Dynamical Pathways of Antarctic Bottom Water in the Atlantic

622 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30

JAMES C. STEPHENS AND DAVID P. M ARSHALL Department of Meteorology, University of Reading, Reading, United Kingdom

(Manuscript received 4 November 1998, in ®nal form 17 June 1999)

ABSTRACT A reduced-gravity model is developed to represent the ¯ow of Antarctic Bottom Water (AABW) over realistic bathymetry in an Atlantic domain. The dynamics are based on the steady, planetary±geostrophic, shallow-water equations, including a linear bottom friction and a uniform diapycnal upwelling through the top of the model layer. The model solutions are broadly consistent with observations of the distribution and transport of AABW. The ¯ows occur predominantly along potential vorticity contours, which are in turn broadly oriented along bathymetric contours. The characteristic weak ¯ow across potential vorticity contours of the Stommel±Arons model is present as a small addition to this stronger forced mode along potential vorticity contours. As a consequence, mass balance is maintained not by hypothesized western boundary currents as in the Stommel±Arons model, but by the interplay between topographic slope currents and interior recirculations. In particular, a transposition is found in the ¯ow of AABW from the western side of the Brazil Basin south of the equator to the western ¯ank of the Mid-Atlantic Ridge north of the equator. This is also consistent with an analytical result derived by extending the Parsons mechanism to an abyssal layer overlying arbitrary bathymetry. The authors suggest that the results provide a more convincing zero-order picture than the Stommel±Arons model for the circulation of AABW and perhaps for abyssal water masses in general.

1. Introduction mel and Arons 1960a,b) has served as a paradigm for Antarctic Bottom Water (AABW) is an abyssal water our understanding of the thermohaline circulation. In the mass, easily distinguishable in hydrography by its cold Stommel±Arons theory, uniform upwelling in the interior (␪ Ͻ 1.8ЊC)1 and relatively fresh (S Ͻ 34.8 psu) sig- of a ¯at-bottomed ocean basin balances a localized source nature, which is also high in silica and low in oxygen. of dense water and drives a barotropic poleward interior In the Atlantic Ocean, AABW is comprised of Weddell ¯ow by vortex stretching; boundary currents are hypoth- Sea Deep Water, which is formed in the Southern Ocean esized to exist on the western side of ocean basins to against the Antarctic continent, and recirculating lower maintain continuity in the circulation. The upwelling in Circumpolar Deep Water, which enters the Atlantic via turn balances the downward diffusion of heat from the Drake Passage. In Fig. 1 we present a schematic of the surface ocean and maintains the permanent thermocline. circulation pathways and approximate transports de- However, one of the most interesting aspects of the duced from observations. The bathymetry of the abyssal circulation of AABW, which is not predicted by the basins and their interconnecting passages strongly in- Stommel±Arons theory, is the transposition of its ¯ow ¯uences the pathways of AABW as it ®nds its way from the western side of the Brazil Basin south of the northward into the western basins of the South Atlantic equator to the eastern side of the basin north of the and then spreads through fracture zones into the eastern equator. Here the current continues northward against basins. For reference, the bathymetric features referred the western ¯ank of the Mid-Atlantic Ridge, as repre- to in the text are represented in Fig. 2. sented in Fig. 1. The existence of such an eastern boundary current contradicts the Stommel±Arons theory, and a. Previous theory a number of mechanisms have been proposed to account The classical view of the abyssal circulation ®rst de- for this. One such mechanism is that of Kawase (1987), veloped by Stommel and Arons (Stommel 1958; Stom- who studied the spinup of a source-driven abyssal circulation numerically in a ¯at-bottomed basin straddling the equator, including a damping term on the interface 1 All temperatures referred to in this paper are potential temperatures. height of the abyssal layer to represent cross-isopycnal buoyancy mixing. In the limit of weak damping, the deep western boundary current (DWBC) generated by Corresponding author address: Dr. James C. Stephens, Geophys- ical Fluid Dynamics Laboratory, NOAA/Princeton University, Post the source in the northwest corner separates along the Of®ce Box 308, Forrestal Campus, Princeton, NJ 08542. equator, forming northward and southward ¯owing cur- E-mail: [email protected] rents along the eastern boundary. The eastern boundary

᭧ 2000 American Meteorological Society

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FIG. 1. A schematic of the major pathways and transports of AABW. Approximate transports in Sverdrups are shown in circles. The pathways connecting obervations of transport are inferred from the general concensus of obervations. The ®gure may in reality only represent the actual circulation in the very broadest sense. Shading indicates depths shallower than 4000 m (bathymetry from Row et al. 1995). currents then radiate long Rossby waves westward from where x and y are eastward and northward distances re- the eastern boundary to set up a Stommel±Arons interior spectively, f ϭ 2⍀ sin␪ is the Coriolis parameter, ␷ is the ¯ow. In the limit of strong damping the propagation of northward velocity, and gЈ is the reduced gravity. Equation long Rossby waves into the interior is prevented and (1) was integrated and rearranged by Nof (1990) to yield this acts to ``freeze'' the solution in the state containing eastern boundary currents. Tziperman (1987) proposed 2fT 1/2 h ϭ h2 Ϫ , (2) a similar mechanism to explain the existence of the we΂΃gЈ eastern boundary Mediterranean Undercurrent. Another explanation for the equatorial transposition where T ϭ # ␷hdxis the northward transport, and he of AABW follows from the work of Nof (1990), who and hw are the depths of the current at its offshore edge by analogy with the Parsons (1969) model of Gulf and the wall respectively. Here hw is always negative Stream separation, demonstrated that a northward-¯ow- in the Northern Hemisphere for he ϭ 0 [this case was ing surface geostrophic current above a motionless low- originally considered by Anderson and Moore (1979)]. er layer and against a western vertical wall can only For a ®nite value of he a jet can penetrate into the North- exist in the Northern Hemisphere if it has no outcrop ern Hemisphere, whereby hw decreases until hw ϭ 0 on the open ocean side. Nof considered a shallow water when the jet must then separate from the wall. Nof and layer of thickness h in the vicinity of the equator, which Olson (1993) extended the work of Nof (1990) by in- is geostrophic in the cross-stream direction; that is, cluding bathymetry in the form of a parabolic channel straddling the equator in a meridional direction. In this hץ f␷ ϭ gЈ , (1) case bathymetry relaxes the outcropping constraint, and -x inertial effects allow their abyssal current to cross isoץ

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FIG. 2. Locations of basins and topographic features referred to in the text. Shading indicates depths shallower than 4000 m (bathymetry from Row et al. 1995). baths and ¯ip sides in the channel as it crosses the closed geostrophic contours, regardless of the sign of the equator, strongly resemblant of the AABW ¯ow. topography, by a vortex stretching effect due to the con- In a related study to explain the transposition of vergence of the ageostrophic frictional ¯ow, which bal- AABW, Speer and McCartney (1992) introduced vari- ances upwelling over the closed contour region. Johnson able layer thickness into the Stommel±Arons model (1998) ®nds support for this mechanism in relation to (thereby distorting the potential vorticity contours from abyssal ¯ows over ocean trenches; alternatively Dewar zonal contours of the Coriolis parameter) and showed (1998) argues for a balance between bottom friction and that, for a prescribed eastern boundary thickness, sep- potential vorticity mixing over the bathymetry determin- aration of the abyssal layer also occured from the west- ing the strength of the anticyclonic circulation. ern boundary. The separation mechanism is analagous to Parsons (1969) and Nof (1990), although the northward ¯ow in this case is driven by upwelling. b. A generalized Parsons mechanism Further studies investigating the effect of bathymetry on the abyssal circulation include Rhines (1989), who In the presence of bathymetry, such as in Nof and considered planetary-scale zonal ¯ows over topography Olson (1993), eastern and western boundary currents and demonstrated blocking and resonance structures. can occur quite naturally as ¯ows that are geostrophic Straub and Rhines (1990) investigated isolated regions in the cross-stream direction, and the strong damping of closed geostrophic contours due to bathymetric hills limit of Kawase (1987) may thus be avoided. We can and bowls submerged in the abyssal layer and found generalize the result of Nof and Olson described above internal jets linking the closed contour region to the west- to an isopycnal layer that has two outcrops (as abyssal ern boundary. Kawase and Straub (1991) examined the water masses do) against arbitrary bathymetry. We rep- spinup of a similar scenario and demonstrated that a vig- resent the AABW as a shallow homogeneous layer over- orous cyclonic circulation is generated over regions of lain by a motionless upper layer of slightly lesser den-

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to achieve a cross-equatorial ¯ow, although Edwards and Pedlosky (1998a) and Edwards and Pedlosky (1998b) have recently pointed out the importance of both inertia and dissipation in the vicinity of the equator.

c. Structure of this paper In this paper we investigate the dynamically simple limit of a reduced-gravity single active layer beneath a motionless upper layer in a numerical study to determine the steady pathways of AABW in an Atlantic domain that incorporates realistic bathymetry. The paper is divided as follows: In section 2 we formulate the numerical model; in sections 3±6, having divided our At- lantic domain into four main subbasins, we discuss the model results for each basin and compare them with observations. In section 7 model sensitivity to various parameters is addressed, and section 8 consists of a concluding discussion.

2. Numerical model

FIG. 3. Schematic of model con®guration showing a layer of thick- a. Dynamical formulation ness h and density ␳ ϩ⌬␳, overlying topography at depth H and beneath a motionless upper layer of density ␳. We represent the AABW as a shallow homogeneous layer overlain by a motionless upper layer of slightly lesser density. Within this dynamical framework we sity, as represented in Fig. 3. With the inclusion of ba- choose a planetary±geostrophic formulation consistent thymetry, the transport integral of Nof (1990) becomes with the smallness of the oceanic interior Rossby num- -ber and include a bottom friction coef®cient in the mo ץgЈ T ϭ ␷hdxϭ h (h Ϫ H) dx mentum equations to represent the frictional decay of x our AABW layer by its interaction with the ocean ¯oorץ f͵͵ ,H beneath. Our formulation, excepting the bathymetryץgЈ ϭϪ A , (3) x and subsequent method of solution is very similar toץ f Ό΍ that of Speer et al. (1993). where H is the resting ocean depth, A is the cross-sec- Pedlosky (1987) demonstrates the equivalence of a tional area of the current, and bottom Ekman layer to that of Rayleigh friction with a 1/2 friction coef®cient, R ϭ (␬z f/2) /h ϭ f␦/2h, where ␬z Hץ H 1ץ ϭ hdx is the vertical eddy viscosity coef®cient, h is the layer x depth, and ␦ is Ekman-layer thickness. Since R ϭ f ϭץ ͵xAץΌ΍ 0 at the equator and we require friction to allow a cross- is the thickness-weighted mean slope on which the ¯uid equatorial ¯ow, we use the multiplier r␦/h in the mo- sits. Since gЈ and A are both positive de®nite, Eq. (3) mentum equations (hereafter we refer to the constant, r, demonstrates that, as the current crosses the equator, the as the friction coef®cient and r␦/h as the friction term). average topographic slope beneath it must change sign In order to avoid the friction term tending to in®nity at to maintain a transport in the same direction. We believe the equator we choose ␦ to be constant. Thus, our friction that the switching of AABW as it crosses the equator term incorporates an inverse dependence on layer thick- may be understood purely as a consequence of the above ness, as per Pedlosky (1987), and in neglecting f we integral constraint; the AABW ¯ow actually requires a allow ourselves to retain a nonzero friction coeffcient at reversal in the slope to continue northward. This result the equator where the friction serves as a crude param- is independent of the mechanism that is, of course, nec- eterization of the effects of inertia, thus enabling us to essary to modify the sign of the potential vorticity of retain our simple dynamical form. We include a uniform the current and enable it to cross the equator. In general diapycnal upwelling, represented by the coef®cient w in dissipation in some form is necessary to achieve mod- the continuity equation. In contrast to Speer and Mc- i®cation of the potential vorticity [although Nof and Cartney (1992), however, we neglect entrainment ¯uxes. Olson (1993) were able to obtain a cross-equatorial ¯ow For simplicity we also neglect the effect of eddies since using inertia alone since their current had zero potential their role in generating topographic recirculation gyres, vorticity]. We choose a purely frictional process in order such as in the Brazil Basin, is not well understood but

Unauthenticated | Downloaded 09/24/21 01:29 PM UTC 626 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30 we will make a posteriori statements about the possible and the Romanche and Chain Fracture Zones, are nar- role of eddies at a later stage in the paper. rower features than we are able to resolve with our In spherical coordinates, where ␪ and ␾ denote latitude model. Even if we could resolve them, their dynamics and longitude respectively, Re is the radius of the earth, undoubtedly involve inertial effects, which we neglect f is the Coriolis parameter, u and ␷ are velocities in the and locally enhanced mixing that both warms and mod- ␾ and ␪ directions, h is the (positive de®nite) layer thick- i®es the transport of AABW exiting the fracture zones. ness, H is the ocean depth; and, denoting partial deriv- Thus, in the regions of the above fracture zones we atives in the j direction by subscipts j, our momentum impose the bathymetry manually. We regard the fracture and continuity equations take the following form: zones purely as a means of connecting the circulation between basins and they have been tuned to yield sen- gЈ ␦ Ϫf␷ ϩ (h Ϫ H)␾ ϭϪru, (4) sible transports. The sensitivity of the results to this Re cos␪ h procedure is discussed at a later stage in the paper. gЈ ␦ Models such as Straub and Rhines (1990) and Kawase fu ϩ (h Ϫ H)␪ ϭϪr ␷, (5) and Straub (1991), where topography is submerged in the Rhe active layer, do not capture the ``subtle interaction between 1 baroclinicity and bottom slope'' (Hallberg and Rhines ␩t ϩ [(hu)␾␪ϩ (h␷ cos␪)]ϭ Ϫw. (6) 1996) that occurs due to isopycnals outcropping against Re cos␪ bathymetry. Since the lateral distribution of AABW is In the absence of upwelling and in the limit r 2 k f 2 de®ned by outcropping isopycnals, which are generally (as per Kawase and Straub 1991), the velocity may be dif®cult to model numerically, we use a ¯ux-corrected eliminated from the above equations to yield a single transport (FCT) numerical formulation according to Za- equation for the interface displacement, ␩ ϭ h Ϫ H, of lesak (1979) on a C grid (Arakawa and Lamb 1977). The the following form: high-order component of the numerical discretization we choose for the FCT is fourth order and centered in space, gЈ HgЈ H and third order Adams±Bashforth in time. ␩ ϩ ␩ Ϫ ␩ t 22␾␪Horizontal pressure gradients are computed according Reecos␪ ΂΃fRcos␪ ΂΃f ␪␾to Scheme 2 in Bleck and Smith (1990), which ensures 1 gЈ␦ gЈ␦r ␩ the reliable computation of velocities where isopycnals ഠ r␩ ϩ ␪ . (7) overlie variable topography. This method relies on an (R cos␪)22fRf␾␾ 2 2 ee΂΃␪ averaging of the pressure gradient computed within the The terms on the left-hand side denote the combined isopynic layer at surrounding grid boxes, subject to planetary±topographic long Rossby wave propagation. weighting coef®cients computed as a function of the The terms on the right-hand side act as a diffusion op- number of massless grid boxes involved in each pressure erator on ␩, which arises from the presence of the fric- gradient computation. tion coef®cient r␦/h. The magnitude of the diffusion 2 2 operator is gЈ␦r/f ϭ Ldr, where Ld is the internal de- c. Boundary conditions formation radius based on the reduced gravity gЈ at the interface between the AABW layer and the layer above, The southern boundary of our model is situated pur- and the Ekman-layer depth ␦. posefully at the latitude of the ¯ow of AABW from the Argentine Basin into the Brazil Basin via the Rio Grande Rise since here the northward transport is horizontally b. Numerical formulation con®ned and has been determined as 6.6 (Ϯ0.4) Sv (Sv We will be seeking to determine the steady distri- ϵ 106 m3 sϪ1) by Speer and Zenk (1993) (using a level bution of AABW in our domain. This is obtained by of no motion at a depth close to 2ЊC). We impose a integrating Eq. (6) numerically to a steady state, com- layer thickness condition to represent this transport, puting the velocities diagnostically from the momentum choosing the 1.6ЊC surface as our layer interface since, equations [Eqs. (4), (5)] at each time step. throughout the passage of AABW around the Atlantic, The model resolution is ½Њ in a domain extending most of the transport is contained below this isotherm from 50ЊNto30ЊS, 80ЊWto20ЊE. The model bathym- (McCartney and Curry 1993). We neglect any ¯ow of etry is taken from Row et al. (1995) and is generated AABW into the eastern South Atlantic that may occur by computing the local depth maximum in ¼Њ regions via the Walvis Ridge, as indicated by cold bottom tem- of the domain, smoothing the result with a moving av- peratures in Fuglister (1960) since Warren and Speer erage ®lter of order 6 and taking every second point. (1991) have inferred this to be very small. The southern The local maximum is computed to avoid constricting boundary thickness condition is presented as a zonal the circulation of our model AABW layer and the section in Fig. 4; out¯ows through the southern bound- smoothing helps to ensure that the horizontal pressure ary of the model do not occur. gradient is able to be resolved by the model. Gaps in At the northern boundary of the model it is necessary the Mid-Atlantic Ridge, such as the Vema Fracture Zone that the interior ¯ow of AABW determines the boundary

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TABLE 1. Transport of AABW as a function of latitude, as computed by McCartney and Curry (1993). Latitude Transport (Sv) 0ЊS 4.3 11ЊS 5.5 23ЊS 6.7 30ЊS 7.0

potential energy store replenishes kinetic energy, which is in turn drained by work done in the bottom Ekman layer. We view the frictional coef®cient not only as a FIG. 4. Zonal section along 30ЊS to show the model layer thickness representation of dissipation within the bottom Ekman condition at the southern boundary (adapted from Speer and Zenk 1993). Bathymetry is represented by light shading and the AABW layer, but also as a device to allow ¯ow across the equa- layer by dark shading. The latitude and longitude of each end of the tor and through the fracture zones; in reality, these pro- section is marked at the base of the ®gure. The depth of the section cesses will involve inertial effects. We will discuss mod- in meters is shown at the left of the ®gure. el sensitivity to the values of upwelling and the pre- scription of the friction term in section 7. Steady solutions for the distribution of AABW are condition. We impose a condition of zero meridional determined by initializing the model with the southern gradient in the interface height ; this corresponds to ␩ boundary condition and allowing AABW to gradually u 0 in the geostrophic limit, thus requiring ¯ow to ϭ ®ll up the model abyss as it propagates around the do- be normal to the boundary. In practice, the ¯ow out of main in a manner resembling a gravity current, at the the northern boundary of the domain is very weak and speed of a long internal topographic wave (ϳ1±2 m has no discernible effect on the interior ¯ow. sϪ1). We do not consider the spinup process itself since we are unable to resolve the internal deformation radius d. Parameter values (typically around 4 km in our model). The model results presented have all been integrated for approximately The reduced gravity g for the model is chosen to be Ј 500±600 years and are very close to a steady state. For constant throughout the domain and is computed as g Ј comparison, the time needed to ¯ush our AABW layer ϭ g[␴ 4(AABW) Ϫ ␴ 4(LNADW)]/␳ 0. We take the grav- 2 Ϫ1 out of the model (the residence time) is around 60 yr. itational acceleration, g ϭ 9.8 m s , ␴ 4(AABW) ϭ Ϫ3 Ϫ3 46.02 kg m , and ␴ 4 (LNADW) ϭ 45.85 kg m [which are approximately average values for the density anom- 3. Circulation in western South Atlantic alies of AABW below the 1.6ЊC isotherm and the lower (Brazil Basin)

North Atlantic Deep Water (LNADW) above], and ␳ 0 ϭ 1000 kg mϪ3, which yields gЈϭ1.7 ϫ 10Ϫ3 m 2 sϪ1. For the purposes of the discussion that follows in this, The Ekman-layer thickness ␦ is ®xed at 25 m. and the following three sections, we divide up the model For the solutions presented in the next four sections, domain into four areas: north and south of the equator 3±6, the diapycnal upwelling velocity is chosen as w ϭ and east and west of the Mid-Atlantic Ridge. We ®rst 2 ϫ 10Ϫ7 msϪ1, suggested as an area-averaged value present a summary of observations and then compare by McCartney and Curry (1993), and the friction co- and contrast the model results in each area in turn. ef®cient as r ϭ 1.15 ϫ 10Ϫ6 sϪ1, which corresponds to a spindown timescale of approximately 10 days for a a. Observations current that is the thickness of the Ekman layer; this implies that a current moving at 0.1 m sϪ1 would travel The ϳ7 Sv ¯ow (Speer and Zenk 1993) of AABW less than 100 km in this time. The observed longevity from the Argentine Basin into the Brazil Basin via the of abyssal slope currents would appear to suggest that Rio Grande Rise at 30ЊS continues northward as a our friction coef®cient is too large: however, MacCready DWBC against the continental slope of South America (1994) has recently demonstrated that the spindown of and ®lls the abyssal Brazil Basin to a depth of over 1500 abyssal slope currents is lengthened considerably due m. Recent transport estimates from McCartney and Cur- to the large potential energy to kinetic energy ratio re- ry (1993), computed using 1983 CTD data from the siding in isopycnals upturned against the topography. R/V Knorr and a level of no motion at the depth 1.9ЊC, MacCready interprets the spindown timescale of abyssal decrease northward, as shown in Table 1. Interestingly, currents as the time required for the cross-slope Ekman a recent ¯oat study by Hogg and Owens (1999) shows transport to drain away the isopycnal displacement char- little evidence for a DWBC of AABW north of 20ЊS. acterizing a current: the transport of such currents is This is clear evidence of the uncertainty in our obser- able to remain fairly constant during this process as the vations of abyssal ¯ows and suggests the need for many

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recirculation gyre to the north; deMadron and Weatherly (1994) explained the existence of the northern recirculation gyre as due to the de¯ection of denser AABW (the Weddell Sea Deep Water component) eastward by shoaling of the bathymetry at the equator.

b. Model In Fig. 6 we show transport vectors in the western South Atlantic from the model. The circulation exhibits both a strong DWBC and a northern cyclonic gyre that is closed by a strong eastward jet along the equator (which is shown separately in Fig. 7), in keeping with deMadron and Weatherly (1994). The interior velocities in our model are very weak: since there are no eddy ¯uxes in our study, this supports the explanation of Spall (1994) that these interior ¯ows are eddy-driven. The corresponding potential vorticity, q ϭ f/h, for 2 FIG. 5. Circulation schematic for Brazil Basin reproduced from the circulation is shown in Fig. 8. The transport vectors deMadron and Weatherly (1994). follow potential vorticity (q) contours closely and in the DWBC also follow the bathymetric contours. Along the equator, however, the ¯ow is across q contours, which more ¯oats over a long timescale in order to obtain a vanish at singularities at the eastern and western extents good picture of the mean circulation. of the basin. Strong cyclonic ¯ows around closed q The decline in transport between 30ЊS and the equator contours are reminiscent of the Kawase and Straub suggests upwelling across isotherms. The decline is un- (1991) mechanism for closed contour spinup. Here, even (0.3 Sv between 30Њ and 23ЊS and 1.2 Sv between however, the mechanism is different since the recircu- 23Њ and 11ЊS), which may be due to either variability in lation cannot be disconnected from the DWBC and the the upwelling rate or uncertainty in the transport esti- eastward de¯ection of part of it across q contours as a mates. The latter can occur due to differences in the frictionally driven jet. The ¯ow is able to conserve q selection of a level of no motion, bottom triangle ap- immediately away from the equator because in the po- proximation, and temporal variability and directly affect tential vorticity equation, estimates of the area-averaged upwelling. The difference in transport between 23Њ and 11ЊS suggests a diapycnal f ␦ w (ϭϪr ␨ Ϫ f , (8 ١ ´ u upwelling rate, w ϭ 3.4 ϫ 10Ϫ7 msϪ1, which is almost ΂΃hhh22 identical to an estimate by Warren and Speer (1991) south of 11ЊS; McCartney and Curry (1993) suggests that this where ␨ is the relative vorticity, and the frictional drain value is suspiciously high for an area-averaged value of q on the right-hand side of the equation has very however. For instance, considering the difference in small contributions from both the friction term and the transports between 30Њ and 11ЊS, an estimate of w ϳ 2 upwelling. ϫ 10Ϫ7 msϪ1 is obtained. In addition, considering a level In Fig. 9 we show a zonal section along 23ЊS from of no motion corresponding to 1.8ЊC, McCartney and the model simulation. This is to be compared with the Curry (1993) show that the upwelling rate between 23Њ observed hydrography in Fig. 10 (recall that the 1.6ЊC and 11ЊS decreases signi®cantly to w ϭ 2.2 ϫ 10Ϫ7 m isotherm represents the top of our AABW layer). The sϪ1. depth of the isopycnal in midbasin is both ¯atter and In the interior of the Brazil Basin, against the strong ϳ200 m greater in the model than in the data. The uptilt northward ¯owing DWBC, deMadron and Weatherly of isopycnals at the western boundary representative of (1994) and Speer and Zenk (1993) ®nd a weak south- the DWBC is clearly evident in both ®gures, although ward transport of AABW and then a reversal back to it is the colder components of AABW that ¯ow more weak northward transport adjacent to the Mid-Atlantic strongly northward in the data. Ridge. Superimposed on this ¯ow are abyssal recirculations, which Spall (1994) suggests are driven by eddy ¯uxes of potential vorticity from instability in the DWBC of AABW ¯owing north. DeMadron and Weath- 2 Our potential vorticity, q ϭ f/h, differs from the Ertel potential z, in that our potential vorticity implicitlyץ/␴ץvorticity, Q ϭϪ␴ Ϫ1f erly's circulation schematic for AABW is reproduced includes a contribution from bottom density gradients. This precludes in Fig. 5 and is broadly similar to that of Speer and comparison with maps of abyssal potential vorticity recently produced Zenk (1993) except that it includes a strong cyclonic by O'Dwyer and Williams (1997).

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FIG. 6. Model transport vectors for circulation in the western South Atlantic (Brazil Basin). The friction coef®cient r ϭ 1.15 ϫ 10Ϫ6 sϪ1 and the upwelling velocity w ϭ 2.0 ϫ 10Ϫ7 m sϪ1. Arrows corresponding to a very strong eastward jet along the equator (approximately four times larger than the maximum interior ¯ow) are limited in magnitude to enable visualization of the interior ¯ow. The magnitude of the transport vector indicated for scale purposes at the top of ®gure encompasses all vectors of size greater than or equal to this magnitude. Model bathymetry is shaded at intervals of 500 m from 4000 m and deeper; the darkest shading represents depths greater than 6000 m.

4. Circulation in western North Atlantic corner of the Brazil Basin. AABW encounters a sill at the entrance to the equatorial channel: the combined a. Observations effect of this and the gradual shoaling of the Ceara AABW exits the Brazil Basin into the western North Abyssal Plain as AABW exits the channel prevents the Atlantic via a zonal equatorial channel in the northwest densest AABW (colder than 1.0ЊC) from ¯owing north-

FIG. 7. Model transport vectors for circulation in western South Atlantic (Brazil Basin) in the vicinity of the equator. The friction coef®cient r ϭ 1.15 ϫ 10Ϫ6 sϪ1 and the upwelling velocity w ϭ 2.0 ϫ 10Ϫ7 msϪ1. Model bathymetry is shaded at intervals of 500 m from 4000 m and deeper; the darkest shading represents depths greater than 6000 m.

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FIG. 9. Zonal section along 23ЊS from the model simulation shown in Fig. 6. Bathymetry is represented by light shading and the AABW layer by dark shading. The latitude and longitude of each end of the section is marked at the base of the ®gure. The depth of the section in meters is shown at the left of the ®gure.

silica and temperature ®elds (Clarke et al. 1980), and north of the Bahama Banks and Hispaniola (Tucholke et al. 1973) have been interpreted by Warren (1981) as FIG. 8. Model potential vorticity, q ϭ f/h, contours for the western fairly de®nite evidence for a general counterclockwise South Atlantic (Brazil Basin). circulation of AABW in the western North Atlantic. AABW has also been found in the vicinity of the Blake± Bahama outer ridge near 30ЊN (Amos et al. 1971). ward (Whitehead and Worthington 1982). McCartney and Curry (1993) estimate that 4.3 Sv of AABW ¯ows b. Model across the equator from the Brazil Basin. A more recent and smaller estimate at the equator of 2.0 Sv has been In Fig. 12 we show transport vectors from the model made by Hall et al. (1997); the equator is a particularly for the western North Atlantic. Potential vorticity (q ϭ dif®cult place to calculate the transport because con- f/h) contours are shown in Fig. 13. In this region, in ventional geostrophic estimates cannot be made. contrast to the Brazil Basin, there is much structure in North of the equator AABW no longer ¯ows as a the transport vectors, also evidenced in the q ®eld which DWBC, and between ϳ8ЊN and 16ЊN the northward ¯ow of AABW is concentrated against the western slope of the Mid-Atlantic Ridge (Fuglister 1960). The western boundary ¯ow at 10ЊN is, in fact, reported by Johns et al. (1993) and McCartney (1993) to be southward; Johns et al. (1993) compute a transport of about 3 Sv for waters colder than 1.8ЊC. Additionally Molinari et al. (1992) report a southeastward ¯ow of waters colder than 1.8ЊC of 2±3 Sv concentrated against the boundary at 14ЊN. Thus, the circulation of AABW north of and in the vicinity of the equator has been interpreted as a recirculation by Friedrichs and Hall (1993), and in Fig. 11 we reproduce their circulation schematic, which is broadly consistent with these observations. At 11ЊN almost half of the AABW transport ¯ows into the eastern basin via the Vema Fracture Zone, and McCartney et al. (1991) estimate the transport of AABW colder than 2.0ЊC here as 2.1±2.3 Sv. This supports the larger estimate of McCartney and Curry (1993) for the cross-equatorial transport of AABW. North of 24ЊN there is no con®ned current of AABW against the Mid-Atlantic Ridge (Fuglister 1960), indi- cating that the water from it spreads out onto the sea ¯oor in some manner. Traces of AABW beneath the FIG. 10. Zonal section along 23ЊS reproduced from McCartney and Gulf Stream on 50ЊW, which show up clearly in the Curry (1993).

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FIG. 11. Circulation schematic for AABW ¯ow in tropical North Atlantic reproduced from Friedrichs and Hall (1993). Estimated transports in Sverdrups are indicated in circles.

FIG. 12. Model transport vectors for circulation in the western North Atlantic. The friction coef®cient r ϭ 1.15 ϫ 10Ϫ6 sϪ1 and the upwelling velocity w ϭ 2.0 ϫ 10Ϫ7 msϪ1. The magnitude of the transport vector indicated for scale purposes at the top of ®gure encompasses all vectors of size greater than or equal to this magnitude. Model bathymetry is shaded at intervals of 500 m from 4000 m and deeper; the darkest shading represents depths greater than 6000 m.

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FIG. 14. Zonal section along 3ЊN from model simulation shown in Fig. 12. Bathymetry is represented by light shading and the AABW layer by dark shading. The latitude and longitude of each end of the FIG. 13. Model potential vorticity, q ϭ f/h, contours for the west- section is marked at the base of the ®gure. The depth of the section ern North Atlantic. in meters is shown at the left of the ®gure. is likely to re¯ect nonlinear control of the ¯ow in the 5. Circulation in eastern North Atlantic manner of Rhines (1989). a. Observations The northward transport at 1ЊN is 4.6 Sv, which con- forms well with the estimate for a cross-equatorial trans- The ϳ2.1 Sv transport through the Vema Fracture port of 4.3 Sv by McCartney and Curry (1993). By about Zone ¯ows eastward. McCartney et al. (1991) ®nds that 3ЊN almost the entire northward transport of AABW the ¯ow subsequently bifurcates into a northward (1.3± lies against the Mid-Atlantic Ridge, as shown in Fig. 3.0 Sv), and a weaker eastward ¯ow (1.8±3.9 Sv) along 14. Thus, friction is suf®cient to break the along-isobath the southern boundary of the Gambia Abyssal Plain. con®nement of the outcrop lines of the current under Thus there is an increase in transport of the AABW by geostrophic balance, and the current switches to ba- at least 50% and a necessary warming of the layer re- thymetry of opposite slope as it crosses the equator, as sults; this is in large part due to the presence of a sill predicted by the transport integral [Eq. (3)]. Without [®rst hypothesized by Heezen et al. (1964)]. McCartney friction in the model, the current is unable to cross the et al. (1991) ®nd no communication of AABW between equator at all. In reality we expect inertia to be important the Cape Verde and Sierra Leone Basins (and therefore in this region too (as in Nof and Olson 1993). the northeastern and southeastern Atlantic Ocean) via The DWBC against the Mid-Atlantic Ridge continues the Kane Gap. northward, where approximately 1.8 Sv is diverted east- The circulation schematic from McCartney et al. ward through the Vema Fracture Zone at 11ЊN. At 16ЊN (1991) for the AABW ¯ow in the eastern North Atlantic the current bifurcates westward and northward. The is reproduced in Fig. 15. In this schematic the southern northward branch continues as a weakened DWBC, boundary ¯ow loops counterclockwise and westward to where beyond ϳ25ЊN it peels off westward to feed a join the northward branch. Friedrichs and Hall (1993) counterclockwise interior ¯ow. Both the westward arm present a different picture for the AABW circulation in of the bifurcation and the interior ¯ow feed a strong the vicinity of the Gambia Abyssal Plain, as shown in recirculation associated with a deep basin along 20ЊN Fig. 11. They ®nd weak southward ¯ow in the vicinity in the west and a southeastward DWBC from 17Њ to of McCartney et al.'s (1991) northward branch, which 8ЊN, consistent with the recirculation of Friedrichs and forms a closed cyclonic recirculation around the perim- Hall (1993) and also Johns et al. (1993) and McCartney eter of the Gambia Abyssal Plain. The northward ¯ow (1993). postulated by McCartney et al. (1991) is motivated by It is striking, in fact, that the broad characteristics of a northward bulge in contours of bottom potential tem- the ¯ow ®eld are consistent with each of the observa- perature, although they note the uncertainty in their tions above. We also note the lack of any coherent signal transport estimate arising from the rough topography of poleward ¯ow in the interior of the basin as predicted above the Mid-Atlantic Ridge. The confusion is en- by the Stommel±Arons model. hanced since a meridional density section near 35ЊWin

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FIG. 15. Circulation schematic for AABW ¯ow in the eastern North Atlantic reproduced from McCartney et al. (1991).

McCartney et al. (1991) clearly exhibits isopycnals in model it is possible to observe the northward branch of the AABW density range tilted upward against the Mid- McCartney et al. (1991). Atlantic Ridge, which would appear to indicate south- There are two northward bifurcations around the pe- ward ¯ow unless there is a strong in¯uence from over- rimeter of a shallower plateau at around 18ЊN, which lying waters. merge to form a broad northward ¯ow at 25ЊN. Some The AABW ¯ow continues northward and is little of this ¯ow turns southward against the Mid-Atlantic documented until the Canary Basin, where at 35ЊN and Ridge and the majority continues into the Canary Basin beyond Saunders (1987) ®nds that the northward ¯ow where there are a number of recirculations and the ¯ow becomes concentrated in the east. structure is quite complicated. Beyond 35ЊN the northward ¯ow becomes more concentrated in the east of the b. Model Canary Basin, as noted by Saunders (1987). Potential vorticity, q ϭ f/h, contours for the model In Fig. 16 we show transport vectors from the model circulation are shown in Fig. 17. South of approximately in the eastern North Atlantic. We recall that the ba- 28ЊN, q contours, transport vectors, and bathymetry are thymetry of the Vema Fracture Zone has been widened closely aligned. North of 28ЊN, however, q gradients are since the model resolution is insuf®cient to resolve this much weaker and there are recirculating elements to the feature. We have tuned the bathymetry to yield a trans- ¯ow, particularly north of 35ЊN where we suspect that port consistent with the 2.1-Sv estimate of McCartney there is some degree of free mode resonance operating et al. (1991); in this simulation it is approximately 1.8 (Rhines 1989). Sv. The circulation ®eld exhibits the strong eastward ¯ow of AABW along the Gambia Abyssal Plain and the lack 6. Circulation in eastern South Atlantic of ¯ow through the Kane Gap, as noted by McCartney a. Observations et al. (1991). There is no bifurcation northward against the eastern ¯ank of the Mid-Atlantic Ridge however, AABW enters the Guinea Basin via the Romanche and, in fact, the ¯ow against the Mid-Atlantic Ridge is Fracture Zone and the Chain Fracture Zone. The com- both southward and weakened by northward bifurcation, bined Romanche and Chain Fracture Zone transport has consistent with the cyclonic recirculation of Friedrichs recently been estimated at 1.22 (Ϯ0.25) Sv by Mercier and Hall (1993). We will discuss this further in a later and Speer (1998), divided fairly equally between frac- section when we see that for different parameters in our ture zones, from two, two-year-long moored-current-

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FIG. 16. Model transport vectors for circulation in eastern North Atlantic. The friction coef®cient r ϭ 1.15 ϫ 10Ϫ6 sϪ1 and the upwelling velocity w ϭ 2.0 ϫ 10Ϫ7 msϪ1. The magnitude of the transport vector indicated for scale purposes at the top of ®gure encompasses all vectors of size greater than or equal to this magnitude. Model bathymetry is shaded at intervals of 500 from 4000 m and deeper; the darkest shading represents depths greater than 6000 m. meter arrays. These are the ®rst long-term measurements and the Chain Fracture Zones in the model. For this of transport at these points. reason we have positioned the through¯ow from the The circulation of AABW in the eastern South At- Brazil Basin into the eastern South Atlantic entirely via lantic has generally been little documented. However, a single fracture zone located at approximately 3ЊS. We Warren and Speer (1991) have conducted a detailed believe that this introduces no more than a cosmetic study and produced circulation schematics as different difference to the resulting transport vectors in the east- depths based on Stommel±Arons dynamics. In Fig. 18 ern South Atlantic, although clearly the magnitude of we reproduce their circulation ®eld for depths greater the ¯ow into the basin is effectively prescribed. In Fig. than 4000 m, which shows the characteristic Stommel± 19 we present transport vectors from the model in the Arons interior poleward ¯ow and a DWBC, which clos- eastern South Atlantic. Potential vorticity, q ϭ f/h, con- es the mass balance; here the DWBC is poleward in the tours are shown in Fig. 20. north and equatorward in the south. Warren and Speer Figure 19 shows an intense boundary current that argue from comparison with sections along 11Њ and follows the bathymetry around a shallow plateau situ- 24ЊS, that this circulation ®eld is consistent with data. ated at approximately 6ЊS and ¯ows southward. This eastern boundary current broadens and weakens between 10Њ and 20ЊS and then intensi®es as the bathym- b. Model etry steepens between 20ЊS and the southern boundary As a result of the along-equatorial proximity of the of the model. There is a northward ¯ow along the eastern Romanche Fracture Zone (along 0ЊS) and the Chain side of the Mid-Atlantic Ridge as a cyclonic continu- Fracture Zone (along 1ЊS), combined with the purely ation of the eastern boundary current. The ¯ows in the frictional nature of the model dynamics at the equator, interior of the relatively ¯at Angola Basin are very we encountered problems representing the Romanche weak.

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FIG. 17. Model potential vorticity, q ϭ f/h, contours for the eastern North Atlantic.

The circulation ®eld in Fig. 19 is very different from the circulation schematic shown in Fig. 18, which was computed by Warren and Speer (1991). Of particular interest is the ¯ow at 24ЊS, along which we show a zonal section of potential density reproduced from War- ren and Speer (1991) in Fig. 21. This very clearly shows the eastern con®nement and uptilt of dense isopycnals

(below around ␴ 4 ϭ 45.87), which appears consistent FIG. 18. Angola Basin circulation beneath 4000 m computed ac- with the strong southward eastern boundary current in cording to Stommel±Arons dynamics and reproduced from Warren our model. Warren and Speer interpret this signal dif- and Speer (1991). The interior ¯ow is poleward (southward); the ferently as newer water carried southward by the Stom- western boundary current ¯ow (hypothesized to maintain continuity) reverses at 15ЊS. mel±Arons interior ¯ow, which is then recirculated as older water to be carried in the northward branch of their hypothesized western boundary current against the which precludes ¯ow across the equator in our model: Mid-Atlantic Ridge. There is clearly much room for in reality, inertia has to be important at the equator. We interpretation in the limited observations available; have investigated the dependence of layer spindown on however, the consistency of our model thus far in our the layer thickness, and have found little detectable dif- basins leads us to believe that our interpretation may ference between model solutions incorporating a friction well be valid. term as either r␦/h or just as the coef®cient r itself (not shown). 7. Model sensitivity For friction coef®cients smaller than we have used in the model solutions presented in sections 3±6, the model a. Friction coef®cient is unstable, as mass is unable to cross the equator ef- We have investigated the sensitivity of our results to ®ciently. Recent work by Borisov and Nof (1998) and both the formulation and the magnitude of the friction Nof and Borisov (1998), in which cross-equatorial ¯ow term in the model. It is common in formulations of a determines its own frictional coef®cient, supports larger bottom friction term to neglect the effect of the Coriolis values at the equator than in the interior, consistent with parameter f and the layer thickness h which should both our observation of instability at the equator for low be present if representation of the effect of a bottom values of the frictional coef®cient. For a friction coef- Ekman layer is desired (Pedlosky 1987). In the solutions ®cient twice as large as that used for the solutions thus presented in sections 3±6 we have neglected the Coriolis far (i.e., with a spindown timescale of around 5 days at parameter dependence since the friction term including the Ekman layer depth as opposed to 10 days) we ®nd an f dependence has zero magnitude at the equator, some differences in the model solutions. In Fig. 22 we

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FIG. 19. Model transport vectors for circulation in the eastern South Atlantic. The friction coef®cient r ϭ 1.15 ϫ 10Ϫ6 sϪ1 and the upwelling velocity w ϭ 2.0 ϫ 10Ϫ7 msϪ1. The magnitude of the transport vector indicated for scale purposes at the top of ®gure encompasses all vectors of size greater than or equal to this magnitude. Model bathymetry is shaded at intervals of 500 m from 4000 m and deeper; the darkest shading represents depths greater than 6000 m.

FIG. 20. Model potential vorticity, q ϭ f/h, contours for the east- FIG. 21. Zonal potential density section along 24ЊS reproduced ern South Atlantic. from Warren and Speer (1991).

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FIG. 22. Model transport vectors for circulation in the western North Atlantic. The friction coef®cient r ϭ 2.3 ϫ 10Ϫ6 sϪ1 and the upwelling velocity w ϭ 2.0 ϫ 10Ϫ7 msϪ1. The magnitude of the transport vector indicated for scale purposes at the top of ®gure encompasses all vectors of size greater than or equal to this magnitude. Model bathymetry is shaded at intervals of 500 m from 4000 m and deeper; the darkest shading represents depths greater than 6000 m. present the western North Atlantic solution for this in- b. Upwelling coef®cient creased friction coef®cient for comparison with Fig. 12. Flows are generally broader as a result of the effect of Upwelling in the model acts to control the spatial the diffusive action of friction on the interface height extent of the AABW layer. We ®nd that increasing the Ϫ7 Ϫ7 Ϫ1 [see Eq. (7)] and weaker as a result of the enhanced upwelling coef®cient from 2 ϫ 10 to 3 ϫ 10 ms spindown, although they are qualitatively very similar has little observable effect on the circulation in the west- in the two cases. In Fig. 23 we present the eastern North ern basins; however, it does act to severely limit the Atlantic solution for the increased friction coef®cient extent of the AABW layer in the eastern basins. Sim- Ϫ7 for comparison with Fig. 16. In this case we note more ilarily decreasing the upwelling coef®cient to 1 ϫ 10 Ϫ1 than a qualitative difference since there is now a north- ms has little observable effect on the western basins ward branch to the circulation at the western edge of but it enhances the transport of the circulation in the the Gambia Abyssal Plain, as found by McCartney et eastern basins (hardly affecting its pathways), particu- al. (1991), as opposed to the cyclonic circulation we larly for the eastern North Atlantic where the excess observed originally, consistent with Friedrichs and Hall ¯ow leaves the model through the northern boundary (1993). It is surprising that we see this difference in at 50ЊN. both the interpretation of observations and the model solutions, although, in view of the uncertainity in both c. Fracture zones magnitude and the parameterization of our frictional term, to suggest the possibility of time variability in the In our model, the fracture zones do little more than path of the real AABW ¯ow would certainly be pre- to connect basins together: In reality, there is signi®cant mature. mixing within fracture zones that modi®es water masses,

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FIG. 23. Model transport vectors for circulation in the eastern North Atlantic. The friction coef®cient r ϭ 2.3 ϫ 10Ϫ6 sϪ1 and the upwelling velocity w ϭ 2.0 ϫ 10Ϫ7 msϪ1. The magnitude of the transport vector indicated for scale purposes at the top of ®gure encompasses all vectors of size greater than or equal to this magnitude. Model bathymetry is shaded at intervals of 500 m from 4000 m and deeper; the darkest shading represents depths greater than 6000 m. unlike our simple model. We require the model fracture that the fracture zones not only control transport mag- zones to be at least two grid boxes wide to obtain a nitudes, but they also segregate water masses. As transport effectively. Their transport is approximately AABW makes its way around the Atlantic, it entrains tuned to observations by increasing their width (which LNADW to make a range of water masses with inter- generally has a large effect) or by varying their depth mediate properties. The fracture zones largely block the (which has a smaller, but still signi®cant, effect). The passage of the densest, pure AABW, but allow these transport in our model is sensitive to the fracture zone lighter hybrid water masses to pass through. The con- geometry, particularly in the case of the Romanche and sequences for the circulation of AABW within the east- Chain Fracture Zones near the equator. Here the com- ern basins could well be signi®cant. The sensitivity of bination of our poor representation of the fracture zones the fracture zone geometry emphasizes the problems of and our simple formulation for the friction term provides representing through¯ows in coarse-resolution ocean additional dif®culties and minor changes to the bathym- models, particularly where there are a number of water etry in the fracture zones (ϳ100 m) can easily change masses in the vertical negotiating a fracture zone. the transport by an order of magnitude. Since the fracture zones effectively provide the eastern boundary for 8. Concluding discussion the circulation in the western basins (Straub et al. 1993), it is important to emphasize that the circulation of We have developed a reduced-gravity model con- AABW may well be sensitive to the detailed dynamics sisting of a single active layer beneath a motionless within these fracture zones. A proper sensitivity study upper layer to represent the ¯ow of AABW over realistic will require a model with vastly improved horizontal bathymetry in an Atlantic domain. The model dynamics and vertical resolution and with a full treatment of the are based on the steady, planetary±geostrophic, shallow- nonlinear accelerations. A reviewer has also pointed out water equations, including a linear bottom friction and

Unauthenticated | Downloaded 09/24/21 01:29 PM UTC MARCH 2000 STEPHENS AND MARSHALL 639 a uniform diapycnal upwelling through the top of the development and supporting experiments. J. Geophys. Res., 95 model layer. Our model solutions are notably consistent (C3), 3273±3285. Borisov, S., and D. Nof, 1998: Deep, cross-equatorial eddies. Geo- with observations of the pathways and transports of phys. Astrophys. Fluid Dyn., 87, 273±310. AABW, even in the eastern basins where we might have Clarke, R. A., H. Hill, R. F. Reiniger, and B. A. Warren, 1980: Current anticipated that the model representation of the AABW system south and east of the Grand Banks of Newfoundland. J. pathways would be somewhat poorer due to mixing Phys. Oceanogr., 10, 25±65. within fracture zones. deMadron, X. D., and G. Weatherly, 1994: Circulation, transport and bottom boundary layers of the deep currents in the Brazil Basin. The modeled ¯ow occurs predominantly along po- J. Mar. Res., 52, 583±638. tential vorticity, q, contours (except in the immediate Dewar, B., 1998: Topography and barotropic transport control by vicinity of the equator), which are in turn generally bottom friction. J. Mar. Res., 56, 295±328. oriented along bathymetric contours. This demonstrates Edwards, C. A., and J. Pedlosky, 1998a: Dynamics of nonlinear cross- the importance of bathymetry in shaping the circulation equatorial ¯ow. Part I: Potential vorticity transformation. J. Phys. Oceanogr., 28, 2382±2406. pathways of abyssal currents, which occurs because ba- , and , 1998b: Dynamics of nonlinear cross-equatorial ¯ow. thymetry modi®es the characteristics along which long Part II: The tropically enhanced instability of the western bound- Rossby waves propagate information [see Eq. (7)]. ary current. J. Phys. Oceanogr., 28, 2407±2417. The existence of a signi®cant ¯ow component along Friedrichs, M. A. M., and M. M. Hall, 1993: Deep circulation in the q contours presents a very different picture for the cir- tropical North Atlantic. J. Mar. Res., 51, 697±736. Fuglister, F. C., 1960: Atlantic Ocean Atlas of Temperature and Sa- culation to that of the Stommel±Arons model. The rea- linity Pro®les and Data from the International Geophysical Year son for the difference is that in the Stommel±Arons of 1957±58. Woods Hole Oceanographic Institution Atlas Series, model the small ¯ow across q contours that results from 209 pp. upwelling constitutes the entire interior ¯ow, whereas Hall, M. M., M. McCartney, and J. A. Whitehead, 1997: Antarctic here it is masked by the larger forced mode along q. Bottom Water ¯ux in the equatorial Western Atlantic. J. Phys. Oceanogr., 27, 1903±1926. Flows are also driven across q by the bottom friction Hallberg, R., and P. Rhines, 1996: Buoyancy-driven circulation in an term, but again this effect is small except at the equator. ocean basin with isopycnals intersecting the sloping boundary. In addition, rather than having to hypothesize western J. Phys. Oceanogr., 26, 913±940. boundary currents to close the mass balance as in the Heezen, B. C., R. D. Gerard, and M. Tharp, 1964: The Vema Fracture Stommel±Arons picture, topographic slope currents are Zone in the equatorial Atlantic. J. Geophys. Res., 69, 733±750. obtained in our model as part of the solution as in the Hogg, N. G., and W. B. Owens, 1999: Direct measurement of the deep circulation within the Brazil basin. Deep-Sea Res., 46, 335± work of Straub et al. (1993). The mass balance at each 353. latitude is maintained by the interplay between these Johns, W. E., D. M. Fratantoni, and R. J. Zantopp, 1993: Deep western currents and interior recirculations. boundary current variability off northeastern Brazil. Deep-Sea We suggest that our results provide a more convincing Res., 40, 293±310. zero-order picture than the Stommel±Arons model for Johnson, G., 1998: Deep water properties, velocities, and dynamics over ocean trenches. J. Mar. Res., 56, 329±341. the circulation of AABW, and perhaps for abyssal water Kawase, M., 1987: Establishment of deep ocean circulation driven masses in general. Work is currently underway to extend by deep-water production. J. Phys. Oceanogr., 17, 2294±2317. this model to more layers and to include the overlying , and D. Straub, 1991: Spinup of source-driven circulation in an North Atlantic Deep Water and possibly Antarctic In- abyssal basin in the presence of bottom topography. J. Phys. termediate Water. Oceanogr., 21, 1501±1514. MacCready, P., 1994: Frictional decay of abyssal boundary currents. J. Mar. Res., 52, 197±217. Acknowledgments. The authors wish to thank Ric Wil- McCartney, M. S., 1993: Crossing of the equator by the deep western liams for thought provoking discussions prior to sub- boundary current in the western Atlantic Ocean. J. Phys. Ocean- mission and for providing JCS with a timely and pro- ogr., 23, 1953±1974. ductive visit. The authors wish to thank Doron Nof and , and R. A. Curry, 1993: Transequatorial ¯ow of Antarctic Bot- an anonymous reviewer for helpful comments on the tom Water in the western Atlantic Ocean: Abyssal geostrophy at the equator. J. Phys. Oceanogr., 23, 1264±1276. original manuscript. NERC Grants GR3/10157 and , S. L. Bennet, and M. E. Woodgate-Jones, 1991: Eastward ¯ow GR8/03760 are gratefully acknowledged. through the Mid-Atlantic Ridge at 11ЊN and its in¯uence on the abyss of the eastern basin. J. Phys. Oceanogr., 21, 1089±1121. Mercier, H., and K. G. Speer, 1998: Transport of bottom water in the REFERENCES Romanche Fracture Zone and the Chain Facture Zone. J. Phys. Amos, A. F., A. L. Gordon, and E. D. 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