AB) (seeFig. 2), and reported to slowly translate northeastward. Campos(2006) modeled VE translational behavior described by Schmidet al. (1995) and noted an additional mode, where the translation

continues towards the equator, crossing the Vitória-Trindade Ridge(VTR). More recently, Arruda et al. (in press) confirmed thistranslation mode through a series of satellite-derived sea surfaceheight (SSH) maps and recent dated data-assimilative numericalexperiments. Both authors discussed that the NBUC and/or inter-action with other vortical feature may have a role on theadvection of VE.

Observation-based patterns within this region were recentlydescribed by Soutelino et al. (2011), who analyzed three synopticVM-ADCP surveys. They reported the near-surface flow to be weakand dominated by eddies between 101 and 201S. Emphasis werebrought to three persistent large anticyclonic eddies, also repro-duced by the OCCAM eddy-resolving OGCM (Webb, 2000).Soutelino et al. (2011) speculated that the eddies are either

Fig. 1. 3-D depiction of the complexity of water masses coming from different sources (which are also part of the meridional overturning circulation) to form the WBCs offthe coast of Brazil.

Fig. 2. Bathymetry at the BC formation region, showing the VTR, RCB, AB and otherseamounts. Source: ETOPO.

R.G. Soutelino et al. / Continental Shelf Research 70 (2013) 46–60 47

recurrent or permanent, based on their presence in annuallyaveraged OGCM fields.

The anticyclonic eddy structures south of 151S may be relatedto the complex bathymetry of the continental margin (Fig. 2). Thenorthernmost anticyclone is located off Ilhéus (15.51S), the other islocated north of the Royal Charlotte Bank (RCB) in the vicinity ofthe Ilhéus Bight, and is centered at 171S in-between the RoyalCharlotte and Abrolhos Banks. The southernmost anticyclone islocated offshore the Abrolhos Bank (AB) and limited to the southby the presence of the VTR (Soutelino et al., 2011). The authorsspeculated that topographic influence on the BC meanders may besimilar to that which forms non-propagating meanders of theNorth Atlantic Current east of the Grand Banks (Clarke et al., 1980),where conservation of potential vorticity plays a crucial role.

As it is known, the BC flow is characterized by strong verticalshear with its immediate adjacent western boundary current(NBUC) of Southeast Brazil (201–251S). Silveira et al. (2008) hasshown that the interaction within the baroclinically unstableBC-IWBC system further south (around 231S) leads to the formationof mesoscale eddies. So, we believe that the existence of this uniquewestern boundary undercurrent (NBUC) north of 201S is anotherpossible player that favors the formation of persistent mesoscaleeddies reported by Soutelino et al. (2011) in our study area.

The ocean region where the eddies were found represents botha preservation and conservation area due to the presence ofendemic nelict coral reef species and also a future site for oilexploitation. Eddy properties can affect the local water quality andthe local distribution of sediment, fauna, nutrients and chemicals(Verron et al., 1991).

This work focuses on the possible roles of topography and BC–NBUC shear on the eddy activity in the near-surface flow in the BCformation region (101–201S), reported by the recent literature(Campos, 2006; Soutelino et al., 2011; Arruda et al., in press).Since there is lack of more complete and recent observational datato tackle this problem, we address it through feature orientedregional modeling process studies [FORMS - Gangopadhyay andRobinson (2002)]. The FORMS approach consists of (i) identifyingthe major circulation features of the region; (ii) parameterizingsuch features in terms of their synoptic characteristics ðu; v; T ; SÞ;(iii) implementing a dynamically balanced three-dimensionalrepresentation of the regional ocean as a nowcast; and (iv)running dynamical simulations using such 3-D initialization fornowcasting, forecasting and process studies. Details of the FORMSimplementation for Eastern Brazilian Continental Margin (EBRA)region is explained in Section 2. The specific parameterizations forthe BC–NBUC–SEC regional setup are described in Section 2.1. Thenumerical model and design of sensitivity experiments are dis-cussed in Section 2.2. The results of the numerical experiments arepresented in Section 3. Section 4 analyzes the dynamics, discussesthe results of the simulations and compare them with the recentstudies for the area. Section 5 concludes this work.

2. Parametric and numerical modeling setup

According to Gangopadhyay and Robinson (2002), each oceanicregion, however unique in their individual behavior, consists of anumber of ‘generic’ or ‘common’ characteristic synoptic circulationstructures. These synoptic entities or ‘features’, when put togetherin a particular region, interact and evolve to generate the com-bined circulation variability due to different regional set-up ofmulti-scale processes, bathymetry, boundaries and forcing due towinds and buoyancy. A regional basin like ours may include a setof multi-scale features such as large-scale meandering currentsand fronts, mesoscale eddies and vortices.

This approach, called feature-oriented regional modeling sys-tem (FORMS) (Gangopadhyay and Robinson, 2002) consists ofempirically/analytically creating initial and/or boundary condi-tions for momentum/tracers for primitive equation model simula-tions. The technique is widely used for atmospheric and oceannowcasting and forecasting (Robinson et al., 1988, 1989; Spall andRobinson, 1990; Fox et al., 1992; Hurlburt et al., 1992; Cummingset al., 1997; Gangopadhyay et al., 1997; Robinson and Glen, 1999;Gangopadhyay et al., 2003; Calado et al., 2008, 2010), but it is alsoapplicable for feature-oriented process studies, as we aim here.Parameterizations of velocity features in the ocean have beenwidely used for theoretical studies of geophysical fluid dynamicsand instabilities (Schmidt et al., 2007).

According to the methodology developed by Gangopadhyayand Robinson (2002), when the typical characteristics of thefeatures from previous observations or studies are known, wecan parameterize them and use as input for different processstudies numerical experiments and study their dynamical pro-cesses. The empirical-analytical design formulation of the three-dimensional velocity and water mass structures of a feature iscalled the ‘feature model’ (FM).

We use this technique in a control experiment to reproduce thetime-averaged smooth flow described mostly by Stramma andEngland (1999) and Silveira et al. (2000). We build FMs for thethree currents that compose the upper 1200 m of the regionlimited by 10–231S and 41–321W (SEC, BC, NBUC). These combinedfeatures in EBRA are required to meet observation-based kine-matic characteristics and mass conservation criteria. This field isthen interpolated to a numerical model grid with the bestavailable bathymetry, and allowed to evolve for 10 years. Thisperiod is typically a reasonable time spawn to study mesoscalevariability.

Thus we include (exclude) each one of FMs, as well as exclude(include) important physiographic features, such as the Abrolhosand Royal Charllote Banks (Fig. 2), in complementary sensitivityexperiments, characterizing the “process-study” type of approach.Dynamical adjustment and evolution of the initial smooth velocityfields in different configurations and different bathymetry canthen bring insights about the role of the different entities involved.The 3D field construction will be detailed in Section 2.1 as the caseof the control experiment. Further descriptions of the sensitivityexperiments will be given in Section 2.2.

2.1. An idealized system formulation

Velocity FMs can be designed through two main approaches(Lozano et al., 1996): forward approach and backward approach.The forward approach consists of parameterizing the shape of Tand S surfaces that composes the baroclinic pressure gradientsthat are in geostrophic balance with the velocity structures ofinterest. In this case, the associated velocity field may be com-puted by the primitive equation model or beforehand. In thebackward approach, the exact aimed velocity structure is para-meterized and the tracers are computed afterwards through avariety of methods (Gangopadhyay and Robinson, 2002). In thiswork, both velocity and tracers are considered as the initial field tothe primitive equation ocean model. Generally, the choice of eitherapproach is based on the available source of observations. Avail-ability of direct velocity measurements favors the backwardapproach; and availability of tracers observations favors theforward approach. The velocity-based backward approach is alsomore suitable for current or front-dominated regions. In thepresent process-study work, the backward approach is employed.

In stage 1 of the FM backward approach, two quasi-meridionaljets (BC and NBUC) are parameterized. In stage 2, geostrophicallybalanced potential temperature (T) and salinity (S) fields are

R.G. Soutelino et al. / Continental Shelf Research 70 (2013) 46–6048

computed from the FM 3D velocity field. The imposition of a NBUCflow that is intensified northward sets up a baroclinic pressuregradient. This gradient serves as forcing for a third parameterizedflow – the southernmost SEC branch. Hence, stage 3 consists incomputing geostrophic velocities for SEC and interpolating themto the two-jet field obtained in stage 1. The fourth and last stageconsists in computing the remaining prognostic variables requiredby the numerical model as initial conditions, which are the depth-averaged velocity field and the sea surface height (SSH). Theapplication of each one of these stages is detailed in the followingparagraphs.

Starting with stage 1, BC and NBUC are both parametrized byEq. (1). To obtain the full three-dimensional system, we sum up Eq.(1) fed with NBUC parameters and Eq. (1) fed with BC parameters.The orientation of the system defined within EBRA is a naturalcoordinate frame of reference, where x is the cross-stream axis, yis the along stream axis and z is the vertical axis. The y axis isroughly parallel to the isobath of 150 m, which represents theinterface between the coastal and the deep oceans.

The full three-dimensional main expression for both jets along-stream velocity V is then

Vðx; y; zÞ ¼ vðy; zÞ exp �ðx�xcÞ22δ2

" #; ð1Þ

which is a cross-stream Gaussian-shaped structure with a variableamplitude defined by a vðy; zÞ, which varies in the along-streamand vertical directions. For the cross-stream structure, a constantwidth proportional to δ is adopted for both jets, where xc definesthe position where the jet core occurs. This position xc is alsoconsidered constant to keep the system at a fixed distance fromthe shelf break, roughly following the local topography. Herein-after, the subscript c refers to core, which is where the maximumvelocity of the jet occurs at a given y location. The subscript t refersto the top of the jet, in respect to the orientation of the z axis(upward), and b refers to the bottom portion of the jet.

For the NBUC jet, vðy; zÞ carries its northward strengthening andshallowing velocity core, as mentioned in Section 1. Thus,

vNBUC ¼ vcðyÞexp �ðz�zcðyÞÞ2

2δ2t

" #; at zcozo0

exp �ðz�zcðyÞÞ22δ2b

" #; at zbozozc:

8>>>>><>>>>>:

ð2Þ

In Eq. (2), vc enables the northward strengthening and zcrepresents the northward shallowing. For the sake of simplicity,both vc and zc increases northward as a linear function that aims tomatch the typical observed values of these parameters in thesouthern and northern limits of the domain. The vertical shear ofthe jet is kept constant in the along-stream axis, as an asymmetricalGaussian-shaped structure. The upper part of the jet is less thickthen the lower part, both represented respectively by δt and δb.Note that when the appropriate choice of parameters is made, thisformulation enables the NBUC to reach surface at the north of EBRA,but keeps it in subsurface in the south of the domain.

In the BC case, the formulation is simpler, since there is novertical migration of the jet core. The vertical and horizontalstructure functions are the same for the NBUC. In other words,we do not need the y-dependence for the parameter zc. Now weaim to model a jet that is surface-intensified and northwardweakened in such a fashion that it completely vanishes at theapproximate latitude of the BiSEC. By the time we sum both BCand NBUC, this parameterization enables a smooth transitionbetween two different regimes: (i) the BC over the NBUC at thesouthern part of the domain and (ii) a surfacing NBUC with no BCat the northern part.

So, the BC three-dimensional structure is parameterized by anidentical Eq. (1) with a different v formulation. As said above, thevertical structure vBC now carries y-dependence only for the jetcore velocity, since the jet core depth zc is constant and at thesurface, as in

vBC ¼ vcðyÞ:exp �ðz�zcÞ22δ2bc

" #; at zo0: ð3Þ

Another difference regarding the BC is that the surface-core jetresults in only one half of the Gaussian-shaped vertical structurefunction, allowing us to write Eq. (3) as a single expression definedin zo0.

Fig. 3. Graphical representation of velocity-based stage 1 of the FM systemconfiguration. (a) Cross-sectional velocity distribution in the southern edge of thedomain with pertinent parameters representation. (b) Same, for the northern edgeof the domain. For simplicity, a linear NBUC northward surfacing and growth isadopted, as well as a linear southward BC growth.

R.G. Soutelino et al. / Continental Shelf Research 70 (2013) 46–60 49

The graphical representation of all the relevant FM parametersare presented in Fig. 3. Recall that the choice of the parameters isbased on literature information, where realistic jet positions,

width, thickness, maximum velocities and transports are aimed.The previous works used as references for these characteristics aresummarized in Table 1. Note that all available information issparse in time and space and small adjustments of the parametersare allowed in order to conserve mass in the EBRA domain.The current transports were computed analytically by integratingEq. (1) from �1 to 1, which results in the simple expression:

T ¼ vcδðδtþδbÞ: ð4Þ

The parameters were chosen to reproduce the values of volumetransport, core velocities, jet depth and jet width presented in theliterature as listed in Table 1. The adopted parameters aresummarized in Table 2. Fig. 4 illustrates the volume transportbalance employed in the model boundaries of the EBRA domain,and which corresponds to the sum of eighth column of Table 2.

Table 1Summary of the previous work used as reference to estimate the FM geometric,kinematic and volume transport related parameters.

Feature Relevant studies

NBUC (101–151S) Silveira et al. (1994)Stramma et al. (1995)Stramma and Schott (1999)Böebel et al. (1999)Silveira et al. (2000)Dengler et al. (2004)Schott et al. (2005)Rodrigues et al. (2007)

IWBC/NBUC (151–251S) Stramma and England (1999)Böebel et al. (1999)Silveira et al. (2000)Silveira et al. (2004)Rodrigues et al. (2007)Schmidt et al. (2007)

BC (101–281S) Stramma et al. (1990)Miranda and Castro (1981)Silveira et al. (2000)Silveira et al. (2004)Campos (2006)Rodrigues et al. (2007)Soutelino et al. (2011)

Table 2Adopted parameters for the velocity-based BC–NBUC FM system. See Fig. 3 forgraphical representation. Linear functions are adopted to transfer parameters fromsouth to north, when appropriate.

Feature xc δ zc δt=2 δb=2 vc T

NBUC-S 160 km 100 km 500 m 100 m 360 m 20 cm s�1 9 SvNBUC-N 160 km 100 km 200 m 100 m 360 m 50 cm s�1 23 SvBC-S 160 km 100 km 0 m � 150 m 20 cm s�1 3 SvBC-N 160 km 100 km 0 m � 0 m 0 cm s�1 0 Sv

Fig. 4. Volume transport values imposed in the borders of the EBRA domain via theapplication of the NBUC-BC feature models.

Fig. 5. Cross-sectional geostrophically balanced sθ distributions in the (a) southernand (b) northern edges of the domain.

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Stage 2 consists in computing T and S fields by inverting thethermal wind relation and using a linearized version of theequation of state, as in Schmidt et al. (2007) and Fernandes(2007). We use local climatological T, S and potential density (ρ)regional averaged vertical profiles to keep water masses andstratification within a realistic range. The first step to obtain Tand S is to compute ρ, from the thermal wind equation:

f 0∂v∂z

¼ � gρ∂ρ∂x

; ð5Þ

where f is the Coriolis parameter, v is interpreted as the along-shelf velocity and ρ is the reference density (1027 kg m�3, fromclimatology). Integrating Eq. (5) in respect to x, we get anexpression to ρ, which is

ρðx; zÞ ¼ ρð0; zÞ� f 0ρg

Z L

0

∂v∂z

dx; ð6Þ

where ρð0; zÞ is a mean density profile (also obtained fromclimatology) at the initial location of the transect and L is thelength of the transect. Fig. 5 shows the resulting sθ fieldscomputed from Fig. 3 velocity fields. Figs. 6 and 7 show how theresulting system sets horizontally, after computing all the trans-ects in the EBRA domain.

The T�S fields, which are actually required for the primitiveequation model as initial and boundary conditions, are computedthrough

ρðx; zÞ ¼ ρ½1þβS0ðzÞ�αTðx; zÞ�; ð7Þ

which is a bi-dimensional linearized equation of state used byFernandes (2007). The mean haline contraction coefficient isrepresented by β (8.0�10�4), α is the mean thermal expansioncoefficient (2.2�10�4 1C�1) and S0 is a mean S profile computedfrom climatology. Temperature is then computed by re-arranging

Fig. 6. Along-shelf velocities horizontal maps for surface (a) and 400 m (b). The gray shade represents depths shallower than 100 m and the dashed line is the smoothedshallow-deep ocean interface that serves as origin for the FM transects. Note the limit between surface southward (BC) and northward (NBUC) flow at 151S representing theBiSEC signature at the western boundary. Note also the strengthening character of NBUC at 400 m.

Fig. 7. Horizontal sθ maps for surface (a) and 400 m (b). The gray shade represents depths shallower than 100 m and the dashed line is the smoothed shallow-deep oceanfront that serves as origin for the FM transects. Note also the meridional density gradient resulting from the meridionally growing BC–NBUC system.

R.G. Soutelino et al. / Continental Shelf Research 70 (2013) 46–60 51

Eq. (7) as

Tðx; zÞ ¼�ρρ

þ1þβS0ðzÞα

: ð8Þ

And finally salinity is obtained following Fernandes (2007) bythe following equation:Sðx; zÞ ¼ S0ðzÞ�10�2Tðx; zÞ: ð9Þ

In stage 3, it is aimed to include the SEC flow to complete thevelocity FM system. The density and T�S fields already contains

the adequate baroclinic pressure gradient (Fig. 7). The modeldomain T�S fields are completed towards the ocean interior byrepeating the last values of the FM transects, as shown in Fig. 7.Since we know that in our idealized EBRA system the velocities arezero at the bottom, it is straightforward to compute the SECgeostrophic velocities from this density field considering 1200 mas a level of no motion. The resulting SEC velocities are shown inFig. 8(b). The SEC volume transport is equal to the imbalance of17 Sv generated by the BC–NBUC system (see Table 2). This SECvelocity field is then repeated column-wise towards the western

Fig. 8. Cross-sectional distributions of (a) sθ and (b) velocities for the SEC feature model.

Fig. 9. Numerical model grid for the two different bathymetric configurations. (a) ETOPO 1’ real topography truncated in 5500 m and (b) flat bottom without banks. Modelgrid setup information is shown.

R.G. Soutelino et al. / Continental Shelf Research 70 (2013) 46–6052

boundary of EBRA up to a distance of 100 km of the easternmostFM transect, being damped to zero within this range. This SECzonal velocity field is then interpolated together with the BC–NBUC system in the model grid. The tracers fields are alsointerpolated to this grid, getting ready to serve as initial conditionsto the primitive equation model.

Finally, in stage 4, to complete the prognostic variables requiredby the numerical model, depth-averaged flow and SSH arecomputed. In that case, SSH is simply computed through

SSH ¼ΔΦg

; ð10Þ

where the geopotential anomaly ðΔΦÞ is obtained through Sand T using the 1200 m as level of no motion.

2.2. Numerical model implementation and description of thesensitivity experiments

The primitive equation model chosen for this study is theRegional Ocean Modeling System (ROMS) (Shchepetkin andMcWillians, 2005). ROMS has curvilinear horizontal coordinatesystem and terrain-following in the vertical. The model domain forEBRA has a 1/241 resolution with 179�271 grid points, whichresults in a 1000 km�1440 km area (231S to 101S and 411W to321W) as in Fig. 9. The total number of vertical levels is 40.Topography is configured in different ways for different experi-ments. For the realistic topography experiment, ETOPO1 data isinterpolated to ROMS grid (Fig. 9(a)), minimizing pressure gradi-ent errors by restricting the bathymetry gradients under anr-factor of 0.2 (Haidvogel et al., 2000). For the flat bottom idealizedtopography, a mean shelf/slope is computed for the region andrepeated throughout the EBRA domain (Fig. 9(b)).

Vertical mixing of momentum and tracers is done by thek-profile turbulent closure model by Large et al. (1994). Harmonichorizontal mixing and diffusivity are used both with 5 m2 s�1

coefficients in the interior of the domain and a mild sponge layerof six grid points is applied at the open boundaries (North, Southand East), linearly increasing the viscosity up to 50 m2 s�1. At thethree open boundaries, we follow Peliz et al. (2003) approach bykeeping the FM fields nearly steady through the use of strongrelaxation in a layer of six grid points. Nudging time scales varyfrom 6 to 1 day from the interior to the boundary. In order to avoidreflections of the flow, additional active/passive conditions werealso used at the boundaries (Marchesiello et al., 2001), with stronginflow time scale of 1 day.

In all the experiments, the FM field is interpolated to ROMS gridwith its particular bathymetry setup. No other forcing areimposed, so all the dynamics are consequence of 10 years evolu-tion of the initial field interacting with itself and the topography. Atotal of three sensitivity experiments were carried out to study themechanisms proposed as scientific hypothesis of this study.Table 3 summarizes those experiments. The results of the threedistinct experiments are described in the following Section.

3. Experiments details and results

The CONTROL experiment accounts for the fully designedsystem described in Section 2.1, i.e. the kinematically balancedBC–NBUC feature models with realistic topography. In the first2 years, the prescribed feature model system seems to go througha spin-up phase, where the imposed geostrophic jets adjusts to thetopography. Fig. 10 shows the domain-averaged kinetic energyevolution during the 10-years simulation as a proxy for dynamicalequilibrium spin-up for the three runs. The prompt velocityadjustment is an advantage of the FM approach (Calado et al.,2008), where geostrophically balanced velocities and termohalinefields in a mass conserving 3D field are both available since thebeginning of the time integration.

The first sensitivity experiment (S1) is designed to study theimpact of the BC–NBUC shear on generating eddies without thepresence of the banks (the RCB and the AB). The S1 is built byimplementing a “bank-free” continental margin extracted from thenorthern part of EBRA. This topographic profile does not vary inthe along-coast direction, e.g. no banks, promontories or sea-mounts (Fig. 9b). The FM formulation is essentially the same,except from the BC–NBUC along-shelf trajectory, which issmoother. According to the domain-averaged kinetic energy, theflow seems much more stable in this case.

Table 3Configuration of the different numerical experiments performed. In the table, IDstands for the name of the experiment, IC stands for initial conditions and TOPOstands for topography.

ID IC TOPO

CONTROL BC, NBUC, SEC RealisticS1 BC, NBUC, SEC Flat bottom, no banksS2 BC, SEC Realistic

Fig. 10. Domain-averaged kinetic energy during the 10 years of the three sensitivity experiments.

R.G. Soutelino et al. / Continental Shelf Research 70 (2013) 46–60 53

Fig. 11. Run-averaged velocity fields computed from the last 5 years of the three experiments at 50 m. The velocities are presented as thickness-variable streamlines to favoreddy development interpretation. The magnitude of the velocities is represented by thickness of the streamline. (a) CONTROL run, (b) S1 Run and (c) S2 run.

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The second sensitivity experiment (S2) is designed to isolatethe topography-related instabilities as a trigger to the observed BCmesoscale activity. By keeping the realistic topography and remov-ing the NBUC flow, we obtain evidences of the importance of BC-topography interaction to the overall pattern. To create the initialfields, we remove the NBUC-FM and adapt the BC-FM to keep thesurface northward flow at the north of EBRA active in the system.In order to do that, we simply allow BC core velocities to intensifyfrom 0 m s�1 by changing the δb=2 and vc parameters in Table 2 to150 m and 10 cm s�1, respectively. This value for vc matches fromthe velocity of NBUC at surface in the CONTROL experiment initialfield. The kinetic energy in S2 run is nearly one order of magnitudesmaller than in CONTROL run, which is expected due to theabsence of the undercurrent (Fig. 10).

Fig. 11 shows near-surface (50 m) run-averaged fields for thethree runs. Those averages were computed from years 6–10, toavoid the initial adjustment period. In the CONTROL run (Fig. 11a),where all dynamical “ingredients” are present, the BiSEC signatureis clearly depicted near the continental margin at 151S, which isconsistent with previous studies (Stramma and England, 1999;Rodrigues et al., 2007). The signature of three anticyclones, at 191S,171S and 15.51S, could be interpreted as the averaging of possiblelow-amplitude and spatially/temporally variable versions of thefeatures observed by Soutelino et al. (2011) and Arruda et al.(in press). This is an indication that these features are fairlyrecurrent during the run. Hereinafter we will refer to them asAbrolhos Eddy (AE), Royal-Charlotte Eddy (RCE) and Ilhéus Eddy(IE), respectively, named after topographic and coastal locationsillustrated in Fig. 2. Note the similarity between the modeled 50 m(Fig. 11a) field and the OCCAM 2003 averaged field from Soutelinoet al. (2011)-Fig. 3a. Evidences of all three anticyclones were alsorecurrently observed on the recent results of Arruda et al. (inpress), using a long time series of satellite-derived altimetry. This

indicates that the major dynamical agents necessary to reproducethe typical mesoscale and large scale patterns in the region areembedded in the CONTROL run. In other words, the kinematicallybalanced regional setup and interaction of this WBC systemwithinits components and topography appear to be sufficient to generatethe general flow patterns.

The S1 run showed a quite different pattern (Fig. 11b). Althoughthe large scale BiSEC seems to be reproduced in the appropriatelocation, the averaged field does not indicate the same mesoscaleenergy during the run (as also depicted in Fig. 10). The southwardBC flow dominates the mean circulation. During the run, veryminimal variability was noted (not shown here). The results of thisexperiment are very conclusive, emphasizing the importance ofrealistic topography and indicating that the shear between the BCand the NBUC cannot, by itself, generate and sustain mesoscaleeddies along the BC site of origin.

Regarding S2 experiment, inspecting several velocity snapshotsof the last 5 years of the simulation, we noted a tendency ofdevelopment of cyclones rather than anticyclones at the tip of thetopographic promontories (not shown here). The eddy-rich time-averaged fields (Fig. 11c) for S2 indicates intense eddy activity andrecurrence. It is worth noting that BiSEC signature is absent in thiscase, and the BC stands out in the flow field. Also, the averagededdy features observed in S2 are slightly different from CONTROLrun. The BC flow is stronger and better organized at the con-tinental margin in S2 run. The mean signature of the eddies (IEand RCE) differs from the observations. These features are largerand centered further offshore, and the AE is absent. According tothe results of S2 experiment, the interaction between BC andtopography still provides sufficient conditions to eddy develop-ment at EBRA, but with different types of mesoscale features beingformed when compared to previous observations and globalmodels (Soutelino et al., 2011; Arruda et al., in press).

Fig. 12. Vertical profiles of the along-shore velocities of the FM-parameterized BC–NBUC jet (left), its vertical shear (center) and the cross-jet mean potential vorticitygradient (right).

R.G. Soutelino et al. / Continental Shelf Research 70 (2013) 46–60 55

The brief analysis of the time-averaged fields of the process-study experiments support the following four statements. (1) TheBC–NBUC shear and realistic topography consist of the funda-mental agents for the dynamical development of realistic mesos-cale activity. (2) The FORMS-modeled EBRA region exhibited therecurrent formation and growth of three mesoscale anticyclones,similar in description to the previous observations and globalmodel outputs. (3) The presence of the banks is absolutely essentialto trigger mesoscale eddy formation in EBRA. (4) Although theinteraction between BC and topography in the absence of NBUCreproduces some of the observed mesoscale features in EBRA, theaverage signature of those are not similar to the observations. In theS2 setting, both cyclones and anticyclones are formed, and theirorientation relative to the BC axis differ from the CONTROL Run andthe Soutelino et al. (2011) study.

In the next section, the dynamics of the model outputs will beaddressed in order to search for physical mechanisms-relatedstatements about the generation of mesoscale features in EBRAregion.

4. Dynamics of the BC–NBUC-topography system

After analyzing the three process study experiments describedin Section 3 one can speculate that the existence of the under-current (NBUC) is fundamental in the synoptic setup for thereproduction of the realistic mesoscale features. In this Section,the dynamics of the systemwill be explored in a quasi-geostrophic(QG) framework, in order to seek a physical explanation for howthe NBUC flow is affecting the formation of the surface features.

According to Magaldi et al. (2008), leeward eddies have beenlargely observed behind topographic features such as prominentheadlands and capes. Eddy generation is connected to the phe-nomenon of current separation occurring in the presence ofobstacles. The eddies formed in the numerical simulations carriedin this work are arguably result of this type of dynamics, whererelative vorticity generation combines with the jet inertia as itmoves away from the promontories. When an organized jet movespast a promontory, its inertia forces it to separate from thedynamical boundary (i.e., the continental slope). Therefore, atthe lee of a promontory, there is a strong velocity gradientbetween the jet and the steal water left close to the boundary.This velocity gradient characterizes the generation of relativevorticity that forces a re-attachment of the jet to the boundary.Depending on the jet strength and the promontory shape, thismechanism would result in an eddy, which we believe to be thecase in the present work.

The above mentioned mechanism does not occur in all types ofscenarios. Magaldi et al. (2008) did a numerical study to investi-gate the roles of stratification and topography in generation ofeddy structures in the lee of capes. They designed a fully idealizedexperiment where a steady barotropic jet impinges on an obstaclein a rotating and linearly stratified environment. They kept theRossby number constant and did sensitivity runs varying theBurger Number (Bu), which measures the ratio between baroclinicDeformation Radius (Rd) and the length scale of the obstacle (D).Their results have shown that for 0:1oBuo1, i.e. D4Rd, the jetflows around the obstacle and for Bu41, i.e. DoRd, eddies emergein the lee of the obstacle. In our case, the RCB and AB obstacleshave length scales high enough to result in Bu41, which supportsthe formation of leeward eddies. That would explain the eddytriggering occurring in the simulations and one would expect thata northward flow like NBUC alone would trigger leeward antic-yclones when flowing through the promontories in the northwarddirection.

Although the interaction with jets and topography discussedabove may explain the eddy triggering, eddy formation andgrowth should be discussed in terms of baroclinic instabilityprocesses, capable of transferring available potential energy fromthe mean flow to the eddy field. Therefore, in order to provide a

Fig. 13. Linear instability properties of the FM-parameterized BC–NBUC jet: growthrate (upper panel) in days�1, phase speeds (solid line) and group velocities (dashedlines).

Fig. 14. Horizontally averaged baroclinic conversion rate (EC) for the IE, RCE and AEsubdomains, at 50 m between years 5 and 10 of CONTROL run. Positive valuesindicate energy flux from the mean flow to the perturbations, interpreted as eddygrowth. Negative values of EC are merely mathematical results with no physicalmeaning.

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dynamical explanation to the eddy formation in the numericalexperiments, the QG approximation is used. We aim to investigatethe model outputs in terms of linear theory of baroclinic stability, aphenomena that is typical in this type of configuration, wherethere is substantially robust vertical shear in the mean flow.

We start by applying the Charney–Stern theorem (see Pedlosky,1987 for details). It consists in evaluating if the mean cross-jetpotential vorticity gradient given by

∂q∂n

¼ ∂∂z

f 2

N2

∂v∂z

ð11Þ

changes sign with depth. N2 is mean stratification frequencysquared. If it does change sign, the necessary but not sufficientconditions for baroclinic instability are met.

We follow Silveira et al. (2008) in evaluating the Charney–SternTheorem and calculating the linear instability properties. Theseauthors employed an 1D quasi-geostrophic (QG) model to isolatethe role of the vertical shear in the BC eddy development andgrowth off Cape São Tomé (211S). We chose the latitude of 191S, offthe AB to perform the same calculations. The average continentalslope declivity of �4:5� 10�2 is scaled by the Rossby number of0.06 to comply with the QG constraints.

Fig. 12 shows the vertical profile of the feature-modeled BC–NBUC jet in terms of its cross-jet velocity, velocity vertical gradientand the cross-jet potential vorticity gradient. It is evident that thepotential vorticity gradient sign indeed changes in the vertical,satisfying the necessary conditions for baroclinic instability occur-rence. It is also noticeable that the main zero-crossing of the ∂q=∂nprofile is located around 400 m and the values of both ∂q=∂n and

∂v=∂z are very small near the surface and nearly zero at the bottom(no shown). According to linear stability theory, such aspectssuggest that instability that occur is of the interior type, i.e., thesteering levels are located in the midst of the water column andnot near to the upper and the lower boundaries.

Fig. 13 presents the results for the growth rates, phase speedsand group velocities. The most unstable wavelengths range from80 km to 500 km. The most unstable wavelength is 185 km. Themost interesting result depicted in the figure is that all phasespeeds are positive (i.e., to the north). Hence, the simple modelcomputation suggest that parameterized BC–NBUC jet coupleswith the waves within the NBUC domain, not in the BC. In otherwords, if the FM designed in this work correctly represents thevertical shear between BC and NBUC, the steering levels occurwithin the portion of water column occupied by the NBUC.

The simple analysis described above only assures that the basic jetin the model runs are potentially baroclinically unstable on linear QGsense. The most linearly unstable wavelengths are not necessarilythe most efficient in draining energy from the mean currents.Additionally, the model setup is fully nonlinear with complextopographic forcing. In order to verify if there is a baroclinicinstability process occurring in the model domain, we performenergy conversion calculations with the method proposed byCronin and Watts (1996), and applied by Mano et al. (2009)and Francisco et al. (2011) to different regions of the BC system.The method consists in decomposing the three-dimensional flowsimulated by ROMS into a higher order geostrophic componentand a small ageostrophic component. To compute the eddy

Fig. 15. Horizontally averaged baroclinic conversion rate (EC) for the IE, RCE and AEsubdomains, at 50 m between years 5 and 10 of S2 run. Positive values indicateenergy flux from the mean flow to the perturbations, interpreted as eddy growth.Negative values of EC are merely mathematical results with no physical meaning.

Fig. 16. Horizontally averaged baroclinic conversion rate (EC) for the IE, RCE and AEsubdomains, at 50 m between years 5 and 10 of S1 run. Positive values indicateenergy flux from the mean flow to the perturbations, interpreted as eddy growth.Negative values of EC are merely mathematical results with no physical meaning.

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Fig. 17. Synoptic velocity fields from the CONTROL run computed for year 6 day 60 (a), year 8 day 1 (b), year 9 day 1 (c), and year 10 day 120 (d). The velocities are presentedas thickness-variable streamlines to favor eddy development interpretation. The magnitude of the velocities is represented by thickness of the streamline.

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energetics, we must split the instantaneous fields into mean andeddy fields. This is done by defining the mean field as the longterm 6–10 years model run average and the eddy field as thedeviations from it.

According to Cronin and Watts (1996), the baroclinic energyconversion, which is relevant to baroclinic instability, is defined as

EC ¼ gαθz

u′T ′∂T∂x

þv′T ′∂T∂y

!; ð12Þ

where α is the salt contraction coefficient and θz a horizontallymean temperature vertical profile. The overbars denote time-average and the primes denote the deviations or perturbations.This expression can be evaluated at any given vertical level of thesystem, but depends on depth-integrated variables (θz). Positivevalues of EC indicates energy conversion from the mean flow tothe perturbations and negative values have no physical meaning(Pedlosky, 1987).

We selected three relevant limited regions to compute EC.These areas are roughly encapsulating RCE, IE and AE occurrencesites to illustrate the baroclinic instability activity in these parti-cular sub-domains. A horizontally mean EC for the three eddieswas computed for each day of the last 5 years of the three runs.

As we can note from Fig. 14, regarding the CONTROL run,positive EC values occurs for most of the run at RCE sub-domain.At IE and AE sub-domains, baroclinic conversion is less recurrent,although at IE the occurrence is more frequent than at AE. Theseresults corroborates the run-averaged fields shown in Fig. 11a,where the RCE is much more robust than IE and AE. According tothese results, the BC–NBUC shear is indeed promoting baroclinicinstability in the CONTROL run, and the process is occurringmostly in the near-surface. This means that the energy flux frommean to eddy flow associated with BC–NBUC interaction is leadingto eddy growth mainly in the BC domain. That result supports themean eddy signature shown in Fig. 11a, and suggests that thisanticyclone pattern may be recurrent.

In the case of the S2 run (Fig. 15), we note much more temporalvariability of the energy conversion values, compared to CONTROLrun, specially in the RCE sub-domain. This result is consistent withthe run-averaged velocities exhibited in Fig. 11b, where BC is morerobust in the flow field, and the anticyclonic eddies' meansignatures are not as clear as they are in Fig. 11a. The occurrencelocations also differ from the CONTROL run. The results of thelinear instability analysis and the Cronin and Watts (1996) methodtogether point to a different instability regime in the S2 run due tothe absence of the NBUC. It is still an unstable hydrodynamicssystem but with different characteristics than those observed inthe real ocean. As one would expect, S1 run (Fig. 16) barely showspositive EC values, since there is no topographic forcing associatedwith the banks to trigger the instability, and therefore, favorableconditions for eddy growth are scarce.

Following on the instability analysis, we selected four randomsnapshots (indicated in Fig. 14) to investigate the synoptic velocityfield of the CONTROL run and compare those with previousobservations (Soutelino et al., 2011; Arruda et al., in press). Threeof them were within a period of baroclinic energy conversion(positive EC) (Fig. 17). First, it is worth noting that the modeledsynoptic signature of the RCE and the IE from year 6 day 60, year9 day 1 and year 10 day 120 present horizontal patterns thatresemble the observations described by Soutelino et al. (2011) andArruda et al. (in press). Throughout the analysis period, RCE and IEare recurrently formed in the top 100 m (not shown here). Asevident from the synoptic daily velocity fields, these features areformed, grow and sustain themselves during periods of nobaroclinic conversion. Moreover, the RCB region seems to be themost dynamic of three analyzed sites. In contrast to the RCB

region, the AB site presents more temporal variability and poorerconversion rates. As result, the ABE seems less recurrent than RCEand IE (as the examples shown in Fig. 17).

5. Conclusion

Our results show that the main realistic mesoscale featuresoccurring in the eddy-rich vicinities of the BC site of origin can besuccessfully reproduced by the dynamical interaction betweenparameterized versions of the mean currents and local topogra-phy. A primitive equation ocean model is initialized by feature-modeled velocity fields (CONTROL Experiment), with no atmo-spheric forcing and no effects of remote dynamics. The numericalsolution compares well with recent in situ observations. The threenoticeable anticyclones (IE, RCE and AE) described by Soutelinoet al. (2011) were successfully reproduced in terms of their spatialscales and velocity magnitudes. All three anticyclones were alsoobserved in the recent analysis of Arruda et al. (in press).

A set of sensitivity numerical experiments designed to testdifferent agents to the eddy formation showed that both BC–NBUCvertical shear and local topography are necessary and sufficient torecurrently form the anticlockwise eddies. The two supposedlyagents were isolated (experiments S1 and S2, respectively) andthe results did not correctly simulated the observations. TheBC-topography interaction (S2) was able to trigger mesoscalevariability in the lee of topographic promontories, but not withsame persistence and spatial scales and characteristics. Moreover,the eddies were not formed in the correct side of the BC axis. Onthe other hand, the BC–NBUC interaction over flat bottom (S1) didnot any generate eddies. It is clear from these two sensitivityexperiments that both mechanisms are necessary for the observededdy formation north of 201S.

As a summary of the sensitivity experiments results, we canformulate the statements below. In the presence of BC–NBUCshear and real topography, baroclinic energy conversion occurredduring the CONTROL and S2 runs, recurrent anticyclonic eddies areformed near the surface, resulting in an eddy-dominated longterm averaged velocity field. In the presence of solely BC shear andreal topography, baroclinic energy conversion is intermittent,producing eddies that show more time-space variability, resultingin a more steady long term averaged flow, dominated by the BCmean signature. In the presence of BC, NBUC, flat bottom and nobank physiography, baroclinic energy conversion barely happensresulting in no eddy formation.

We suggest as future work the addition of new sensitivityexperiments changing both BC and NBUC transports, studying theflow field response. Studies like these could be useful in the sensethat annual and interannual variability on these WBCs strengthand different ratios of BC/NBUC transports could lead to differentmesoscale scenarios. The presence of cyclones or anticyclonescould lead to different patterns of shelf-deep ocean exchanges inthe area.

Acknowledgments

We are grateful to the Brazilian agencies CNPq and CAPES forsupporting the first author. This work is part of the PROABROLHOSProject funded through CNPq's Millenium Initiative. We thankSMAST and UMASSD for supporting the first author as a visitingscholar. Thanks are also given to A. Peliz, G. Flierl (MIT), A. Schmidt(UMassD), W. Arruda (UFRJ), R. Matano (OSU), S. Baker-Yeboah(MIT) and I. Belkin (URI), for all the suggestions and personaldiscussions. We thank the three anonymous reviewers for the

R.G. Soutelino et al. / Continental Shelf Research 70 (2013) 46–60 59

constructive suggestions and pertinent criticism that certainlyhelped the manuscript to achieve the current form.

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