On the Upwelling of Downwelling Currents - Hunter College · On the Upwelling of Downwelling...

On the Upwelling of Downwelling Currents

RICARDO P. MATANO

College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon

ELBIO D. PALMA

Departamento de Física, Universidad Nacional del Sur, and Instituto Argentino de Oceanografı́a (CONICET),Bahia Blanca, Argentina

(Manuscript received 23 February 2007, in final form 21 April 2008)

ABSTRACT

The term “downwelling currents” refers to currents with a downslope mass flux in the bottom boundarylayer. Examples are the Malvinas and Southland Currents in the Southern Hemisphere and the Oyashio inthe Northern Hemisphere. Although many of these currents generate the same type of highly productiveecosystems that is associated with upwelling regimes, the mechanism that may drive such upwelling remainsunclear. In this article, it is postulated that the interaction between a downwelling current and the conti-nental slope generates shelfbreak upwelling. The proposed mechanism is relatively simple. As a down-welling current flows along the continental slope, bottom friction and lateral diffusion spread it onto theneighboring shelf, thus generating along-shelf pressure gradients and a cross-shelf circulation pattern thatleads to shelfbreak upwelling. At difference with previous studies of shelfbreak dynamics (e.g., Gawar-kiewicz and Chapman, Chapman and Lentz, and Pickart), the shelfbreak upwelling in the proposed modelis not controlled by the downslope buoyancy flux associated with the presence of a shelf current but by thealong-shelf pressure gradient associated with the presence of a slope current. As these experiments dem-onstrate, shelfbreak upwelling will occur in flat-bottomed domains or even in the absence of a bottomboundary layer. The shelfbreak upwelling, moreover, is not evidence of the separation of the bottomboundary layer but of the downstream divergence of the slope currents, and its magnitude is proportionalto the volume transport of that current. To prove this hypothesis, the results of a series of process-orientednumerical experiments are presented.

1. Introduction

The term “downwelling currents” refers to currentswith a downslope mass flux in the bottom boundarylayer (BBL). They are also known as cyclonic currentsbecause they flow in the direction of the coastallytrapped waves. Examples are the Malvinas and South-land Currents in the Southern Hemisphere and theOyashio in the Northern Hemisphere. Paradoxically,many of these currents generate the same kind of highlyproductive ecosystems usually associated with up-welling regimes. The Malvinas and Oyashio ecosys-tems, for example, have productivity rates that equalthose of the Peru/Chile Current and even surpass thoseof the California Current (http://woodsmoke.edc.uri.

edu/Portal/). An outstanding example of this biologicalabundance is the spring blooms of the Malvinas Cur-rent, which show surface peaks of chlorophyll a of 25–30 mg m�3, values an order of magnitude larger thanthose observed in typical offshore locations (Fig. 1)(Acha et al. 2004; Romero et al. 2006; Garcia et al.2008). The biological abundance of this region cascadesfrom phytoplankton to higher trophic levels: scallops,anchovies, hake, squid, etc. (Lasta and Bremec 1998;Bogazzi et al. 2005). In fact, the food supply in the Malvi-nas region is so plentiful and reliable that elephant seals,which breed and molt on the Argentinean shores, crossthe wide Patagonian shelf (�400 km) to feed there(Campagna et al. 1998). Unsurprisingly, this regionhosts one of the largest fisheries in the Southern Hemi-sphere. Nighttime satellite pictures, for example, rou-tinely show a dense conglomerate of squid fishing ves-sels whose illumination rivals the Buenos Aires, Argen-tina, and Montevideo, Uruguay, urban centers (Fig. 1).

The chlorophyll blooms of the Malvinas Current are

Corresponding author address: Ricardo Matano, College ofOceanic and Atmospheric Sciences, 104 COAS AdministrationBuilding, Oregon State University, Corvallis, OR 97331-5503.E-mail: [email protected]

2482 J O U R N A L O F P H Y S I C A L O C E A N O G R A P H Y VOLUME 38

DOI: 10.1175/2008JPO3783.1

© 2008 American Meteorological Society

JPO3783

symptomatic of the upwelling of nutrient-rich waters tothe surface, but the mechanisms that may drive suchupwelling are still unknown. External forcing does notappear to be the cause: the winds in the Patagonia re-gion are not upwelling favorable, tidal mixing is rela-tively small in the shelfbreak region, and the MalvinasCurrent does not show the eddy shedding and mean-dering that drive the upwelling of other western bound-ary systems (e.g., Campos et al. 2000). Previous studies,however, have shown that the internal processes asso-ciated with the formation of shelfbreak fronts in regionsdominated by cyclonic currents can also generate shelf-break upwelling. The most studied of these fronts is theone located in the Middle Atlantic Bight (MAB; Loderet al. 1998, and references therein), which has beenlinked to the southward displacement of a relativelyfresh plume originating in the Labrador Sea (Gawar-kiewicz and Chapman 1992; Chapman and Lentz 1994;Pickart 2000). Although recent models of this fronthave been favorably compared with observations (e.g.,Houghton and Visbeck 1998; Pickart 2000), it is unclearwhether the same theories can be applied to the Pat-

agonia shelf on account of the physical differences be-tween the two regions. The MAB, on the one hand, ischaracterized by a strong horizontal density gradient,externally imposed by the inflow of low-density watersfrom the north and the absence of a well-defined west-ern boundary current. The Patagonia region, on theother hand, is characterized by a nearly homogeneousdensity structure and the presence of a distinct westernboundary current in the offshore region. As we shallshow, in the absence of an externally imposed horizon-tal density gradient, the magnitude of upwelling gener-ated by the shelf circulation is very small. To accountfor the strong upwelling of the Patagonia shelfbreakregion, therefore, we present a new model for the de-velopment of shelfbreak upwelling that is based on itslocal conditions—specifically, a weakly stratified shelfbounded by a cyclonically flowing slope current. Weargue that the upwelling observed in the inshoreboundary of the Malvinas Current, and other similardownwelling currents, is driven by the meridional pres-sure gradient generated by the downstream spreadingof the western boundary current onto the shelf. We also

FIG. 1. (a) Summer values of surface chlorophyll-a derived from SeaWiFS (mg m�3) in the Patagonia region; (b) nighttime lights inthe southwestern Atlantic. The lights over the Patagonian shelf break are generated by squid fishing vessels (inset) (after Rodhouse etal. 2001).

NOVEMBER 2008 M A T A N O A N D P A L M A 2483

Fig 1 live 4/C

argue that the magnitude of the upwelling is propor-tional to the volume transport of the downwelling cur-rent.

This article is organized as follows: after this intro-duction, in section 2, we introduce our working hypoth-esis. To prove this hypothesis, in section 3, we presentthe results of a series of process-oriented numericalsimulations using the Princeton Ocean Model. In sec-tion 4, we discuss the sensitivity of these experiments tospecific changes of the model configuration. Section 5summarizes and discusses all results.

2. The hypothesis

The two most outstanding characteristics of the Pat-agonia region are a weak density stratification and astrong slope current (the Malvinas Current). To illus-trate how the combination of these characteristics leadsto the development of shelfbreak upwelling, let us con-sider first the dynamics of a linear, steady, quasigeo-strophic jet flowing in the direction of the coastallytrapped waves. The momentum and continuity equa-tion for such a flow can be written as (Csanady 1978)

�f� � �g��

�x,

fu � �g��

�y�

r�

h, and �1�

��hu�

�x�

��h��

�y� 0,

where h is the sea surface elevation, x and y are thecross-shore and alongshore coordinates, r is the bottomfriction coefficient, f is the Coriolis parameter (negativein the Southern Hemisphere), and h is the water depth.In this model the alongshore component of the flow isin geostrophic equilibrium while the cross-shore com-ponent includes the effect of bottom friction. In theparticular case of a sloping bottom with no alongshorevariations, the elimination of u and � in (1) yields thefollowing equation for the sea surface elevation:

��

�y�

r

f ��h

�x��1 �2�

�x� 0. �2�

Equation (2) is known as the arrested topographic waveequation, and it has provided useful insight into thecoupling between the continental shelf and the deepocean (e.g., Wang 1982; Chapman 1986; Wright 1986;Hill 1995). Csanady (1978) noted that if the y coordi-nate is replaced by time, then (2) becomes the heatdiffusion equation; if the topographic slope is constant,the term ks � r/( fhx) is the equivalent of the thermal

diffusion coefficient (“bottom diffusivity”). Hill (1995)found analytical solutions to a slightly more compli-cated version of (2) that included bottom friction andhorizontal diffusion in both directions. His solutionsshowed that as the slope current moves downstream, itspreads out in the cross-shore direction with one por-tion extending onto the shelf while its axis shifts towarddeeper waters (Fig. 2a). We hypothesize that these dis-placements will lead to a divergence of the velocity fieldnear the shelf break and hence to shelfbreak upwelling(Fig. 2b).

To understand the dynamical mechanisms thatshould lead to the divergence of the zonal flow, let usconsider first the downstream equilibrium over a shelf-break point. If the meridional velocity (�) at this pointis in geostrophic equilibrium and the zonal shear (�� /�x) is continuous (the validity of both assumptions willbe demonstrated in the next section), then near theshelf break, we can assume that

�2��

�x2 �2��

�x2 , �3�

where the minus/plus superscripts note points on theshelf/slope sides of the shelf break. Replacing (3) in (2)and assuming that the zonal flow (outside the BBL) isalso in geostrophic equilibrium, we get

u� ks

�

ks�

u�, �4�

where u is the zonal velocity. Because the bottom dif-fusivity over the shallow side of the current is largerthan that over the deep side, it follows that at the shelfbreak there should be a divergence of the horizontalflow, which is proportional to the ratio of the slopes ofthe two regions, and hence shelfbreak upwelling. Equa-tion (4) is in agreement with the early findings of Chap-man and Lentz (1997), who also noted that the transi-tion from the shelf to the slope should produce achange of the spreading rate of the zonal flow (e.g., seetheir Fig. 10b). It is also in agreement with the findingsof Chapman (2000), who noted that the zonal spreadingof a cyclonic current flowing over a bottom of constantslope (u� � u�) is largely compensated by meridionaladvection so that the horizontal divergence (and up-welling) is almost nil (e.g., see Fig. 3 of Chapman 2000).

The above arguments indicate that the downstreamspreading of the slope current onto the shelf shouldlead to a horizontal divergence over the shelf breakbecause the portion of the flow over the shelf spreadsfaster than that over the slope. In the next section, wewill show that this divergence leads to shelfbreak up-


welling and that this result is robust to changes of themodel configuration and parameterization.

3. Testing

To test the proposed hypothesis, we did a series ofhighly idealized, process-oriented numerical experi-ments. The experiments’ aim is to examine whether theproposed mechanisms lead to the development of shelf-break upwelling and whether these results are robust tochanges in the model parameterization. Although theshelfbreak upwelling of the Patagonia region inspiredthis study and the model is set in the Southern Hemi-sphere, other particulars of the model configurationsfollow previous studies and are not meant to representany particular region of the World Ocean.

a. The model

The numerical model used in this study is the Prince-ton Ocean Model. The model equations and the nu-merical algorithms used to solve them have been de-scribed in detail by Blumberg and Mellor (1987) andwill not be repeated herein. The model solves the 3Dprimitive equations on an Arakawa C grid; it uses sigma

coordinates in the vertical and curvilinear coordinatesin the horizontal. For the purposes of this study, wereplaced the prognostic equations for temperature andsalinity with a density equation. Horizontal mixing ofmomentum was parameterized using either a Laplacianoperator with a mixing coefficient AM � 50 m2 s�1 orthe Smagorinsky scheme. Vertical mixing was param-eterized with a constant mixing coefficient, KM � 2 10�3 m2 s�1, and the Mellor and Yamada (1982) sec-ond-order turbulence closure model (MY). The modeldomain used in most of the experiments is set in theSouthern Hemisphere, but it is otherwise identical tothat used by Gawarkiewicz and Chapman (1992) tostudy the formation of shelfbreak fronts and the gen-eration of shelfbreak upwelling (Fig. 3). It consists of arectangular basin with a 400-km extent in the meridio-nal direction and 200 km in the zonal direction. Thebottom topography consists of a shelf and a slope withconstant slopes (0.002 and 0.03) and no meridionalvariations. The shelf, slope, and abyssal plain are con-nected by quadratic polynomials to avoid sharp discon-tinuities in the bottom topography and hence the gen-eration of numerical noise. The western boundary ofthe model is closed, but the other three are open; therewe impose the conditions recommended by Palma and

FIG. 2. Schematic representation of the development of shelfbreak upwelling by a cyclonic current. (a) Thedownstream spreading of the streamfunction associated with the slope current. The dotted line marks the positionof the shelf break. A small portion of the downwelling current spreads onto the shelf while its axis shifts towarddeep waters. This diverging motion generates downstream pressure gradients of opposite signs at each side of theshelfbreak. (b) The cross-shelf circulation patterns associated with this diverging motion.


Fig 2 live 4/C

Matano (1998, 2000). For the external velocities, weimpose a Flather radiation condition at the southernand eastern sides and an Orlanski radiation condition atthe northern side. For the internal velocities, we use anOrlanski condition, and for the density an advectionequation. The magnitude of the specified inflows willbe discussed in the following sections. The model has ahorizontal resolution of 4 km in the meridional direc-tion, 3 km in the zonal direction, and 15 sigma levels inthe vertical. The buoyancy frequency in our benchmarkexperiments was set to N � 2 10�3 s�1, which is areasonable approximation to the Brünt–Väisäla fre-quency over the Patagonian shelf and slope. TheBurger numbers of the shelf and slope are B � 0.04 andB � 0.6 (B � N�/f ; � is the slope of the bottom topog-raphy). Additional sensitivity experiments used N � 0(barotropic case) and N � 4 10�3 s�1. To character-ize the model solutions, we will show cross sections aty � 150 km (Fig. 2). This choice was guided by theprevious work of Gawarkiewicz and Chapman (1992)and, as we shall show, is an adequate representation ofthe downstream equilibrium of the flow. Table 1 lists

the general characteristics of all the experiments dis-cussed in this article and appendix A describes the dif-ferent terms of the momentum balance.

b. The benchmark experiment

To prove our hypothesis, we initialized the first ex-periment with a vertically uniform inflow of 0.1 m s�1

extending over the continental slope of the upstreamboundary (50 km � x � 100 km, and y � 0) (Fig. 3).This particular value of the inflow allows for a directcomparison with the results of previous studies (e.g.,Gawarkiewicz and Chapman 1992). Vertical mixingwas parameterized using the MY scheme, and all theother model parameters were as described in Table 1(EXP1). The experiment was started from rest and runfor 300 days. The steady state was defined as the timeaverage of the last 30 days of the numerical integration.To corroborate the steadiness of the solutions, we ex-tended the integration to 5 yr but found no significantdifferences with the 300-day simulation.

During the spinup, coastally trapped waves transmitdownstream the information on the specified inflow; in

FIG. 3. Model domain and bottom topography. The inflow shown in this picture correspondsto the experiments forced with a slope inflow. The experiments discussed in section 4g havean inflow over the slope, and those in section 4h have inflows over both regions. The stippledarea ( y � 150 km) marks the location of the cross sections shown in following figures.


their wake, they establish a slope current. The effects ofbottom friction and horizontal viscosity change the ini-tial shape of the inflow, so that the steady-state patternresembles that predicted by the arrested topographicwave theory, that is, a diverging jet with one portionspreading onto the shelf and axis shifted toward deeperwater (Fig. 4). The along-shelf component of the mo-mentum balance shows that the downstream diver-gence of the slope current generates meridional pres-sure gradients of opposite signs at each side of the shelfbreak (Fig. 5; appendix A). These gradients drive across-shelf circulation pattern with horizontal velocitiesof opposite signs at each side of the shelf break and arelatively strong upwelling cell on its top (Figs. 6a,b).To understand the dynamical mechanisms that lead tothe reversal of the meridional pressure gradient, it isconvenient to remember that the downstream equilib-rium of a cyclonic current is characterized by asymmet-ric cross-stream velocities, with relatively large magni-tudes on the deep side of the current and small magni-tudes on the shallow side (e.g., see Fig. 3d in Chapmanand Lentz 1997; Fig. 2 in Chapman 2000). This asym-metry is associated with the offshore displacement ofthe mean flow. In the case of a bottom with a constantslope (i.e., no shelf), the meridional pressure gradienton the shallow side of the current is relatively small andthe streamlines closely follow the isobaths (e.g., Fig.2a). However, when a shelf is included, the small zonalvelocities on the shallow side of the current (onshore)are augmented upon crossing the shelf break due to theincrease of the bottom diffusivity [Eq. (4)]. This leadsto an increase of the meridional pressure gradient overthe shelf region. The meridional pressure gradient, nev-ertheless, still decreases in the offshore direction and

reverses sign somewhere over the continental slope.For steep bottom slopes, the reversal occurs within arelatively short distance from the shelfbreak, as ob-served in our experiment.

The strength and structure of the upwelling in EXP1is relatively constant in the downstream direction (Fig.6c). This is consistent with the fact that the time scale inwhich a boundary current diffuses horizontally is muchlarger than the advective time scale, and therefore aparcel of water should be able to travel from the DrakePassage to the Brazil/Malvinas Confluence and sufferonly a small lateral spreading. It should be reiterated,however, that although the spreading is small, it is stillsufficient to generate a relatively strong shelfbreak up-welling on account of the large volume of the slopecurrent. Although frictional effects should be relativelysmall, it is obvious that in an infinitely long domain theywill eventually eliminate any incoming jet and hencethe associated shelfbreak upwelling. In the real ocean,however, the relatively small frictional forces generatedby western boundary currents are compensated by theoffshore pressure gradient generated by the integratedeffect of the wind stress curl (i.e., the Sverdrup bal-ance). Because this scenario is difficult to model with-out adding unnecessary complexity to the analysis, weopted for the very simple setting used in previous stud-ies. The cross section at y � 150 km could be thought ofas representing a region that is relatively close to agiven inflow from the deep ocean circulation.

4. Parameter sensitivity

To test the sensitivity of the shelfbreak upwelling tothe model parameterization, we did an ancillary set of

TABLE 1. General description of the numerical experiments.

Expt No.Topography

(m)

Verticalmixing

(m2 s�1)

Horizontaldifference(m2 s�1)

Shelfvelocity(m s�1)

Slopevelocity(m s�1)

N2

(s�1)

Bottomboundary

current

1 Fig. 3 MY 50 0.0 0.1 2 10�3 Nonslip2 ” ” ” ” 0.5 ” ”3 ” 2 10�3 ” ” 0.1 ” ”4 ” MY ” ” 0.2 ” ”5 ” ” ” ” ” 4 10�3 ”6 ” ” ” ” ” 0 ”7 ” ” ” ” ” 2 10�3 Slip8 ” ” 500 ” ” ” ”9 x � 50 � 100

x 50 � 1600” ” ” ” ” Nonslip

10 Fig. 3 ” ” 0.1 0.0 ” ”11 ” 2 10�3 ” ” ” ” ”12 ” MY ” ” 0.05 ” ”13 ” ” ” ” 0.1 ” ”14 ” ” ” ” 0.2 ” ”


experiments in which we varied the magnitude of theinflow, the parameterization of vertical and horizontalmixing, the magnitude of the density stratification, theexclusion of bottom friction, the specification of thebottom topography, and the effect of horizontal shear(Table 1).

a. The inflow

The speed of the inflow specified in EXP1 is on thelower side of the range observed in the real ocean. Thevolume transport of the slope current in this experi-ment is �4 Sv (1 Sv � 106 m3 s�1), which is one-half thevolume transport of the Southland Current (Sutton2003) and an order of magnitude smaller than the trans-port of the Malvinas Current (Peterson 1992; Piola andMatano 2001). For a more realistic representation of aslope current, we did a new experiment with an inflow

of 0.5 m s�1, which generates a meridional transport of�20 Sv, and kept all the other model parameters as inthe previous case (EXP2, Table 1). The experiment wasstarted from rest and run to equilibrium. Although thecirculation patterns of EXP2 are qualitatively similar tothose of EXP1, the magnitude of the shelfbreak up-welling is an order of magnitude larger than the previ-ous case (Fig. 7). The nonlinear increase of the up-welling is due to the fact that bottom friction is modeledas a nonlinear process (Blumberg and Mellor 1987).Note that in this more realistic case the magnitude ofthe vertical velocities is of the same order of magnitudeas those observed in typical wind-driven upwelling sys-tems O(10�4 m s�1). The difference, however, is thatwhile wind-driven upwelling events last just a few days,the upwelling of slope currents could be sustainedthroughout the entire year.

b. Vertical mixing parameterization

To test the effects of the vertical mixing parameter-ization, we replaced the MY second-order turbulencescheme with a constant vertical mixing coefficient anddid a new series of experiments using inflows of 0.1, 0.2,and 0.5 m s�1. For the purposes of illustration, we willdescribe only the experiment forced with a slope cur-rent of 0.1 m s�1 (EXP3, Table 1). The use of a constantmixing coefficient leads to an overall enhancement ofthe vertical mixing and, as a consequence, to the gen-eration of larger density anomalies (Figs. 8a2,b2).

FIG. 4. Streamfunction distribution in EXP1 (Table 1). Theheavy dashed–dotted line marks the shelfbreak location. Theslope of the zero contours illustrates the spreading of the slopecurrent onto the shelf.

FIG. 5. Along-shelf component of the vertically averaged mo-mentum balance at y � 150 km for EXP1. Note the change of signof the along-shelf pressure gradient at the shelfbreak (x � 50 km).This pressure gradient is balanced by cross-shelf velocities of op-posite signs at each side of the shelf break (Coriolis � fU ).


These anomalies are not confined to the deep portionof the ocean, as in EXP1, but extend throughout theentire water column. The larger density anomalies,which enhance the baroclinic pressure gradient, lead toa reversal of the meridional flow and the developmentof a deep slope countercurrent (Fig. 8b1). This coun-tercurrent generates upslope velocities that reinforcethe shelfbreak upwelling, which is larger than in EXP1(Figs. 8b3,a3). Experiments using larger inflows (notshown) do not develop a deep countercurrent becausethe baroclinic pressure gradient is unable to compen-

sate for the imposed barotropic pressure gradient, butall the experiments using a constant mixing coefficientdevelop a stronger vertical shear and upwelling thanthose using the MY scheme (e.g., Figs. 8a1,b1) (see alsothe discussion of Chapman 2002). The threshold for thedevelopment of a deep countercurrent not only de-pends on the magnitude of the inflow but also on themagnitude of the background density stratification andthe slope of the bottom topography. Note that the ve-locity structure associated with the slope current ex-tends onto the shelf (Fig. 8). These shelf intrusions lead

FIG. 6. Cross-shelf velocities (vectors) and vertical velocities (contours) in EXP1. (a) Cross-shelf velocity vectorsat y � 150 km; (b) vertical velocities at the same cross-shelf section; (c) plan view of the vertical velocities in anintermediate sigma level. The location of the cross sections in (a) and (b) is indicated by the dotted line in (b). Thedepth of the sigma level in (c) is indicated by the gray dotted line in (a). Note that the cross section in (a) and (b)extends only to x � 100 km. Blue colors mark upwelling and red colors downwelling.


Fig 6 live 4/C

to a near homogenization of the water column and theformation of a shelfbreak density front similar to thatreported by Gawarkiewicz and Chapman (1992), albeitfor a different reason.

c. Density stratification

While its simple elegance is illustrative and appeal-ing, Eq. (2) is not broadly applicable because it assumesa barotropic flow. In a stratified fluid, the downslopeadvection of low-density water by a downwelling cur-rent generates density gradients within the BBL, whichvia thermal wind reduce the effect of the bottom stress(e.g., Trowbridge and Lentz 1991, 1998; MacCreadyand Rhines 1993; Chapman and Lentz 1997). Thus, in astratified fluid, the lateral spreading of a current bybottom friction is less likely to occur than in a homo-geneous fluid. To investigate this effect, we did a seriesof new experiments that vary both the Brünt–Väisälafrequency and the inflow. These experiments show thatwhile the mechanism of shelfbreak upwelling postu-lated herein is robust, the overall effect of a givenchange of the density stratification depends on the rela-tive magnitude of the currents to which it is applied.Although our experiments offer a glimpse of thesecomplex interactions, they are clearly insufficient tofully address the issue, which is beyond the scope of thisstudy. Rather, we will focus our discussion on the topicthat is most relevant to this article—the robustness ofthe shelfbreak upwelling to the magnitude of the den-sity stratification—and leave a more detailed discussionon other subjects for a separate study.

To demonstrate that the occurrence (not the magni-

tude) of shelfbreak upwelling is insensitive to the mag-nitude of the density stratification, we show a series ofexperiments forced with a slope inflow of 0.2 m s�1 andN � 2 10�3 s�1 (EXP4), N � 4 10�3 s�1 (EXP5),and N � 0 (EXP6) (Table 1). In the two stratified cases(EXP4 and EXP5) the increase in N leads to a rela-tively small increase of the shelfbreak upwelling that iscaused by changes in the vertical structure of the cur-rent (Figs. 9b,c). The doubling of N increased the ver-tical shear of the slope current and hence the transportin the upper half of the water column. Although thesechanges lead to a slight increase of the shelfbreak up-welling, they did not lead to the development of a fullyarrested BBL (i.e., a layer where the meridional veloc-ity and bottom stress vanishes). The robustness of theproposed hypothesis is further demonstrated in the ex-periment without stratification (N � 0; EXP6), whichshows that shelfbreak upwelling occurs even in unstrati-fied fluids (Fig. 9a). Note, moreover, that in this par-ticular experiment the magnitude of the upwelling issubstantially larger than in the previous case. This isdue to the enhanced influence of the bottom friction onthe downstream spreading of the slope current.

d. Arrested BBLs and slip conditions

Theoretical studies predicted that a downslope buoy-ancy flux should lead to the development of a fullyarrested BBL (e.g., Garrett et al. 1993; Ramsden 1995;Middleton and Ramsden 1996; Chapman and Lentz1997). Such occurrence can affect the shelfbreak up-welling because it should eliminate the contribution ofbottom friction to the downstream spreading of theslope current. None of our numerical experiments,however, ever reached that state. Time series of EXP2,for example, show that although there is a downstreamreduction of the meridional bottom velocities, theynever completely vanish (Fig. 10). These results areconsistent with the early findings of Chapman (2000),who reported that even in a strongly stratified experi-ment (N � 9 10�3 s�1), the BBL is not fully arrestedand that halving the magnitude of N leads to an equi-librium that is close to the nonstratified case.

Although none of our experiments, nor those ofChapman (2000), developed a fully arrested BBL, it isstill possible to test whether such occurrence wouldlead to the elimination of the shelfbreak upwelling. Tosuch an end, we did an additional experiment in whichwe replaced the nonslip bottom boundary conditionwith the slip condition,

�U�z

� 0 at z � �h,

FIG. 7. Vertical velocities in EXP2. Contours are in units of10�5 m s�1.


which halts the development of a BBL (EXP7). Theexperimental results indicate that the elimination of theBBL does not lead to the elimination of the shelfbreakupwelling (Fig. 11). As expected, however, the elimina-tion of the bottom friction led to a substantial reductionof the lateral spreading of the current, which is now

totally controlled by horizontal viscosity, and conse-quently to a similar reduction of the vertical velocities(cf. Figs. 11, 9a). Therefore, EXP7 demonstrates thatthe development of the shelfbreak upwelling is notcritically dependent on the BBL dynamics, although itis clearly influenced by it.

FIG. 8. Meridional velocities, density anomalies, and vertical velocities in the experiments forced with a slopeinflow of 0.1 m s�1 and using (a) the Mellor and Yamada (1982) second-order turbulence scheme and (b) a constantvertical mixing coefficient. For a definition of the experiments, see Table 1. Vertical velocity contours are in unitsof 10�5 m s�1.


EXP7 demonstrates that shelfbreak upwelling occurseven in the absence of a BBL. Nevertheless, it seemsreasonable to wonder whether such development oc-curs in the Patagonian region, that is, whether there isa fully arrested BBL underneath the Malvinas Current.The answer, although far from conclusive, seems to benegative. From long-term observations, Vivier and Pro-vost (1999) reported that even at 41°S, where there is asubstantial advection of warm subtropical waters fromthe Brazil/Malvinas Confluence, and hence an increaseof the density stratification of the water column, theMalvinas Current maintains a strong barotropic struc-ture with bottom mean velocities on the order of 10cm s�1 at 3000-m depth and higher values over theshelfbreak (�20 cm s�1). The buoyancy frequency atthe mooring location described by Vivier and Provost isapproximately N � (�g�z /�0)1/2 � 2 10�3 s�1, whichis the value used in most of our experiments. There areno long-term current measurements farther south, buthistoric datasets show a progressive weakening of thedensity structure. Observations, therefore, indicate thatthe relatively weak stratification of the southwesternAtlantic does not allow the development of arrestedBBLs. The strong influence of the bottom topographyon the path of the Malvinas Current is one of the prob-able causes for the remarkable steadiness of its path(Peterson 1992; Piola and Matano 2001).

e. Horizontal viscosity

Because the shelfbreak upwelling depends on thehorizontal spreading of the slope current, it follows thatits magnitude should be sensitive to the value of theviscosity coefficient used in the numerical simulations.To test this proposition, we repeated EXP7 using aviscosity coefficient that is an order of magnitude largerthan in the previous experiments (EXP8). To isolatethe effects of horizontal diffusion, we used a slip-bottom boundary condition in this experiment. TheEXP8 shows that (as expected) the increase of horizon-tal viscosity leads to a proportional increase of the up-welling velocities, which are now an order of magnitudelarger than in EXP7 (Fig. 12). The new experimentshows a generalized upwelling over the shelf due to theincrease in the enhanced spreading of the slope currentonto the shelf region.

The observed sensitivity to the magnitude of the vis-cosity coefficient raises the question of what valueshould be used in numerical experiments. This questionhas no obvious answer because viscosity coefficientsusually represent physical processes that are beyondthe model’s resolution and its values are chosen moreon considerations of numerical stability than on physi-cal principles. Nevertheless, we tested the robustness of

FIG. 9. Cross-shelf sections of the vertical velocities correspond-ing to the experiments forced with a slope inflow of 0.2 m s�1 andbackground stratification of (a) N � 0; (b) N � 2 10�3 s�1; and(c) N � 4 10�3 s�1. Contours are in units of 10�5 m s�1.


our results by running an additional experiment inwhich the viscosity coefficient is determined as a func-tion of the horizontal velocity shear of the flow (Sma-gorinsky 1963). The results (not shown) are almostidentical to those of the benchmark case, which indi-cates that the value of AM � 50 m2 s�1 is a robustestimate of the minimum value that our model resolu-tion allows. This conclusion is consistent with the earlyfindings of Gawarkiewicz and Chapman (1992), whonoted that the formation of shelfbreak fronts is largelyinsensitive to the parameterization of horizontal diffu-sion. This statement, however, is only valid if the vis-cosity coefficient is small.

f. Bottom topography

To examine the effects of the shape of the bottomtopography on the magnitude of the shelfbreak up-welling, we did an additional experiment in a basinwithout a continental slope and with a shelf and deepregions of constant depths. The experiment was forcedat the upstream boundary with a slope inflow of 0.1m s�1 (EXP9, Table 1). The magnitude of the shelf-break upwelling in this experiment is an order of mag-nitude larger than in the benchmark case, which indi-cates that the proposed mechanism of shelfbreak up-

FIG. 11. Vertical velocities for EXP7. V � 0.2 m s�1 and nonslipbottom boundary condition. Contours are in units of 10�5 m s�1.

FIG. 12. Vertical velocities for EXP8. V � 0.2 m s�1, nonslipbottom boundary condition and AM � 500 m2 s�1. Contours are inunits of 10�5 m s�1.

FIG. 10. Time series of the along-shelf velocities within the BBL at x � 60 km and y � 100km (light gray line), y � 200 km (gray line), and y � 300 km (black line). The meridionalvariation of the adjustment time is in good agreement with the advective time scale.


welling is robust to changes in the particulars of thebottom configuration (Fig. 13). Although Eq. (4) doesnot strictly apply to EXP9, the basic mechanisms delin-eated in section 2 are valid because bottom friction stillcauses a zonal spreading of the current and the depthdiscontinuity at the shelfbreak still provides a conduitfor the downstream propagation of the inflow. In thiscase, however, there are no potential vorticity restric-tions to the magnitude of the zonal frictional spreadingof the portion of the slope current that is entrained ontothe shelf (i.e., u� → �), while the frictional spreading ofthe portion of the slope current flowing over the deepocean is hindered by the depth of the water column,that is, over the deep ocean region u� → 0. Because theshelfbreak upwelling is proportional to the divergenceof the downstream transport (not the inflow velocities;i.e., w � ��u/�x dz), the magnitude of the upwelling isalso augmented by the fact that the meridional trans-ports in EXP9 are an order of magnitude larger thanthose in EXP1. Thus, even in this extreme case thedifference of depths between the shelf and the deepocean leads to a substantial divergence of the zonalflow and an enhanced shelfbreak upwelling.

g. A shelf current

Because shelf currents generally flow in the samedirection as slope currents, it is natural to explore theirrelative contribution to the shelfbreak dynamics. Manyarticles have addressed this topic, but the most relevantis that of Gawarkiewicz and Chapman (1992, hereafterGC92). While studying the formation of shelfbreakfronts, they noted that cyclonic shelf currents generateshelfbreak upwelling and ascribed it to a separation ofthe BBL by the downslope flux of buoyancy. To furtherinvestigate this, we ran two experiments forced with aninflow of 0.1 m s�1 over the shelf portion of the domain(0 � x � 50 km, y � 0). The only difference betweenthese experiments is that one uses the MY scheme forthe representation of vertical mixing (EXP10) while theother, mimicking GC92, uses a constant mixing coeffi-cient (EXP11). The EXP10 allows for a direct compari-son with the results discussed in the previous section,while EXP11 is comparable with the results of GC92. Inprinciple, EXP11 should be identical to the benchmarkexperiment of GC92. Our simulation, however, uses adifferent model and, more importantly, a different defi-nition of steady state (GC92 used snapshots of a 30-daysimulation). The repetition of the experiment of GC92,therefore, provides us with a dynamically consistentframework to make quantitative comparisons.

The general circulation patterns associated with ashelf current have been described in great detail byother authors. Therefore, we will focus only on those

aspects of the shelf experiments that are relevant to thegeneration of shelfbreak upwelling, that is, the com-parisons between EXP10 and EXP1 (the slope experi-ment) and between GC92 and EXP11 (our version ofGC92). The outstanding difference between EXP10and EXP1 is that the vertical velocities generated by ashelf current are an order of magnitude smaller thanthose generated by a slope current (cf. Figs. 14a1, 6, andnote that to show the shelfbreak upwelling we had toreduce the contour interval). This result, which demon-strates that slope currents are the main contributor tothe shelfbreak upwelling, is not surprising. Vertical ve-locities are proportional to the meridional transports,and these are an order of magnitude smaller in EXP10than in EXP1. What is surprising, however, is that theupwelling in EXP10 is also substantially smaller thanthe values reported by GC92 (cf. Fig. 14a1 of this articlewith Fig. 6b of GC92). As noted above, part of thediscrepancy can be attributed to the definitions ofsteady state used by the two studies. We used 30-dayaverages of a 300-day simulation, while GC92 usedsnapshots of a 30-day simulation. Analysis of our ex-periments indicates that our model doesn’t reach dy-namical equilibrium until day 40 and, even then, thesteady state is masked by the presence of bottom-trapped waves (e.g., Rhines 1970), hence the need totake time averages. As Fig. 14b1 and the early experi-ments of Chapman (2002) demonstrate, however, mostof the discrepancy between the results of GC92 andEXP10 can be attributed to the parameterization ofvertical mixing, which strongly influences the overallstructure of the density and velocity fields. The densityanomalies of EXP10, for example, are largely restricted

FIG. 13. Vertical velocities in EXP9, which was done in a basinwith a shelf and deep ocean of constant depths. Contours are inunits of 10�5 m s�1.


to the shelf portion of the BBL where the downslopeflux of low-density water generates a strong verticalmixing that leads to a loss of buoyancy. The densityanomalies of EXP11 (Fig. 14b2) and those of GC92 (seetheir Fig. 10), however, extend over the entire modeldomain (including the deep ocean) because the magni-tude of the vertical mixing is constant throughout theentire domain and hence independent of the circulationdynamics. The unrealistic effects of this particular mix-ing parameterization are particularly noticeable overthe shelf where it leads to a complete homogenizationof the water column and the generation of a shelfbreakfront that extends from the bottom to the surface (seeFig. 7c in GC92). In contrast in EXP10, there is only achange of density of the shelf BBL (Fig. 14a2).

In summary, our analysis suggests that the upwellinggenerated by a shelf current is substantially smallerthan that generated by a slope current with the same

speed. The difference is attributed to the magnitudes oftheir respective transports. It also indicates that themagnitude of the shelfbreak upwelling is sensitive tothe parameterization of vertical mixing. The observedsensitivity explains why the magnitude of the upwellingin our experiments is smaller than the values reportedby GC92.

h. Horizontal shear

To complement our previous experiments, we did anadditional series of simulations forced with inflows overboth the shelf and slope regions. These experimentswere aimed to investigate the interactions between ashelf and a slope current as well as the effects of thehorizontal shear on the generation of shelfbreak up-welling. The shelf inflow was kept at 0.1 m s�1 while theinflow over the slope was set to: i) 0 m s�1 (EXP10); ii)0.05 m s�1 (EXP12); iii) 0.1 m s�1 (EXP13); and iv) 0.2

FIG. 14. Vertical velocities, density anomalies, and cross-shelf momentum balance of (left) EXP10 and (right)EXP11. (a1), (b1) The contours of the vertical velocities are one-half the value of those plotted in the previousfigures (e.g., Fig. 6).


m s�1 (EXP14) (Table 1). The zonal circulation pat-terns in these experiments can be rationalized in termsof the previous results. Experiments with very weakslope currents, for example (EXP10 and EXP12), arequalitatively similar to the results discussed in section4g, while the experiments with a relatively strong slopeinflow (EXP13 and EXP14) resemble the results of sec-tion 3. The overall influence of the slope current on theshelf circulation can therefore be illustrated from themomentum balances of the two extreme cases: EXP10and EXP14 (Fig. 15). The zonal momentum balanceshows that the experiment with a slope current haslarger meridional velocities than the experiment with-out, because of the increase of the barotropic zonalpressure gradient (Fig. 15a). This increase peaks in theouter shelf, where the meridional velocities are �30%larger than in the experiment without a slope current.Although the increase of the meridional velocities issubstantial, the zonal velocities are even more affectedby the presence of the slope current. Of particular in-terest is the reversal of the zonal flow in the outer shelf,which, as shown previously, leads to a strengthening ofthe shelfbreak upwelling (Fig. 15b).

As shown in the previous sections, the zonal circula-tion determines the sign and magnitude of the verticalvelocities at the shelfbreak. In the experiments with anull or a weak slope current (e.g., EXP10 and EXP12),

there is a small upwelling in the outer shelf and a gen-eralized downwelling over the shelf break (Figs. 16a,b).The lateral spreading of the shelf current generates ameridional pressure gradient and a zonal circulationwith offshore velocities in the outer shelf. Because thehorizontal divergence of these experiments is con-trolled by the zonal component of the continuity equa-tion, �(hu)/�x, the monotonic increase of the offshorevelocities from the inner shelf to the outer shelf leads toa mass divergence and a relatively weak upwelling onthe inner side of the shelfbreak. The deceleration of theflow over the slope causes mass convergence and down-welling over the shelf break. The zonal circulations inEXP13 and EXP14 are qualitatively similar to the casediscussed in section 3. As shown, there the lateralspreading of the slope current generates meridionalpressure gradients of opposite signs at both sides of theshelf break and a divergence of the zonal flow (Fig.15b).

Shelf and slope currents generate opposite verticalvelocities over the shelf break. A shelf current gener-ates a small upwelling in the outer shelf but strongdownwelling over the shelf break (e.g., Fig. 14a1). Con-versely, a slope current generates a strong upwellingover the shelf break and a weaker downwelling over theshelf’s interior (e.g., Fig. 6). Thus, the sign and magni-tude of the shelfbreak vertical velocities in the case in

FIG. 15. Comparison of the surface momentum balance of the experiments forced with a shelf inflow of 0.1 m s�1

and no slope inflow (EXP10; red lines) and the experiment forced with the same shelf inflow and a slope inflowof 0.2 m s�1 (EXP14; blue lines). Solid lines correspond to the Coriolis term and dashed lines correspond to thepressure gradient term. The (a) cross-shelf and (b) along-shelf components.


Fig 15 live 4/C

which both currents coexist depends on their relativespeeds. In EXP10 and EXP12, the shelf current domi-nates the zonal circulation and, consequently, there isdownwelling over the shelf break (Figs. 16a,b). InEXP13 and EXP14, the presence of the slope currentcontrols the zonal circulation and there is upwellingover the shelf break (Figs. 16c,d). As expected, the in-teraction between shelf and slope currents is most evi-dent when both have comparable velocities. The verti-cal velocities in EXP14 (Fig. 16d), for example, are onlyslightly smaller than those where there is no shelf in-flow (Fig. 9a). That is, for a sufficiently strong slopecurrent the shelf circulation has no significant influenceon the shelfbreak upwelling. In light of these results, itseems reasonable to ask what the relation is betweenthe shelf and the slope inflows in the real ocean. Ourexperiment with a shelf inflow of 0.1 m s�1 and a slope

of 0.2 m s�1 has transports of �0.4 and 5 Sv over eachregion. Although in this case the slope transport is anorder of magnitude larger than that over the shelf, thedifference in the real ocean is even larger. The shelftransport over the Patagonian shelf, for example, hasbeen estimated at 0.5 Sv, while the transport over theslope has a value that ranges between 40 and 70 Sv, thatis, two orders of magnitude larger (Palma et al. 2004;Peterson 1992; Piola and Matano 2001). For such con-trasting values it seems reasonable to conclude that theshelfbreak upwelling will be entirely controlled by theequatorward flow of the Malvinas Current.

5. Discussion

There is nothing paradoxical about the upwelling ofdownwelling (or cyclonic) currents, because the two

FIG. 16. Cross-shelf section of the vertical velocities for the experiments in which the shelf and the slope inflowswere (a) 0.1 and 0.0 m s�1 (EXP10); (b) 0.1 and 0.05 m s�1 (EXP12); (c) 0.1 and 0.1 m.s�1 (EXP13); (d) 0.1 and0.2 m.s�1 (EXP14). The shaded area corresponds to downwelling velocities and the unshaded to upwelling. Notethat experiment (a) has a different contour interval than the other experiments due to the smallness of theupwelling velocities. Contours are in units of 10�5 m s�1. (See Table 1.)


phenomena occur in different portions of the water col-umn. The downwelling is restricted to the BBL whilethe upwelling to the layers above it. In this article, weshow that the shelfbreak upwelling is associated withthe spreading of these currents onto the shelf, whichgenerates a diverging horizontal velocity field that iscompensated by upwelling from below. In the proposedmodel, the shelfbreak dynamic is not controlled by thedownslope buoyancy flux generated by a shelf current,as postulated by previous authors, but by the meridio-nal pressure gradient generated by the slope current.As our experiments demonstrate, shelfbreak upwellingwill occur in flat-bottomed domains or even in the ab-sence of a BBL. The shelfbreak upwelling, moreover, isnot evidence of the separation of the BBL but of thedownstream divergence of the slope currents, and itsmagnitude is proportional to the volume transport ofthat current.

The MAB has inspired the vast majority of studies onshelfbreak dynamics, and therefore it seems importantto mark its differences with the Patagonia shelf. Firstand foremost, it should be noted that the thermohalinestructures and circulation patterns of both regions aresubstantially different. The MAB, on the one hand, ischaracterized by a well-defined horizontal density gra-dient, which is imposed by the inflow of low-densitywaters from the Labrador Current and the absence of awell-defined western boundary current. The Patagoniashelf, on the other hand, is characterized by a nearlyhomogeneous density structure and the presence of oneof the largest western boundary currents of the WorldOcean (the Malvinas Current). The observed physicaldifferences explain the differences in their respectivemodels of shelfbreak upwelling. The upwelling in theMAB, on the one hand, has been related to the south-ward inflow of low-density waters, which, through ther-mal wind balance, lead to a reversal of the meridionalvelocities and a convergence and upwelling near thebottom boundary layer (Chapman and Lentz 1994;Pickart 2000). The key element in this system is thevertical shear of the current, which is generated by thehorizontal density gradient. The upwelling in the Pat-agonia shelf, on the other hand, is related to the pres-ence of the Malvinas Current. The key element in thissystem is the horizontal divergence of this current,which is caused by frictional effects. It is not possible touse the arguments exposed in this article to explain theupwelling in the MAB because that region doesn’t havea well-defined slope boundary current. The horizontaldivergence created by a shelf current is relatively smalland hence any strong upwelling should be attributed toother phenomena (e.g., the mechanisms postulated byChapman, Lentz, and Pickart). Similarly, it is not pos-

sible to use the arguments of their models to explain theupwelling in the Patagonia region because there is nocyclonic flow of low-density waters over the shelf.There is a cyclonic, wind-driven flow over the Patago-nia shelf, but this flow is largely unstratified (except bya thin mixed layer during the summer that doesn’t fulfillthe condition of a bottom trapped plume). Further-more, we demonstrate that such flow is quite ineffectivein generating shelfbreak upwelling.

The differences between the proposed models for theMAB and the Patagonia shelf becomes clearer whenconsideration is given to the fact that the former re-quires a stratified fluid (a sine qua non condition), whilethe latter does not. In fact, we show that the strongestupwelling is observed in completely unstratified fluids(EXP6; Fig. 9c). The two models also predict differentstructures for the BBL and the upwelling cell. TheMAB model predicts a convergence of the flow in theBBL, with an onshore component on the offshore sideof the shelfbreak front and an offshore component in-shore of it. It also predicts that the upwelling is startedin the BBL (e.g., Figs. 1, 19 in Pickart 2000). Thesepatterns are driven by the offshore migration of thefreshwater plume and have been well documented fromin situ observations (e.g., Houghton and Visbeck 1998;Houghton 1997; Pickart 2000). In the model proposedherein, however, there is no convergent pattern in theBBL. All the flow is directed offshore due to the factthat the horizontal density gradients are not strongenough to lead to a reversal of the inflow and the de-velopment of a deep countercurrent. Moreover, the off-shore downwelling in our experiments is much largerthan that in the inshore side, which is in obvious con-trast with the patterns proposed by Pickart.

The lateral spreading of a jet is a robust physicalphenomenon because its occurrence does not dependon a single process. If, for example, the bottom frictionis set to zero, the spreading of the jet will continuebecause of horizontal diffusion. The only case in whichthe presence of a slope current might not generateshelfbreak upwelling is the highly unrealistic limit ofvanishing diffusion and friction. In this limit, however,the jet will become very sensitive to small perturbationsand develop instabilities that should lead to lateralspreading with the consequent formation of meridionalpressure gradients. Thus, while the magnitudes of thehorizontal diffusion and bottom friction are poorlyknown parameters in numerical simulations, the lateralspreading of a slope current and the consequent forma-tion of shelfbreak upwelling should be a robust physicalprocess. It is important to note that because of the dis-parity of transports over the shelf and slope, only a verysmall portion of the slope current needs to spread onto


the shelf to generate a substantial shelfbreak upwelling.In the Patagonia region, for example, 2% of the Malvi-nas Current transport accounts for the entire shelftransport (Palma et al. 2004). Note also that the gen-eration of shelfbreak upwelling does not depend on theactual entrainment of slope waters onto the shelf but onthe influence of the offshore pressure gradient on theshelf circulation.

Acknowledgments. This article greatly benefitedfrom the criticism of three anonymous reviewers. R.Matano acknowledges the financial support of NSFGrant OCE-0726994, NASA Grants NAG512378,NNX08AR40G, and JPL contract 1206714. E. Palmaacknowledges the financial support of ANCYPT GrantPICT04-25533, CONICET Grant PIP04-6138, Univ.Nac. del Sur Grant F032 and Grant CRN2076 from theInter-American Institute for Global Change Research,supported by the U.S. National Science FoundationGrant GEO-045325.

APPENDIX

Momentum Balance

Momentum balance can be expressed with the fol-lowing equation:

1D

��DV�

�t

Tendency

� f VCoriolis

� g��Barotropic

PressureGradient

�1D

��

BaroclinicPressureGradient

�1D

�

�� KM

D

�V��

Vertical Difussion

� AAdvection& Horiz.

Dif

� 0,

where V is the horizontal velocity vector, f � fk is theCoriolis vector, � is the free-surface elevation, D is thewater depth, KM is the coefficient of vertical viscosity,and A encompasses all the terms related to advectionand horizontal diffusion. The barotropic and baroclinicpressure gradients are computed as

��

�x,��

�y�T

,

��

�x,��

�y�T

,

�gD2

�o��

0

��

�x�

�

D

�D

�x

��

��,��

�y�

�

D

�D

�y

��

��T

d�.

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