The life cycle of a coherent Lagrangian Agulhas ring

0.87 MB·

by  Y. Wang

JOURNALOFGEOPHYSICALRESEARCH,VOL.X,XXXX,DOI:10.1029/2016JGRXXXXX,2016
The life cycle of a coherent Lagrangian Agulhas ring
Y. Wang1, F. J. Beron-Vera2 and M. J. Olascoaga1
Abstract. We document the long-term evolution of an Agulhas ring detected from satel-
lite altimetry using a technique from nonlinear dynamical systems that enables objec-
tive (i.e., observer-independent) eddy framing. Such objectively detected eddies have La-
grangian (material) boundaries that remain coherent (unfilamented) over the detection
period. The ring preserves a quite compact material entity for a period of about 2 years
even after most initial coherence is lost within 5 months after detection. We attribute
6 this to the successive development of short-term coherent material boundaries around
1 the ring. These boundaries provide effective short-term shielding for the ring, which pre-
0 vents a large fraction of the ring’s interior from being mixed with the ambient turbu-
2 lent flow. We show that such coherence regain events cannot be inferred from Eulerian
n analysis. This process is terminated by a ring-splitting event which marks the ring demise,
a near the South American coast. The genesis of the ring is characterized by a ring-merging
J event away from the Agulhas retroflection, followed by a 4-month-long partial coherence

7 stage, scenario that is quite different than a simple current occlusion and subsequent eddy
pinch off.

]
h
p
1. Introduction the Cape Basin, which is in line with the fast decay of the
-
o ring’s SSH anomaly amplitude. Beyond the Walvis Ridge a
a The long-term ability of Agulhas rings detected from large fraction of the ring (about 6×104 km3, correspond-
. satellitealtimetrymeasurementsofseasurfaceheight(SSH) ing to a 2-km-deep, 200-km-diameter ring) is observed to
s
to maintain Lagrangian (i.e., material) coherence has been preserve a compact Lagrangian entity far beyond the the-
c
i demonstrated using satellite ocean color imagery [Lehahn oretical Lagrangian coherence horizon. This is shown to
s et al., 2011]. This suggests a long-term transport ability becausedbysuccessiveshort-termcoherenceregainevents.
y
for such rings, which has been the subject of recent inves- Demise of the ring eventually occurs, triggered by a ring
h
tigation using nonlinear dynamical systems techniques that splitting event, after a rapid decay of the area enclosed by
p enable objective (i.e., observer-independent) framing of La- theshort-termcoherentLagrangianloopsthatprovidedthe
[ grangiancoherence. Usingtheovertwo-decade-longaltime- interiorfluidshieldingfromturbulentmixingwiththeambi-
1 tryrecord,Wangetal.[2015]foundthatlong-lived(ofupto entfluidalongtheringpath. Notalloftheseaspectsofthe
v atleast1yearofduration)ringshavesmall(about50kmin evolution of the ring are inferable from Eulerian analysis of
0 diameter)coherentLagrangiancores,suggestingafastdecay SSH, which although signals coherence gain upon crossing
6 fortherings. Ontheotherhand,theyfoundthatsuchcores theWalvisRidge,suggestsslowdecaythereafter. Itisnoted
5 carry a small (about 30%) fraction of water traceable into finally that even if this behavior generalizes to all Agulhas
1 the Indian Ocean. The two findings together question the rings,whichneedstobeverified,theirlong-rangetransport
0 long-range ability of rings in transporting Agulhas leakage. ability is still limited.
. In turn, Froyland et al. [2015] found that the rings decay The rest of the paper is organized as follows. Geodesic
1 slowly, enabling long-range Agulhas leakage transport, and eddy detection is briefly reviewed in Section 2, which con-
0 thatthisisinferablefromtheEulerianfootprintsoftherings tains basic information of the altimetry dataset and some
6 on SSH. numerical details. The life cycle of the ring is described
1 The goal of the present paper is to bridge the gap be- in Sections 3–5. Implications for transport are discussed in
: tweentheaboveseeminglycontradictingresultsbycarrying Section 6. Finally, Section 7 includes concluding remarks.
v
out a detailed objective investigation of the genesis, evolu-
i
X tion, and decay of the ring priorly investigated by Froyland
et al. [2015]. This is done using Haller and Beron-Vera’s 2. Geodesic eddy detection
r
[2013; 2014] technique, which enables optimal detection of
a
rings with Lagrangian boundaries that exhibit no signs of We are concerned with fluid regions enclosed by excep-
filamentation over the coherence assessment time interval. tional material loops that defy the exponential stretching
Lagrangian coherence is found to emerge quite sponta- that a typical loop will experience in turbulent flow. As
neouslyfromturbulence,processthatdiffersfromtheideal- Haller and Beron-Vera [2013, 2014] have shown, such loops
ized scenario in which an Agulhas ring forms as a result of have small annular neighborhoods exhibiting no leading-
the occlusion of, and subsequent pinch off from, the Agul- order variation in averaged material stretching.
hasretroflection. Thisinitialcoherenceisrapidlylostwithin
1DepartmentofOceanSciences,RosenstielSchoolofMarineandAtmosphericScience,UniversityofMiami,Miami,Florida,
USA.
2DepartmentofAtmosphericSciences,RosenstielSchoolofMarineandAtmosphericScience,UniversityofMiami,Miami,
Florida,USA.
Copyright2016bytheAmericanGeophysicalUnion.
0148-0227/16/2016JGRXXXXX$9.00
1
X - 2 WANG,BERON-VERA&OLASCOAGA: THELIFECYCLEOFANAGULHASRING
Morespecifically,solvingthisvariationalproblemreveals 2013,2014;Beron-Veraetal.,2015;Wangetal.,2015;Kar-
that the loops in question are uniformly stretching: any of rasch et al.,2014]andasoftwaretoolisnowavailable[Onu
their subsets are stretched by the same factor λ under ad- et al., 2015]. Here we set the grid width of the computa-
vection by the flow from time t to time t. The time t tionaldomainto0.1kmcontainingthering,whichenabled
0 0
positionsofλ-stretchingmaterialloopsturnouttobelimit us to push the Lagrangian coherence detectability horizon
cycles of one of the following two equations for parametric close to 1.5 years. All integrations were carried out using a
curves s(cid:55)→x (s): step-adaptingfourth/fifth-orderRunge–Kuttamethodwith
0
interpolations done with a cubic method.
(cid:115) (cid:115)
dx λ (x )−λ2 λ2−λ (x )
ds0 = λ (x2 )0−λ (x )ξ1(x0)± λ (x )−1λ (0x )ξ2(x0). 3. Lagrangian coherence detection
2 0 1 0 2 0 1 0
(1)
Here λ (x ) < λ2 < λ (x ), where {λ (x )} and {ξ (x )}, Webeginbyapplyinggeodesiceddydetectionont0 =31
1 0 2 0 i 0 i 0 March 1999, date by which the ring in question is in a suf-
satisfying
ficiently mature Lagrangian coherence stage. On that date
1 the ring is found inside the region indicated by the square
0<λ1(x0)≡ λ (x ) <1, ξi(x0)·ξj(x0)=δij i,j =1,2, in the left panel of Fig. 1a. Geodesic eddy detection was
2 0 carried out over t through t = t +T for Lagrangian co-
(2) 0 0
herence time scale T increasing from 30 d in steps of 30 d
are eigenvalues and (normalized) eigenvectors, respectively,
out to 480 d, the longest T from which it was possible to
of the Cauchy–Green tensor,
extract a coherent Lagrangian eddy boundary. This is a
very long Lagrangian coherence time scale, consistent with
Ct (x ):=DFt (x )(cid:62)DFt (x ), (3)
t0 0 t0 0 t0 0 thestatementabovethattheringisinamatureLagrangian
coherencestageonthedetectiondate. Infact,buildingma-
an objective (i.e., independent of the observer) measure of
terial coherence takes a few months, as we show in Section
material deformation, where Ft : x (cid:55)→ x(t;x ,t ) is the
t0 0 0 0 5. Application of geodesic eddy detection as just described
flow map that takes time t positions to time t positions of
0 resulted in a nested family of Lagrangian boundaries with
fluid particles, which obey coherence time scale increasing inward.
Theextractedboundariesareindicatedinredonthede-
dx
=v(x,t), (4) tection date in Fig. 1a (the right panel shows a blow-up
dt of the region indicated by the rectangle in the left panel).
For each T considered there is a nested family of λ-loops;
where v(x,t) is a divergenceless two-dimensional velocity
the loop shown is the outermost one in each family. For
field.
T between 30 and 210 d the loops have λ = 1; for T in-
Limitcyclesof (1)eithergroworshrinkunderchangesin
creasing from 210 d, λ increases from 1.05 to 1.75. Thus
λ,formingsmoothannularregionsofnonintersectingloops.
as T increases the largest fluid area enclosed by a coherent
The outermost member of such a band of material loops
material loop shrinks and the ability of a loop to reassume
is observed physically as the boundary of a coherent La- itsinitialarclengthdiminishes,reflectingthattheringturns
grangian eddy. Limit cycles of (1) tend to exist only for unstable after a sufficiently long time.
λ ≈ 1. Material loops characterized by λ = 1 resist the The outer, shorter-lived boundaries provide a shield to
universallyobservedmaterialstretchinginturbulence: they the inner, longer-lived boundaries surrounding the core of
reassume their initial arclength at time t. This conser- the coherent Lagrangian ring. This is evident in the suc-
vation of arclength, along with enclosed area preservation cessive advected images of the boundaries under the flow.
(whichholdsbyassumption),producesextraordinarycoher- These are shown in Figs. 1b–f on selected dates over more
ence[Beron-Veraetal.,2013]. Finally,limitcyclesof (1)are than 2 years of evolution (an animation including monthly
(null) geodesics of the generalized Green–Lagrange tensor snapshots is supplied as supporting information Movie 1 at
Ct (x )−λ2Id, which must necessarily contain degenerate https://www.dropbox.com/s/s6qr2bkrqtiltkr/SI1.mov?dl=0).
pot0ints0ofCt (x )whereitseigenvectorfieldisisotropic. For An advected boundary is depicted red when it is within
t0 0
this reason the above procedure is known as geodesic eddy its theoretical Lagrangian coherence horizon and light blue
detection. when is beyond it. As expected, no noticeable signs of fila-
The specific form of the velocity field considered here is mentation are observed up to that time scale. The filamen-
given by tation observed beyond the coherence horizon reveals that
v(x,t)= g∇⊥η(x,t), (5) theevolutionoftheringischaracterizedbyadecayprocess
f Fig. 1g shows the area enclosed by the largest coherent
Lagrangianboundaryasafunctionofthegeographicallon-
where g is the acceleration of gravity, f stands for Corio-
gitudetakenbytheringasittranslateswestward. Notethe
lis parameter, and η(x,t) is the SSH, taken as the sum of a
drop,nearlyexponential,beforetheringreachestheWalvis
(steady)meandynamictopographyandthe(transient)alti-
Ridgeandtheslowdecaythereafter. Indeed,withinthefirst
metricSSHanomaly. Themeandynamictopographyiscon- 5monthstheareachangesfromabout4.5×104 to7.5×103
structedfromsatellitealtimetrydata,in-situmeasurements, km2 (or the mean diameter from roughly 240 to 100 km),
and a geoid model [Rio and Hernandez, 2004]. The SSH
yetoverthefollowing11monthstheareadecaysveryslowly
anomalyisprovidedweeklyona0.25◦-resolutionlongitude– atarateofnomorethan15km2d−1untilvanishing. Nearly
latitude grid. This is referenced to a 20-year (1993–2012) 90% of the ring interior loses its initial material coherence
mean, obtained from the combined processing of data col- prior to crossing the Walvis Ridge.
lected by altimeters on the constellation of available satel- Therapiddecayofthering’smaterialcoherenceisnotre-
lites [Le Traon et al., 1998]. flectedinthetopologyofthetotalaltimetricSSHfield,but
Forthepurposeofthepresentinvestigationwehavecho- isaccompaniedbyasimilarrapiddecayintheSSHanomaly
sen to focus on the ring detected and tracked by Froyland amplitude. ThisisillustratedinFig.2,whichdepictsinstan-
et al. [2015] over the period 1999–2001. This ring was con- taneous total SSH field streamlines (a) and maximum SSH
sideredbyWangetal.[2015]intheircoherenttransportcal- anomaly (b) in the domains occupied by the ring indicated
culations. The numerical implementation of geodesic eddy inFigs.1a–f. Firstnotethatthestreamlinesareclosedboth
detection is documented at length [Haller and Beron-Vera, beforeandaftertheringcrossestheWalvisRidge,signaling
WANG,BERON-VERA&OLASCOAGA: THELIFECYCLEOFANAGULHASRING X - 3
Figure 1. (a) Nested family of coherent Lagrangian ring boundaries extracted from altimetry-derived
velocity by applying geodesic eddy detection on t = 31 March 1999 inside the region indicated by a
0
rectangle. Each member of the family has a different Lagrangian coherence time scale T ranging from
30 d (outermost) to 480 d (innermost) in steps of 30 d. Selected isobaths (in km) are indicated in gray.
Theoutsetisablowupoftheindicatedregion. (b–f)Advectedimagesundertheflow(i.e.,evolution)of
thecoherentLagrangianeddyboundariesin(a)onselecteddates. Anadvectedboundaryisdepictedred
whenitiswithinitstheoreticalLagrangiancoherencehorizonandinabluetonewhenisbeyondit. The
boundary from an additional detection from t with T =65 d is depicted green over the whole tracking
0
process. (g) As a function of longitude, area of the largest domain enclosed by advected boundaries
within their theoretical Lagrangian coherence horizon.
acoherenteddyfromanEulerianperspective. Furthermore, region filled with streamlines dominates over the transla-
the tangential geostrophic velocity at the periphery of the
X - 4 WANG,BERON-VERA&OLASCOAGA: THELIFECYCLEOFANAGULHASRING
Figure 2. (a) Streamlines of the altimetric sea surface height (SSH) field in each rectangular region
indicated in (a–f). (b) As a function of longitude, maximum SSH anomaly associated with the ring.
tional speed of the region, indicating an eddy capable of stretchesawayfrom,norspiralsinto,theringcore. The65-
maintainingacoherentstructure[Flierl,1981]. Second,the dboundaryenclosesabout55%ofthefluidenclosedbythe
anomaly falls from about 35 cm in March 1999 to nearly 30-d material boundary on 31 March 1999. Any boundary
20 cm in August 1999, before the ring reaches the Walvis larger than the 65-d boundary is found to develop long fil-
Ridge. Similar behavior for other altimetry-tracked rings aments far to the east of the ring as it translates westward
within the western Cape Basin was reported by Schouten beyond 2 months or so. Effectively, however, about 70% of
et al. [2000]. the fluid enclosed by the 30-d boundary is actually seen to
However, a change in SSH anomaly does not necessarily evolve quite coherently for about 2 years. This conclusion
implyacorrespondingchangeinmaterialcoherence. Infact, follows from tracking passive tracers lying in between the
theamplitudeoftheSSHanomalyrecoverspasttheWalvis 30- and 65-d boundaries.
Ridge, reachinginNovember1999almost90%ofitsampli- The enduring Lagrangian coherence of the ring is ex-
tudeinMarch1999. BeyondNovember1999,theamplitude plained as a consequence of successive short-term La-
of the SSH anomaly falls again, at a rate of about 0.9 cm grangian coherence regain events. To illustrate this, in Fig.
month−1. But meanwhile the ring interior loses material 3a we show (in green) selected advected positions of the
coherence gradually with no interruption. 65-d boundary. Overlaid on each we depict (in red) a 30-
AnincreaseintheSSHamplitudemayneverthelessbein- d boundary identified on the date when the advected 65-
dicativeofinteractionwiththebottomtopography. deSteur d boundary is shown. (An animation including monthly
and van Leeuwen’s [2009] numerical experiments reveal an snapshots is supplied as supporting information Movie 2 at
upward transfer of kinetic energy accompanied by an in- https:/www.dropbox.com/s/tl4f5h8n3upuy9j/SI2.mov?dl=0)
creaseoftheSSHamplitudewhenabarocliniceddycrosses For nearly 2 years the advected 65-d boundary is instanta-
a meridional ridge. A large vertical extent for the ring can neously closely shadowed by a 30-d boundary, which pro-
thusbeexpected, giventhatthecharacteristicdepthofthe vides an effective short-term shield to mixing of the fluid
WalvisRidgeisover2km[Byrne et al.,1995]. Suchalarge near and inside the advected 65-d boundary with the am-
vertical extent is in line too with in-situ hydrographic ob- bient fluid stirred by turbulence. Furthermore, because a
servations [van Aken et al., 2003]. shielding boundary is the outermost member of a nested
family of coherent material loops that fill up the ring in-
terior, the ring core remains impermeable over such an ex-
4. Enduring Lagrangian coherence tendedperiodaswell. Thisismanifestedbytheincapability
ofthe65-dboundarytopenetratetheringcorebyspiralling
While filamentation of the ring is observed starting 30 inward. Suchalong-lastingtangentialfilamentationisfound
d after detection on 31 March 1999, a large fraction of the toapplyto65-dthrough120-dboundaries. Inotherwords,
ring’sfluidpreservesastrikinglycompactentityover2years thematerialbeltdelimitedbythe65-and120-dboundaries
of evolution. This is manifested in the evolution of the ma- provides a thick barrier that provides isolation for the fluid
terialloopindicatedingreeninFig.1. Thisloopistheout- inside the 120-d boundary. This accounts for 27% of the
ermost of a nested family of arclength-reassuming (λ = 1) total fluid trapped inside the ring, which has a diameter of
loopsobtainedfromaT =65dcalculation. Beyonditsthe- about 120 km.
oretical coherence horizon and for nearly 2 years, this 65- Beyond approximately 2 years filamentation of the ad-
d boundary develops only tangential filamentation. More vected65-dboundaryceasestobetangential,signalingmore
specifically, even after formal coherence is lost, it neither intense mixing with the ambient fluid. Consistent with this
WANG,BERON-VERA&OLASCOAGA: THELIFECYCLEOFANAGULHASRING X - 5
Figure 3. (a) In green, advected images on selected dates of the third-to-outermost material loop in
Fig. 1a, corresponding to the Lagrangian ring boundary with coherence time scale T = 65 d. In red,
shielding boundaries detected from 30- or 15-d integration from the dates shown. (b) Area enclosed by
the short-time shielding boundaries as a function of their geographic longitude location.
the 30-d boundaries start to shrink, loosing their shielding 480-d boundary on 31 March 1999). By 30 January 1999,
power, until no 30-d boundary can be detected (Fig. 3b no boundary with T = −30 d could be extracted, so we
shows the area enclosed by the shielding boundaries as a switched to T = −15 d and reduced the detection step to
function of longitude position taken). This happens on 19 two weeks. This led to the isolation of 2 boundaries with
May 2001. Beyond this date only a 15-d boundary can be T =−30don31and1March1999,and6boundarieswith
extracted. Eventuallyby3June2001noshort-termbound- T =−15dfrom30January1999backto16November1998
aryispossibletobeidentified,theringdetectedon31March every 15 d.
1999losesLagrangianentitycompletely,andcanbedeclared Figure4depictsonselecteddatesthesebackwardbound-
dead, prior to reaching the South American coast. aries (in red) overlaid on the backward-advected images of
Not surprising due to the observer-dependent nature of
the forward boundaries extracted on 31 March 1999 (light
Euleriananalysis,thedemiseoftheLagrangianringcannot
blue). Thebackwardboundaryon31March1999issmaller
be inferred from the inspection of the topology of the SSH
than the outermost forward boundary on that date, which
field. In fact, a compact region of closed SSH streamlines
provides only partial shielding for the ring when advected
existsevenwhentheringhasvigorouslyfilamented(cf.left-
in backward time. Note the filaments stretching away from
most SSH contours in Fig. 2a and Fig. 1f). Also, that the
the ring into the South Atlantic.
areaenclosedbytheshieldingboundarieshasshrunkconsid-
A closer look reveals that some filaments spiral inward
erablybyFebruary2001explainswhyFroyland et al.[2015]
to the center of the ring. This is evident from the inspec-
could not extract any coherent sets beyond February 2001.
tionofthebackward-advectedimagesof120-dboundaryon
ThustheslowdecayreportedbyFroyland et al.[2015]is
attributed to the occurrence of successive coherence regain 31 March 1999 (depicted in dark blue in Fig. 4 on selected
events. ThisenduringLagrangiancoherenceisnotinferable dates). The inward spiraling of this boundary happens at
from a direct application of geodesic eddy detection on a least up to 16 December 1998.
fixed date as done in Wang et al. [2015]. Revealing it re- Theshieldingboundariesshrinkconsiderablypast16De-
quiresonetoapplyitonsuccessivedates. Theimplications cember1998,andfilamentationofthe120-dboundaryturns
of slowly decaying rings for transport are discussed in Sec- both inward and outward spiraling. By 16 November 1998
tion 6 below. the shielding boundary has shrunk considerably and a part
ofthe120-dboundaryisseentospiralintoaswirlingstruc-
ture from which neither forward- nor backward-time coher-
5. Genesis
ent material loops are possible to extract. On 1 November
Anattemptwasmadetootoshedlightonthegenesispro- 1998the120-dboundarytakesahighlyconvolutedfilamen-
cessoftheringbyapplyingagaingeodesiceddydetectionon tal structure.
t =31March1999,butinbackwardtime.1 Thisprocedure The genesis process thus resembles the demise stage but
0
enabledisolatingcoherentLagrangianeddyboundariesonly in reversed time. The ring in question is seen to be the re-
with T >−60 d. Because the short-termed forward bound- sult of a ring-merging event rather than a simple occlusion
arieswerefoundtoprovideshieldingfortheringoveralong of,andsubsequentpinchofffrom,theAgulhasretroflection
time scale, we set T = −30 d and performed the analy- [Dencausseetal.,2010;Pichevinetal.,1999]. Suchamerg-
sisaroundthebackward-advectedlocationsoftheringcore ing event occurs right within Cape Cauldron, a highly tur-
(taken as the center of mass of the fluid lying inside the bulent region well separated from the Agulhas retroflection
X - 6 WANG,BERON-VERA&OLASCOAGA: THELIFECYCLEOFANAGULHASRING
Figure 4. Backward-advected images on selected dates of the ring boundaries in Fig. 1 corresponding
to several Lagrangian coherence time scales (all depicted light blue, except the 120-d boundary, shown
indarkblue)withtheshort-termshieldingboundaryobtainedfrombackward-timeintegrationfromthe
date indicated overlaid (red).
[Boebel et al.,2003]. Thisisconsistentwiththeobservation 6. Implications for transport
made by Wang et al. [2015] that material Agulhas rings
An important question is how material coherence regain
are organized from incoherent fluid away from the Agulhas events affect the conclusions of Wang et al. [2015] if they
retroflection. Furthermore, quite a good deal of the fluid were to be verified for all Agulhas rings. A quick compu-
tation reveals that rings would carry yearly about 6 Sv (1
(morethan75%asalongbackwardadvectionreveals)that Sv = 106 m3s−1) across the South Atlantic. This rough
ends up forming the ring comes from the South Atlantic. estimate follows from assuming that annually about 3 co-
WANG,BERON-VERA&OLASCOAGA: THELIFECYCLEOFANAGULHASRING X - 7
herentmaterialringsareformed[Wang et al.,2015],andas [2015]conclusionsaboutthelimitedabilityofAgulhasrings
inferred for the ring investigated here, the diameter of the tocarryAgulhasleakageacrosstheSouthAtlanticwouldre-
ringsisabout240km,thecoherenceresponseatthesurface mainvalidasthesecorrectedtransportestimateswouldstill
extends down to 2 km, and 70% of the ring fluid on the be much smaller than reported leakage estimates. The con-
detectiondateiscarriedwellacrossthesubtropicalgyre. If tributionofcoherentLagrangianAgulhasringstothetrans-
we further assume that about 25% of the ring contents are portofsaltisalsosmallerthanestimatesbypreviousstudies
traceableintotheIndianOcean,asisapplicabletothering [vanBallegooyenetal.,1994;LutjeharmsandCooper,1996]
investigatedhere,thentheAgulhasleakagetrappedinrings suggesting that over 95% (more than 70×1012 kg year−1)
which is able to traverse the South Atlantic would amount of interbasin salt flux is attributable to rings. Neverthe-
to up to 1.5 Sv. less, the excess salt associated with a coherent Lagrangian
Overall, the transport results of Wang et al. [2015] may ringmaybetoolargetobeneglected, whichdeservestobe
beunderestimatedbyoneorderofmagnitude. Butthemain investigated in more detail.
conclusions of Wang et al. [2015] should remain unaltered
Acknowledgments. Thealtimeterproductswereproduced
because Agulhas leakage estimates are still almost an order
by SSALTO/DUCAS and distributed by AVISO with sup-
of magnitude bigger [e.g., Richardson, 2007]. On the other
port from CNES (http://www.aviso.oceanobs). Our work was
hand, there is large uncertainty around the behavior of the supported by NASA through grant NNX14AI85G and NOAA
rings below the surface. For instance, according to numer- throughtheClimateObservationsandMonitoringProgram.
ical simulations the vertical structure of a ring may decay
muchfasterthanitssurfacesignature[deSteuretal.,2004].
Notes
Moreover,Wang et al.[2015]showedthatonlyaverysmall
fraction of fluid trapped inside rings detected over the last
1. Allofthebackward-timeintegrationresultsreportedaresuch
twodecadesiseventuallypickedupbytheNorthBrazilCur-
thatatleast90%reversibilityoftheinitialtracerpositionsis
rent. ThuswhilecoherentLagrangianAgulhasringsprovide guaranteed.
adirectroutefortheAgulhasleakageacrossthesubtropical
gyre, most of it may be advected incoherently.
The genesis of coherent material rings in the Cape Caul-
dronalsoimpliesaverydistinctprocessoftransportofsalt
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