On the Generation of North Brazil Current Rings

Journalof MarineResearch, 61, 147–173, 2003 Journal of MARINE RESEARCH

Volume61, Number 2

Onthe generation of North Brazil Current rings

byMarkus Jochum 1 andPaola Malanotte-Rizzoli 1

ABSTRACT Ahighresolution general circulation model (OGCM) isused to investigatethe life cycle of North BrazilCurrent (NBC) rings.The focus of thestudy is on explainingthe generationmechanisms of the ringsand their vertical structure. The OGCM isused in aconguration simpli ed asmuchas possible butcapableof reproducinga realisticmean circulation of thetropical Atlantic. Threenumerical experiments are analyzed:no wind;steady wind; seasonally varying winds. With windforcing, a consistentscenario emerges for thegeneration of NBC rings.It is shown rstthat the NECC isbarotropically unstable, radiating Rossby waves of the rstbaroclinic mode with a periodof 63days(steady wind) or 50 days(variable wind). These waves re ect at the Brazilian coast and createabout 6 –7anticyclonesper year. These anticyclones intensify as they propagate northwestwardalong the Brazilian coast because of potential vorticity conservation and become NBC rings.Among them, about one per year reaches a depthbelow 1000 m. These deep rings are created bythe merger of a surfaceNBC ringwith an intermediate eddy. The intermediate eddies are producedby the Intermediate Western Boundary Current (IWBC) which becomes unstable upon crossingthe equator.

1.Introduction Sincetheir rst descriptiona decadeago (Johns et al., 1990;Didden and Schott, 1993), NorthBrazil Current (NBC) ringshave received increasing attention. First, the mecha- nismsgoverning their generation, detachment and propagation pose a veryinteresting dynamicalproblem. Second, NBC ringsmay constitute an important component of the upperlimb return owofthemeridional overturning circulation (MOC) bycontributingto thenorthward transport of southernAtlantic water intothe northern subtropical gyre.

1.Department ofEarth, Atmospheric and Planetary Sciences, MIT,Cambridge, Massachusetts, 02138,U.S.A. email:[email protected] 147 148 Journalof MarineResearch [61, 2

Figure1. The yearly mean wind stress over the domain. The pattern shows the high resolution along theBrazilian coast and the equator (only every fourth gridpoint is shown).The Caribbean Sea is notpart of the modeldomain.

TheNBC ringsare shed at thewestern boundary of thetropical Atlantic where the NBC forms astrongmeander that retro ectsinto the North Equatorial Countercurrent (NECC). After separatingfrom theretro ectionregion, the rings travel northwestward along the Braziliancoast. Their relevance for thenorthward transport of South Atlantic water clearly dependson their frequency of generation as well as on their horizontal and vertical structure. Beinggenerated by theNBC, therings are one of themajor components of thecomplex tropicalAtlantic current system. Observationally, it is rather dif cult to de ne a mean tropicalAtlantic circulation because of the strong seasonal signal superimposed on the annualmean (Johns et al., 1998;Schott et al., 1998).Even in thestandard mean scenario commonlyaccepted, in situ observationalevidence of the ring birth and structure is dif cultto obtainthrough traditional measurements because of thehigh variability of the retro ectingmeander and detachment region. Satellite observations are mostly descriptive innature,possibly providing a censusof therings over time but no informationabout their three-dimensionalstructure. 2003] Jochum& Malanotte-Rizzoli:North Brazil Current rings 149

Figure2. The annual mean barotropic transport streamfunction (in Sv).

Theoretically,it is also dif cultto apply traditional approaches to studythe instabilityof theNBC becauseof its proximity to the western boundary and its nonzonal nature (Pedlosky,1979). Finally, the jet-like structure of the NBC andthe nature of the ring formationmake the process a highlynonlinear one (see however da Silveira et al. (2000) for aquasi-geostrophicstudy). A possibleapproach to study the dynamics of the NBC ringsis tousean oceangeneral circulation model (OGCM) inacon gurationas simpli ed aspossible that reproduces the basic observational features of the equatorial current system,of the NBC andof the rings. In the present investigation we followsuch an approach,focusing on thefollowing two major questions:

c Whichare the dynamical mechanisms responsible for NBCringgeneration and detachment? c How cantheir vertical structure be explained? Thepaper is organized as follows. In Section 2 themodel con gurationis described and comparisonsare made between the mean properties of thesimulated circulation and the observationalevidence. In Section 3 thenumerical experiments are discussed and results areshown aimed to provideanswers tothe above questions. Section 3 isdividedinto three parts,discussing respectively the results of thesimulations, the role of theNECC, and the 150 Journalof MarineResearch [61, 2

Figure3. The annual mean zonally integrated transport streamfunction in theupper 1000 m ofthe watercolumn (contour interval: 2 Sv).

deepstructure of the rings. Finally, in Section 4, an overall discussion is provided summarizingthe major novel results.

2.The model con guration Themodel used is theMOM2b version of theGFDL-OGCM. Themodel con guration isanidealized basin from 25Sto 30Nin latitude and from 70Wto 15Ein longitude, with a atbottom at 3000 m. Theresolution is 1/4 ° by 1/4° atthewestern boundary between the equatorand 12N, becoming coarser toward the eastern, northern and southern boundaries. Thelatitudinal resolution is reduced from 1/4 ° to 1° atthe meridional boundaries, and the longitudinalresolution is reduced from 1/4 ° to 1.5° atthe easternboundary. Figure 1 shows themodel con gurationand the variable resolution. Thirty levels are used in thevertical with10 mresolutionin the top 100 m. Horizontalmixing is performed by a Laplacianscheme with eddy viscosity and diffusivitylinearly dependent on the resolution: from 200m 2s21 for 1/4° to 2000 m2s21 for 1° resolution.In the vertical, a Richardsonnumber-dependent vertical mixing scheme 2003] Jochum& Malanotte-Rizzoli:North Brazil Current rings 151

Figure4. The simulated alongshore velocity at 4Naveraged over 16 monthsas inJohns et al. (1998) (seehis Fig. 9).

isused.Unstable temperature gradients are eliminated by mixingheat vertically to adepth thatensures a stabledensity gradient. Theinitial condition is a stateof rest. Salinity is kept constant in time and space at a valueof 35psu.The wind stress (Hellerman and Rosenstein, 1983) and the resulting depth integratedcirculation are shown in Figure 1 andFigure 2, respectively.The anticyclonic circulationsnorth of 18N and south of 10S will be referred toas northern and southern subtropicalgyres (STGs). Thecyclonic circulation between 5N and18N will be calledthe tropicalgyre (TG) andthe equatorial gyre (EG) isbetween 10S and 5N. The initial temperaturedistribution is symmetric about the equator and is basically a zonally averaged,idealized climatology (as shownin Fig. 1 ofLiu and Philander, 1995). This meridionalpro leis also used at the surface to restore the surface temperature with a 40-dayrelaxation time. The numerical simulation was integratedfor 18yearsbefore analyseswere performed.The short spin-up time is due to the fast adjustment of the tropicalcirculation (Liu and Philander, 1995). The effect of the global MOC was representedby open boundary conditions (OBC). Itis well known that OBC renderthe 152 Journalof MarineResearch [61, 2

Figure5. The zonal velocity across 38W in April (in cm/ s).The eastward NECC canbe seenat 6N, thewestward South Equatorial Current at 3N,and the westward Ekman oweverywherein the upper 20 m. problemof solving the primitive equations ill posed (Oliger and Sundstrom, 1978). Neverthelessthe simulations are reasonably accurate if the errors introducedby the OBC aresmall enough and do notgrow in time(see Spalland Robinson (1989) for adetailed discussion).At theopen boundaries temperatures and meridional velocities need to be speci ed.Furthermore, the tangential velocities of the in owpoints have also to be de ned,while at out owpoints they can be calculated by assuming conservation of relativevorticity (Spall and Robinson, 1989). Thecode used provides subroutines for OBCthatwere modi edfor ourpurposes. At the openboundaries the temperatureand thebarotropic streamfunction are speci ed.Using the Sverdrupbalance and geostrophy the meridional velocity eldis calculated (Stevens, 1990).The zonal velocity at the boundaries is zero. The barotropic streamfunction and temperatureat the meridional boundaries are taken from thesteady state solution of the purelywind-driven circulation simulated in a basinextending from 40Sto 40N. To simulatethe through owof the MOC return ow,the barotropic streamfunction is modi edso that 15 Sv owinto the South Atlantic in the upper 1000 m allalong the southernboundary and leave the North Atlantic in thenorthwest corner through a western 2003] Jochum& Malanotte-Rizzoli:North Brazil Current rings 153

Figure6. The ow eldat the surface of thewestern tropical Atlantic in NW. Onecan see how the owbreaks up intoeddies that travel north along the coast. boundarycurrent. For adiscussionof thein uenceof theMOC for thetropical circulation seeJochum and Malanotte-Rizzoli (2001), even though it must be pointed out that the presentmanuscript describes rather different simulations. The MOC in owatthesouthern boundary and out owinthe western boundary current atthe northern one are evident in Figure 2 thatshows the time-mean, depth-integrated transport.Figure 3 showsthe time-mean zonally integrated transport in theupper 1000 m. Thesouthern subtropical cell in the southern hemisphere is evident,as well as thestrong wind-inducedequatorial cell at the equator and the through owof intermediate water belowthe thermocline. Thus, across each latitude there is a netnorthward transport of 15Sv;the model dynamics determine at which depth, longitude and within which dynamicalstructure (boundary current, Ekman ow,vortices) this transport takes place. These15 Svare roughly consistent with the values available in the literature (Schmitz and McCartney,1993). A deepwestern boundary current was notsimulated,the focusbeing on thewarm water return owof the MOC andits interaction with the wind-driven circulation. To gain con dencein themodel ’sperformance,the model results were comparedwith availableobservations. Figure 4 showsthe mean alongshore velocity of theNBC at 4N. 154 Journalof MarineResearch [61, 2

Figure7. The annual mean owat100 m depth.The NBC canbe seen owingnorthwestern along thecoast and feedingthe eastward EUC at2N andthe NECC at7N.

Thestructure of the owisverysimilar to thatinferred by Johnset al.(1998) from their currentmeter moorings (compare with their Fig. 9). The NBC transportat this latitude variesfrom 9Svin March to 36 Svin July, which once again compares well with the observationsof Johns et al. (1998).The zonal transport in theupper300 m between3N and 9Nacross38W has a similarcycle with no transport from Aprilto May and a maximumof 28Svin September, very similar to the observations discussed in Katz (1993). This transportcontains the NECC transportand the Ekman transport, which cancel each other in latespring. This compensation between the NECC and Ekman transports can be seen in Figure5, which shows the zonal velocity at 38W in April. Although the NECC ows eastwardthroughout the year, in springthe transport between 3N and9N is zero. TheNBC ringsalso compare well with the observations described in Fratantoni et al. (1995),Goni and Johns (2000) and Fratantoni and Glickson (2002). In the model, the NBC ringsare shed on average every 50 daysand their propagation speed varies from zeroto 15cm/s.At 8.5Nthe average maximum swirl velocityis 85 cm/satthe surface and the averagepenetration depth of the 10 cm/ sisotachis 650 m 1/2 50m(see snapshotsof the NBCringsin Figure 16 and 24). The NBC ringsin our simulation seem to be slightly 2003] Jochum& Malanotte-Rizzoli:North Brazil Current rings 155

Figure8. The ow eldof aneddythat has beenformed by theIWBC at700 m depth(from MW). strongerand deeper than the ones generated in thesimulation of Fratantoni et al. (1995). Weattributethis to thehigher vertical resolution in ourmodel and a lowerviscosity. Theabove discussion is bynomeansa detailedcomparison between observations and thepresent results. Its purposeis solely to demonstrate that the simulation, even though idealized,is ableto reproducereasonably well the NBC ringsand the two most important currentsof this region, the NECC andthe NBC. Three different experiments were performedand will be discussedin thenext section: SW isthe experiment conducted with seasonalvarying wind, MW theexperiment with annual mean winds and NWiscarriedout withoutwinds.

3.Ring shedding a.Simulation results Inthe previous section the properties of themean circulation were shownto be rather realisticwhen compared with the observations. This realism gives con dencethat the simulationscan be analyzedto explore the mechanisms of ring generation. It is helpful to analyzeNW (withoutwind) rst.In this experiment the water enters the domain through thesouthern open boundary, moves north along the western boundary as only there can it 156 Journalof MarineResearch [61, 2

Figure9. The pro leofthemeridional velocity in the intermediateeddy of Figure8 attheequator (in cm/s).The center of the eddy is at 42.5W and it reaches from 400 m downto 1500 m depth.

changeits potential vorticity and leaves the basin again through the northern boundary. Near theequator the owbreaks up into eddies (about 6 peryear) that propagate northwestwardalong the coast as shownin Figure6. This mechanism has been thoroughly analyzedby Edwards and Pedlosky (1998). Upon crossing the equator the sign of the planetaryvorticity changes. Outside the frictional boundary layer (20 km wide in this experiment),the owmust change the sign of itsrelative vorticity to conserve potential vorticity.If thefriction is small enough and the inertial boundary layer (60 km wide at intermediatedepths) is wider than the frictional boundary layer, a portionof the ow lies outsidethe frictional boundary layer and the resulting shear causes the ow to become barotropicallyunstable and to breakup into eddies (Edwards and Pedlosky, 1998). If windis added as an additional forcing, the surface and thermocline waters mayhave othermeans of changing their potential vorticity, as described in the discussion of Killworth’s(1991)work later in this section. However, the water below the thermocline willbe largelyunaffected by thewind (most of the upwelling occurs in the upper 300 m). Therefore,for subthermoclineand intermediate ow,which are not distinguished in the 2003] Jochum& Malanotte-Rizzoli:North Brazil Current rings 157

Figure10. The mean transport in theupper 200 m ofthetropical gyre indicated by anapproximate streamfunction(in Sv). presentanalysis, a similarbehavior as for the owwithout wind is tobe expected. This expectationwill be con rmedby thesimulations carried out with winds, as shown below. Observationsshow that after crossing the equator most of thesurface and thermocline waterfeeds the EUC andthe NECC at around 2N and 7N, respectively (Schott et al., 1998).The numericalsolution shows that a smallpart of itenters a recirculationgyre that is partof theNBC/ NECCretro ectionand is centered at approximately 5N (see Fig.7). This recirculationgyre is the seed for aNBCring(as shownobservationally by Johns et al., 1990).It is importantto notethat in SW andMW the owinthe upperlayer does not break upintoeddies before 4 °N.However,as previously discussed, the owintheintermediate layerbreaks up upon crossing the equator. This is shown in Figures 8 and9 from MW. After theIWBCcrosses the equator, an intermediate eddy is generated having a subthermo- clinewidth and strength very similar to thoseof theNBC (Fig.4). From Figure9 itcan be seenthat the eddy ’s ow eldhas a coherentstructure between 500 m and1500 m thatis verydifferent from the owabove 500 m depth.In both SW andMW thereare about 4 –5 intermediateeddies created every year. Thus, the intermediate owcan create eddies that haveno thermocline expression. The intermediate eddies continue north along the coast withspeeds of approximately10 cm/s. 158 Journalof MarineResearch [61, 2

Figure11. Hovmoeller diagram of theanomalies of themeridional velocity at 6.8Nand 100m depth (incm/ s).Thephase speed of thoseanomalies is approximately 210 cm/s.

Since the owin the intermediate layer breaks up uponcrossing the equator (Fig. 8), the dynamicsbetween the upper layer (0 –300m) andthe intermediate layer (300 –1000 m) mustbe different.First, the NBC entrains water with a relativelyhigh potential vorticity from thenorthern South Equatorial Current that replaces the low potential vorticity water whichthe NBC lost to the EUC (Schott et al., 1998).Second, the upper layer ow is more nonlinearthan the intermediate ow.This can be veri edby comparing their Reynolds numbers, de ned as UL/Ah where L isthe current width. The intermediate layer as a Reynoldsnumber of ;30withspeeds of approximately10 cm/swhereasthe upper layer canreach Reynolds numbers of morethan 500 and speeds of upto2m/s(see Fig.4 which showsthat even in the meanthe owcanreach speeds of 120cm/ s). Thissuggests that one maytreat the upper layer owasan inviscid system. Killworth(1991) studied the inviscid adjustment problem for crossequatorial ow and foundthat a nonlinear owcanpenetrate up to two Rossby radii of deformationinto the NorthernHemisphere without any adjustment of its potential vorticity. However, to compensatefor thelower angular momentum of thehigher latitudes, the water has to gain eastwardmomentum upon owingnorthward. This leads to a thirdmajor difference 2003] Jochum& Malanotte-Rizzoli:North Brazil Current rings 159

Figure12. Anomalies of themeridional velocity at 100 m depth(in cm/ s).This is anindicationof a Rossbywave approaching the coast and reducingits wavelength upon re ectionto the north. betweenthe upper and the intermediate layer. The intermediate layer water has to ow northwardnot only by twoRossby radii but all the way to the northern boundary where it leavesthe basin because of thenorthern open boundary conditions. On the other hand, the upperlayer water has an immediate sink two Rossby radii away from theequator —the wind-drivenNECC. Eventually also the upper layer water has to ownorthward,but itcan dosoin the Ekmanlayer of thetropical gyre where the wind changes its potential vorticity. Figure10 illustratesthis path: the water enters the NECC and then leaves it in theinterior to ownorthward in the Ekman layer which contains most of the transport of the tropical gyre.This comparison between Killworth ’sandthe present experiments suggests that potentialvorticity dynamics is not suf cientto explain the ring generation in the upper layer. Themechanism of sheddingof NBCrings in the present experiments is now discussed. Theresults from MW(steadywinds) will be discussed rst.The main differences between SWandMW withregard to therings are that the rings in SWaremore variable in strength andthat the generation frequency in the two experiments is slightly different (every 50daysin SW andevery 63 daysin MW).Ma(1996)proposed the following generation mechanism:a longRossby wave re ectsat the western boundary and creates a short 160 Journalof MarineResearch [61, 2

Figure13. Variance conserving spectrum of themeridional velocity at 6.8Nat 100m depthat 42W (brokenline) and 48W (solid line).

Figure14. Dispersion relation for a rstbaroclinic mode Rossby wave with a backgroundvelocity of 10cm/sanda meridionallength scale of 1200 km. The box indicates the range of the waves observedin MW andthedots the phase speed of the most unstable modes (see later in the text). 2003] Jochum& Malanotte-Rizzoli:North Brazil Current rings 161

Figure15. The vectors of velocityanomalies at 10mdepth.

Rossbywave with its characteristically high anomalies in relative vorticity. Due to the b-effect andthe interaction with the boundary, those potential vorticity anomalies detach from the re ectionregion and propagate northwestward along the coast. While this is a qualitativedescription of what happens in the model, Ma (1996) does not provide a detaileddiscussion of theprocess. Acloselook at the properties of thedominant waves in the model reveals a phasespeed c between 29 cm/s and 213cm/s,a meridionalwavenumber 1 ofapproximately 2 p/ 1200km, a zonalwavenumber k between 2p/700 km and 2p/900km, and a periodof approximately63 days(from theanalysis of Figs. 11, 12, and 13 respectively). The backgroundvelocity U was calculatedby averaging over an area 500 km 3 500 km centeredat 7N/44Wand estimated to be10 cm/ s. Thewavelength and phase speed of the rst baroclinicmode Rossby waves are connectedthrough the dispersion relation:

U~k2 1 l2! 2 b c 5 (1) k2 1 l2 1 l22 with b 5 2.3e 2 11/ms andthe deformation radius of the rst mode l 5 115 km (Pedlosky(1979)). Figure 14 visualizes the dispersion relation and shows the values of 162 Journalof MarineResearch [61, 2

Figure16. The vectors of absolute velocity for the sametime and depth as forthe previous gure. wavelengthand phase speed as found in themodel. This shows that the model spectrum is dominatedby longRossby waves of the rst baroclinicmode. Observational evidence for westwardpropagating SSH anomalieson the NECC can be found in Leeuwenburghand Stammer (2001). The re ectionof such a waveat the Brazilian coast is now discussed. Following LeBlondand Mysak (1978), Rossby wave energy is re ectedaccording to Snell ’s law. Thisyields the wavenumbers of the re ectedwave, and graphically the results can be obtainedby usinga slownesscircle with an inclined coastline. For aRossbywave with lx between700 km and900 km and ly 5 1200km,the re ectedzonal wavelength would be between400 km and500 km. The resulting group velocity would be northwestwardalong theBrazilian coast. This compares well with the model result of 400 km (Fig.12). Johns et al. (1990) nd rst modebaroclinic Rossby waves at 8.5N/ 51.2W,where the re ected wavewould already be present,with a timescaleof 40 – 60daysand wavelengths between 390km and740 km. It is dif cultto prove that what is observed is indeed a rst modeRossby wave. The background owand the strati cationare by nomeansuniform, the waves are nonlinear andthey are growing while they are propagating westward (Fig. 13). The re ection problemis clearly not straightforward either, because a partof the Brazilian coast is 2003] Jochum& Malanotte-Rizzoli:North Brazil Current rings 163

Figure17. The yearly mean value of uy y 2 b at46W for MW (scaledwith a factorof 1 z 102 1 1 (ms)21 ).

dominatedby thestrong NBC. However,the close resemblance of themodel results with theoreticalpredictions and observations gives a reasonablecon dencein this interpreta- tion. Therelationship between the Rossby waves on the NECC andthe NBC ringsis now discussed.There are about six NBC ringsgenerated every year as amanifestationof the 63dperiodRossby waves. The analysis of the model results show that indeed every anticyclonesheds a ring.The details of this process are displayed in Figures 15 and 16. Figure15 shows the velocity anomalies created by a Rossbywave. The wave, which consistsof equally strong cyclones and anticyclones, becomes de ectednorthwestward andpropagatesalong the coast.After re ection,however, the cyclonesbecome weaker and broaderthan the anticyclones as itcanbe seenby comparingthe anticyclone at 57Wwith thecyclone at 55W. This behaviour is qualitativelyexplained by conservationof potential vorticity;the anticyclones intensify to compensate for theincreasing planetary vorticity, whileat the same time the cyclones must progressively weaken. The intensi ed anticy- clonesbecome NBC rings.It is dif cultto observe the cyclones; not only they become weakeras they move northward, they are also superimposed on the strong anticyclonic 164 Journalof MarineResearch [61, 2

Figure18. Yearly mean baroclinic conversion averaged between 50W and42W (contourinterval 1 z 102 9 m2 /s3 ).Positivevalues indicate a uxfrom eddy available potential energy to eddy kinetic energy. circulationof the NBC/ NECCretro ection.Figure 16 shows in fact that along the Braziliancoast the cyclones are almost impossible to detectin theactual ow. b.The role of theNECC Finally,the generation mechanism of the Rossby waves in MW isdiscussed. MW is chosenbecause it is thesimplest case where the circulation eldand the eddy shedding is quasi-steady.At theselow latitudes it is dif cultto achieve baroclinic instabilities in eastward owingcurrents (Pedlosky, 1979, Ch. 7.9); however, the NECC ful lls the necessaryconditions for barotropicinstability ( uyy . b)inSW(notshown) as wellas in MW(Fig.17). Moreover, the variance of the wave almost doubles while the wave propagatesfrom 42Wto48Was shown in Figure13. These results are different from those ofMcClean and Klinck (1995), who found that the NECC inthe CME modelis not barotropicallyunstable. The question is then what is the energy source for theRossby waves.Following Masina et al. (1999)the energy uxfrom eddyavailable potential energyto eddykinetic energy (baroclinic conversion, 2gr9w9)andfrom themean kinetic energyto eddy kinetic energy (barotropic conversion, 2u9v9Uy)arecomputed. Figures 18 2003] Jochum& Malanotte-Rizzoli:North Brazil Current rings 165

Figure19. Yearly mean barotropic conversion averaged between 50W and42W(contourinterval 5 z 102 9 m2 /s3 ).Positivevalues indicate an energy uxfrom the mean kinetic energy to the eddy kineticenergy. and19 show the results. Locally, the baroclinic conversion is an order of magnitude smallerthan the barotropic conversion. This strongly suggest that barotropic instability is a generationmechanism for theRossby waves. However, if theenergy uxesare averaged overthe unstable area of the NECC (5N –10N, 50W–42W, 0–100m), thebarotropic conversionaverages to 2.0 z 1029 m2/s3 andthe baroclinic conversion averages to 0.7 z 1029 m2/s3,whichshows that baroclinic processes cannot be neglectedin the growth of the instabilities. Furtherevidence for theinstability of the NECC canbe obtained through a linear instabilityanalysis. A jetmay only be asourceof radiatingwaves if wavelength and phase speedof theinstabilities lie on thedispersion curve for awavein the surrounding medium (Talley,1983). A linearquasi-geostrophic stability analysis is applied to an idealized modelof theNECC toshow that the NECC satis esthis radiation condition. In the present experimentsthe NECC has a Rossbynumber of 0.2 and the ratio between the average thermoclinedepth and its meridional deviation is estimatedat 0.4. This clearly stretches the validityof the QG approximation,but the strong similarity to be shown between its predictionsand the OGCM resultsgives us con dencein the results. 166 Journalof MarineResearch [61, 2

Figure20. The idealized NECC pro leusedfor the instability analysis. Shown is zonal velocity in cm/s.

Thelinear form oftheQG equationsis writtenin termsof thestreamfunction c as:

2 ¹ Ct 1 bCx 2 fowz 5 0 (2)

2 Czt 5 ~N /fo!w (3) Themean density pro leis taken from themodel results and the mean NECC pro le, shownin Figure 20, is obtained by averaging snapshots of MW. Bothpro les should representthe unperturbed state which, of course,is unknown. Therefore we chosepro les thatresemble the typical NECC pro lesfrom themodel output in terms of strati cation, maximumspeed, width and depth. The results of thefollowing analysis can be shownto be notoverlysensitive to the chosen mean states. These reference density and velocitypro les de nea meanstreamfunction C( y, z)thattogether with a perturbationstreamfunction F( x, y, z, t)constitutethe total streamfunction. Following the average of Beckmann (1988)and Spall (1992), the perturbations are assumed to be wavelike:

F 5 M~y!F~z!exp@i~kx 2 vt!#. (4)

Substitutionof Eq.(4) intoEqs. (2) and(3) givesan eigenvalue problem for thecomplex frequency v 5 vr 1 ivi.Thesystem of equationsis solvedusing a second-order nite differencesscheme in the horizontal and Chebyshev polynomials in the vertical. Details of thesolution procedure can be foundin Beckmann(1988). The horizontal grid spacing is 2003] Jochum& Malanotte-Rizzoli:North Brazil Current rings 167

Figure21. The spatial pattern of the strongest growing mode. Note its vertical structure which resembles a rstbaroclinic mode and the second maximum at 10N (compare with Fig. 12).

15.6km and12 polynomialsare used in thevertical. Figure 14 showsthe phase speed for thefastest growing westward propagating modes. The predicted values clearly cross the dispersioncurve within the observed range. The spatial pattern of the 850 km mode is shownin Figure21. Its verticalstructure compares well with the vertical structure of the rst baroclinicmode and its meridional structure predicts the secondmaximum at 10N(see Fig.12). The predicted growth rate for an800 km waveis 2.85 z 1027 s21 (’ (40 days)21), andtheratesobserved in themodelare between 2.6 z 1027 s21 and 6.5 z 1027 s21. As in the previoussubsection it isclearthat the simulated ow eldis more complex than the one analyzedhere. Nevertheless the strongsimilarity between the theoreticalprediction and the modelresults justi esthis approach. c.The deep structure of therings Arecentlyconcluded observational campaign, the NBC RingsExperiment (Wilson et al., 2002)showed that the NBC ringscan reach well below the thermocline. The retro ectiondoes not reach below the thermocline and has its maximum velocity near the surface.Thus, the mechanism discussed in the previous section is not suf cientto explain thedeep structure of theNBC rings.The model results suggest that the deep signal can be explainedby themerger of adeepintermediate eddy (see Section3a) withthe retro ection eddy.Figure 22 showsfour successive snapshots of negative relative vorticity for SWin twolayers, the solid lines being contours of z at100 m depthand the broken line contours 168 Journalof MarineResearch [61, 2

Figure22. Four successive snapshots of negativerelative vorticity ( z)toillustratethe merger of an intermediateeddy with the shallow retro ectionring. The solid lines show z in100 m depth between 20.6 z 102 5 s2 1 and 21.4 z 1025 s21 .Thebroken lines show z in700m depthwith each contourindicating 20.2 z 102 5 s21 . of z at700 m depth.The negative relative vorticity indicates anticyclones: the retro ection eddyat 100 m andthe intermediate eddy at 700 m. One can see in this gure how the intermediateeddy (see Figs.8 and9) travelsnorth along the coast and becomes stronger to balancefor theincreasing planetary vorticity. Eventually it merges with the retro ection eddy.Figure 23 showsthe shallow retro ectioneddy before the merger, with only a very weaksignal below the thermocline. This changes after the merger when the newly created NBCringshows a strongsignal beyond 100 m asshown in Figure24. Even though there are about 4 –5intermediateeddies generated per year, only 1 or2 ofthem propagate northwardbeyond 5N whilethe others dissipate on theway. Thisexperiment shows that shallow NBC ringscan merge with intermediate eddies. The detailsof theinteraction between the eddies before and during the merger have not been examined,because such an analysis would require a simpler,more idealized approach, for instancewith a 2layermodel. 2003] Jochum& Malanotte-Rizzoli:North Brazil Current rings 169

Figure23. Contours of meridionalvelocity across the shallow retro ectionring at 5N(contourlines every5 cm/s).This snapshot was taken 40 daysafter the rst z plotof Figure 22.

4.Summary and conclusions Thefocus of the present investigation has been on explaining the generation mecha- nismsof NBC ringsand their vertical structure, capitalizing on theavailable observational evidenceand on previous modeling studies. An idealized OGCM ofthetropical Atlantic was usedwhich is able to reproduce the basicfeatures of thetropical Atlantic circulation as wellas the NBC rings. Threenumerical experiments were carriedout, one without winds and two including the windeffects, either steady or including the seasonalcycle. In NW, withoutwinds, the NBC current owsnorthwestward along the western boundary where it can change its potential vorticity.As explainedin Edwardsand Pedlosky (1998), if theinertial boundary layer is broaderthan the frictional one, the owoutsidethe frictional boundary layer must change thesignof itsrelative vorticity to conservepotential vorticity, thus it becomesunstable and breaksup into eddies. With the vorticity input provided by the wind, the surface and thermoclinecurrent does not become unstable and the owdoesnot break up. Both with steadywinds (MW) andwith variable ones (SW), aconsistent,unique scenario emerges for thegeneration of NBC rings. 170 Journalof MarineResearch [61, 2

Figure24. Contours of meridionalvelocity across the NBC ringof Figure 22 (7N, after a 100days) afterthe merger (contourlines every 5 cm/s).

First,it is shown that the NECC is barotropicallyunstable, radiating Rossby waves of the rst baroclinicmode with a periodof about 63 daysin MW andof 50 days in SW. Thesewaves re ectat theBrazilian coast creating about six anticyclones per year in MW andseven in SW. Amongthese NBC rings,about one per year reaches a depthbelow 1000m. These deep rings are created by the merger of a surfaceNBC ringwith an intermediateeddy, produced by theinstability of theIWBC. The main difference between SWandMW isthat,with variable winds, the ring generation frequency is slightlyhigher andthey are more variable in strength. Eventhough with the present model con gurationthe generation of NBCringscan be studiedand explained, the resolution used is too coarse to study the details of thedecay process.A generalstatement can however be made. As shownby Anderson and Corry (1985),the tropical gyre spins up and down in phase with the tropical wind. As a consequence,the propagationspeed of rings is modulated by the seasonal cycle of thewind eld.Although this does not affectthe generation frequency, the resultingbackground ow acceleratesor deceleratesthe rings, and the modulation determines for howlong the rings areexposed to dissipative processes before they cross the boundary between the tropical 2003] Jochum& Malanotte-Rizzoli:North Brazil Current rings 171

Figure25. 4 yeartime series of meridionalvelocity (in cm/ s)at 10N/ 56Win 100 m depth(for SW). Thebroken lines indicate the standard deviation around the mean. NBC ringscan be identi ed as peaksabove or belowthe standard deviation. One can see that NBC ringspreferentially pass by 10Nin thelate spring at anaverage rate of approximately3 –4ringsper year. andsubtropical gyres. In the time series of meridional velocity at 10N/ 56Wand 100 m depthshown in Figure 25; the NBC ringscan be identi edas peaksabove or belowthe standarddeviation around the mean, marked by straight lines. Even though rings are generatedevery 50 days,the period of the rst baroclinicmode in SW, onlyabout 3 to 4ringsper year reach as far as10N,preferably in latespring. Thequestion of whether NBC ringsare an important contributer to the upper warm limb oftheMOC intransportingnorthward southern Atlantic water cannot be answeredby the presentstudy and remains an openone. The observational study by Fratantoni et al. (1995) givesa valueof 3 Svas the lower bound for thesouthern Atlantic water transported northwardby the rings. This value is muchhigher than the transport we estimatefrom SW onthe basis of 3 – 4ringspassing through 10N per year and on the basis of theirvertical structurein the simulations. For thistransport we havevalues ranging from 0.8Sv to 1.8Sv. Various reasons may account for thisdifference, the most important one being that therings generated in the simulations rarely reach penetration depths greater than 1000 m, 172 Journalof MarineResearch [61, 2 whilethe transport evaluated by Fratantoni et al. (1995)is based on observations containingdeep rings, with penetration depths well beyond 1000 m. According to our explanationof the deep structure of the rings, one could argue that the water below the thermoclinealways owsnorthwards. Whether it does so in aringor in the IWBC maynot beso important as far asthe MOC return owisconcerned. Regarding the study of the ringsdecay process, a higherresolution, both in theverticaland the horizontal, is necessary toobtaina morerealistic representation of therelevant processes.

Acknowledgment. Theauthors are thankful for the useful comments of Bill Johns and Dave Fratantoni.Furthermore they bene ttedfrom the helpful suggestions of Tony Busalacchi, Glenn Flierl,Breck Owens and Mike Spall. Aike Beckmann is thankedfor providing the solution procedure forthe linear stability analysis and Arne Biastoch for help with the open boundary conditions. The computationshave been performed at theNCAR facilitiesin Colorado and this research was funded withNASA grantNAG5-7194 and with NOAA grantNA16GP1576 at MIT.

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Received: 26September,2002; revised: 21March,2003.