Three-Dimensional Dynamics of the Subsurface Countercurrents and Equatorial Thermostad. Part I: Formulation of the Problem and Generic Properties

Bach Lien Hua Laboratoire de Physique des Océans, CNRS-IFREMER-UBO, Plouzané, France

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Frédéric Marin Laboratoire de Physique des Océans, CNRS-IFREMER-UBO, Plouzané, France

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Richard Schopp Laboratoire de Physique des Océans, CNRS-IFREMER-UBO, Plouzané, France

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Abstract

A fully three-dimensional primitive equation simulation is performed to “reunite” the local equatorial dynamics of the subsurface countercurrents (SCCs) and thermostad with the large-scale tropical ventilated ocean dynamics. It captures (i) the main characteristics of the equatorial thermostad, the SCCs' location and their eastward evolution, and the potential vorticity budget with its equatorial homogenization to zero values and (ii) the large-scale meridional shoaling of the thermocline equatorward. It supports the idea that the two-dimensional Hadley cell mechanism proposed by Marin et al. is a candidate able to operate in a fully three-dimensional ocean. The main difference between the 2D Hadley cell mechanism and the oceanic 3D case is that for the 3D case the large-scale meridional velocity at zeroth order is geostrophic, while the cell mechanism is a next-order, small-scale mechanism. A detailed budget of the zonal momentum equation is provided for the ageostrophic dynamics at work in the SCCs. The mean meridional advection and the Coriolis term dominate, discounting the possibility that lateral eddies play a major role for the SCCs' creation. A 3½-layer idealized ventilation model, calibrated to the three-dimensional simulation parameters, is able not only to capture the tropical density structure, but also to isolate the main controlling factors leading to the triggering of the equatorial secondary cells with its associated jet and thermostad, namely, the shoaling of the equatorial thermocline because of low potential vorticity injection at distant subduction latitudes. It is also shown that equatorial recirculation gyres play a quantitative role that may be of the same order of magnitude as ventilation from higher latitudes.

Current affiliation: Program in Atmospheric and Oceanic Sciences, Princeton University, Princeton, New Jersey

Corresponding author address: Dr. Richard Schopp, Laboratoire de Physique des Océans, UMR6523 CNRS-IFREMER-UBO, BP70, Plouzané 29280, France. Email: rschopp@ifremer.fr

Abstract

A fully three-dimensional primitive equation simulation is performed to “reunite” the local equatorial dynamics of the subsurface countercurrents (SCCs) and thermostad with the large-scale tropical ventilated ocean dynamics. It captures (i) the main characteristics of the equatorial thermostad, the SCCs' location and their eastward evolution, and the potential vorticity budget with its equatorial homogenization to zero values and (ii) the large-scale meridional shoaling of the thermocline equatorward. It supports the idea that the two-dimensional Hadley cell mechanism proposed by Marin et al. is a candidate able to operate in a fully three-dimensional ocean. The main difference between the 2D Hadley cell mechanism and the oceanic 3D case is that for the 3D case the large-scale meridional velocity at zeroth order is geostrophic, while the cell mechanism is a next-order, small-scale mechanism. A detailed budget of the zonal momentum equation is provided for the ageostrophic dynamics at work in the SCCs. The mean meridional advection and the Coriolis term dominate, discounting the possibility that lateral eddies play a major role for the SCCs' creation. A 3½-layer idealized ventilation model, calibrated to the three-dimensional simulation parameters, is able not only to capture the tropical density structure, but also to isolate the main controlling factors leading to the triggering of the equatorial secondary cells with its associated jet and thermostad, namely, the shoaling of the equatorial thermocline because of low potential vorticity injection at distant subduction latitudes. It is also shown that equatorial recirculation gyres play a quantitative role that may be of the same order of magnitude as ventilation from higher latitudes.

Current affiliation: Program in Atmospheric and Oceanic Sciences, Princeton University, Princeton, New Jersey

Corresponding author address: Dr. Richard Schopp, Laboratoire de Physique des Océans, UMR6523 CNRS-IFREMER-UBO, BP70, Plouzané 29280, France. Email: rschopp@ifremer.fr

1. Introduction

A remarkable feature of the equatorial Pacific Ocean is the presence, at the base of the thermocline, of two intense and narrow eastward jets, the subsurface countercurrents (SCCs), on both sides of the equator. These jets are persistent both in time and space, and are observed at 3°S and 3°N in the western part of the basin (Fig. 1a). They can reach up to 30 cm s−1, with a maximum velocity core that is quite distinct from the equatorial undercurrent (EUC), which is located right at the equator within the thermocline. The SCCs are continuous across the whole equatorial basin and experience a poleward shift from about midbasin to the eastern boundary (Johnson and Moore 1997). It must be noted that the cumulated transport of the south and north SCCs is comparable to the transport of the EUC. A detailed review of the SCCs properties in the Pacific Ocean can be found in Rowe et al. (2000). The SCCs are the location of narrow fronts in potential vorticity (PV), with fronts in both the planetary and relative components, suggesting that the dynamics of these jets is essentially nonlinear. A downstream decreasing density within the jet cores suggests the occurence of nonconservative dynamics. These jets are the poleward limits of a homogeneous region (Fig. 1b), the 13°C thermostad, in which temperature, salinity, and low potential vorticity are uniform (Gouriou and Toole 1993). This thermostad is located at the base of the thermocline, which is seen to shoal from the subtropics toward the equator in the Southern Hemisphere. The SCCs are also observed in the Atlantic Ocean, where they are called North and South Equatorial Undercurrents (Stramma and Schott 1999). Nevertheless, even though the South Atlantic subsurface countercurrent seems to have similar properties to its Pacific analogs, the North Equatorial Undercurrent is located farther away from the equator and presents stronger temporal variability (Cochrane et al. 1979).

Detailed numerical studies of the SCCs, from realistic high-resolution simulations, were performed in the case of the Pacific Ocean (Ishida et al. 1998; Donohue et al. 2002). Some primary (and secondary) SCCs are produced in these models, but (i) the jets are seen to be highly variable in time and position, (ii) the relative component of PV plays no role in the creation of a PV front at the latitude of the jet, and (iii) the simulated jets do not experience any poleward shift from west to east.

A first explanation for the SCCs was proposed by McPhaden (1984): a linear and vertically diffusive model can produce weak downward diffusive extensions of the EUC, but the so-formed eastward currents cannot have a local maximum distinct from the EUC, and nonlinearities cannot be neglected. Assuming an a priori eastward jet in the western part of the basin, Johnson and Moore (1997) explained the SCCs poleward shift from the equator as the consequence of potential vorticity conservation, in an inertial jet model in which an eastward shoaling of the thermocline is imposed in the vicinity of the equator. Finally, McCreary et al. (2002) proposed that the local eastern boundary upwelling, induced by a meridional wind stress, can force a rather broad current in the equatorial region beneath the thermocline. Unlike the previous local equatorial mechanisms for the SCCs, a distant formation mechanism was proposed by Tsuchiya (1981, 1986) to explain the equatorial thermostad: he advocated that the 13°C water mass was formed by convection at a distant location (in the Tasmania Sea for the Pacific), before being advected to the equator along a large-scale isopycnal route characterized by a minimum of potential vorticity.

Marin et al. (2000) proposed a unified mechanism to explain the formation of the ensemble SCCs—13°C thermostad. This mechanism is based on an analogy in the observations between the tropical atmosphere and the equatorial ocean. In the atmosphere, two intense eastward jets, the jet streams, are observed near the tropopause at about 35°N and 35°S, and delimit a tropical region in which potential temperature is homogenized. Even though the meridional scales are different in the atmosphere and in the ocean, and in spite of the presence, in the ocean, of the EUC that complicates the picture, Marin et al. (2000) proposed that the SCCs and 13°C thermostad are the oceanic analogs to the atmospheric jet streams and tropical homogeneous region. Applying the atmospheric Hadley cells theory (Held and Hou 1980) to the equatorial ocean, they show, in an idealized two-dimensional framework, that the SCCs could be the result of an angular-momentum redistribution process within secondary meridional cells. These oceanic Hadley cells take place in the lower thermocline, and are triggered by the large-scale meridional gradient of density, due to the equatorward shoaling of the thermocline. By thermal wind, the equatorial uplift of the thermocline induces a westward shear that is surface intensified: at the SEC latitude near the equator, the surface flow is westward while at the SCC latitude, because of angular momentum redistribution, this shear expresses eastward flow at the SCC depth with weaker amplitude surface velocity. The involved dynamics is not only nonlinear, but also nonconservative since diapycnal mixing is efficient within the meridional cells. The mechanism is essentially local (equatorial), but forced at distance by the large-scale meridional slope of the thermocline.

In this paper, we present a numerical simulation that attempts to generalize the oceanic Hadley cells mechanism to the fully three-dimensional ocean. In the atmosphere, the meridional gradient of density, which is the forcing of the Hadley cells, is imposed externally by the radiative balance. In the ocean, the forcing of the Hadley cells is internally provided by the large-scale meridional shoaling of the thermocline, which is itself the dynamical result of a large-scale three-dimensional circulation within the thermocline, as predicted by the ventilation theory (Luyten et al. 1983). A three-dimensional model of the subsurface countercurrents must thus simulate the dynamics of both the forcing and the secondary equatorial circulation. Consequently, this model is required to be both a basin-scale model capable of reproducing the ventilated thermocline and a high-resolution primitive equation model capable of simulating the local Hadley cells mechanism in the vicinity of the equator.

In section 2, we present a simple configuration for a layered model of the ventilated thermocline that can reproduce the meridional slope of the thermocline in the vicinity of the equator. In section 3, we present the idealized primitive equation model used to simulate both the ventilated thermocline and the equatorial circulation. This model is a continuous extension, in the vertical, of the previous layered model for the ventilated thermocline. In section 4, a simulation is presented in which the equatorward large-scale shoaling, the SCCs, and the equatorial thermostad are present.

2. The equatorial slope of the thermocline

The key feature to force the 2D Hadley cell mechanism in the ocean is the existence of a meridional slope for the thermocline. The question that arises is to identify the physical parameters that govern its dynamics in the vicinity of the equator. One common explanation for the thermocline structure in the subtropics is provided by the ventilation theory, whose cornerstone is PV conservation for water columns once they have subducted (Luyten et al. 1983). In this context, the barotropic circulation is directly given by the Ekman pumping, and the knowledge of PV distribution at the subduction latitudes is required to determine entirely the shape of the thermocline. The latter point led us to formulate an analytical layered model that gives a straightforward control of the PV prescription at the subduction latitudes, in the spirit of Pedlosky and Robbins (1991), who have indeed shown that a sloping mixed layer leads to a quantitative augmentation of the thermocline ventilation. However, our model proposes a different approach for parameterizing the effects of the meridional variations of a finite mixed layer depth.

a. The ventilation framework

Our 3½-layer model to simulate the thermocline (three moving layers over a resting ocean) follows Luyten et al. (1983), Liu (1994), and McCreary and Lu (1994), and is detailed in the appendix. It is based on the zonal integration of the total meridional geostrophic Sverdrup transport from the eastern boundary to a given longitude leading to the relation
i1520-0485-33-12-2588-e1
where γi = g(ρi+1ρi)/ρ is the reduced gravity for layer i. Notations correspond to those of Fig. 2. Here D20(x, f) is a function of the Coriolis parameter f and the Ekman pumping
i1520-0485-33-12-2588-eq1
and is given by
i1520-0485-33-12-2588-eq2

In our layered model, layer 3 corresponds to the lower thermocline (where SCCs occur), layer 1 is in contact with the forcing, and layer 2 is the upper thermocline.

In this model, the wind stress is imposed as a body force in a surface layer of constant thickness Z0 (Liu 1994). The subduction latitudes are defined as the equatorward limit of a region where the density surfaces are prescribed to remain horizontal (Fig. 2). In this configuration, the variable mixed layer depth corresponds to the finite depths Z1 and Z2 of the flat isopycnal surfaces at the subduction latitudes. Even though we do not have a mixed layer per se, as in Pedlosky and Robbins (1991), this formulation allows us to control the PV prescription at the subduction latitudes and the strength of lateral induction. This is a generalization of McCreary and Lu's (1994) PV forcing to a 3½-layer case. As shown in Pedlosky (1996), the finite depth of the layers at the outcrop generates shadow zones in all layers. Note that, in this configuration, the isopycnal distribution along the eastern boundary is identical to the prescribed isopycnal distribution in the density-forced region. This implies that (i) the problem is well posed at the eastern boundary in terms of mass budget and (ii) that there is no flow in the absence of wind forcing, in contrast with Pedlosky and Robbins's (1991) formulation in which the meridional density gradient in the mixed layer generates a zonal geostrophic flow that must be balanced at the eastern boundary, by a reverse zonal flow beneath the thermocline. For the sake of simplicity, we impose a zonally invariant zonal wind stress and zonally invariant mixed layer depths.

In the following, we will use this layered model by taking its equatorial limit, although the original ventilation theory has been built foremost for the dynamics of the thermocline in the subtropics. Such an approach has already been taken by Liu (1994) and McCreary and Lu (1994), arguing that the Sverdrup relation (1) for the layer depths presents no singularity at the equator.

b. Equatorial pathways for the ventilation

Our purpose is to identify a simple criterion for controlling the meridional slope of the various layers of the thermocline near the equator, which is needed to activate secondary meridional motions. A necessary condition for a finite meridional slope at the equator is that ventilation reaches the equator to permit zonal shearing motions. As shown in Liu (1994), this is controlled by the position at the equator of the western boundaries of the shadow zones in each layer (Fig. 3) given in our model by
i1520-0485-33-12-2588-e2
for the deeper layer and
i1520-0485-33-12-2588-e3
for the middle layer.
  1. In case the xS2 streamline does not reach the equator but rather the western boundary (xS2 < 0), layers 2 and 3 will be motionless, and no meridional slope is expected for the thermocline at the equator.

  2. In case only the xS2 streamline reaches the equator (xS1 < 0 < xS2), there is a supply of ventilated waters in layer 2 at the equator via the ocean interior, but layer 3 lies in the shadow zone. A meridional slope develops at the base of layer 2 in the vicinity of the equator, but the base of layer 3 remains flat.

  3. In case both xS2 and xS1 streamlines reach the equator (i.e., xS1 > 0), the direct supply with ventilated waters at the equator occurs in both layers. In such case a meridional slope occurs at the base of both layers 2 and 3.

As noted by Liu (1994) and according to (2)–(3), an interior pathway for the ventilated waters toward the equator is favored by intense trade winds, by large equatorial basins, and by a low stratification (i.e., low values of γ1 and γ2). In the remainder of this section, we focus on the case in which xS2 > 0, that is, where ventilated waters reach the equator in layers 2 and 3.

c. The meridional slope

The meridional slope of the equatorial thermocline, the base of layer 3, can be inferred from the Sverdrup relation in each of the dynamical regions through Taylor expansions in the Coriolis parameter f. The algebraic details are given in the appendix. For instance, the meridional slope of the equatorial thermocline in the fully ventilated region V is given by
i1520-0485-33-12-2588-e4
where Q2 and Q3 are the values of potential vorticity, respectively, for layers 2 and 3 at the equator, and Γ3 = γ1 + γ2 + γ3 is the total reduced gravity g(ρ4ρ1)/ρ. The values of Q2 and Q3 are provided by their values at the subduction latitudes f2 and f3, which are advected to the equator by the ventilated pathways. It is obvious from the previous formulas, based on conserved finite PV reaching the equator, that the slope of the base of the deepest moving layer (z3 here) is positive, whereas the slope of z1 is always negative. This property remains valid in the semiventilated regions R, and means that the base of the thermocline shoals equatorward, while the top of the thermocline deepens equatorward, in agreement with the thermocline fanning, which is observed in the tropical oceans. In the fully ventilated region V, the slope of the intermediate interface can be positive, negative, or can even vanish. According to (4), the meridional slope of the equatorial thermocline is a function of the reduced gravities and of the magnitude of potential vorticity at the subduction latitudes. A detailed examination of Q2 and Q3 (appendix) shows that the meridional slope of layer 3 near the equator is an increasing function of Z2 and Z3, and a decreasing function of the subduction latitudes f2 and f3. Thus, the meridional slope at the equator is remotely controlled by the way we constrain PV at subduction in our model.

d. The zonal slope

Figure 4 presents a schematic zonal section of the equatorial thermocline. According to conservation of PV (A5)–(A6), (A7), and (A8), the ventilated layers have zero thickness right at the equator. The depth z(x) of the thermocline at the equator is thus defined as z(x) = z3(x, 0) = z2(x, 0) = z1(x, 0) in the fully ventilated region (V), as z(x) = z2(x) = z1(x) in the semiventilated regions (M) and (R), and finally z(x) = z1(x) in the shadow zone (S). The zonal thermocline slope can easily be computed by the Sverdrup relation. It experiences a large variation from east to west, given by
i1520-0485-33-12-2588-e5
It is weak in the western part of the basin, because of the parabolic shape of the thermocline depth in each of the dynamical regions, and because of the decrease of the coefficient Γ from east to west, which indicates a zonal change in the true reduced gravity for the equatorial thermocline. Schematic Fig. 4 agrees with observations in the equatorial Pacific Ocean (Colin et al. 1971), where the zonal slope of the thermocline is seen to increase from west to east with a progressive eastward flattening of the deepest isopycnal layers of the thermocline. We want to emphasize that the zonal slope of the thermocline will be very weak in the western part of the basin due to an increase of the stratification, and we can thus expect 2D dynamics, which assumes zonal invariance, to apply in the western region.

3. A primitive equation model that constrains potential vorticity injection

Our main conjecture is that SCCs result from secondary circulations triggered by the large-scale meridional shoaling of the thermocline. Such dynamics cannot be simulated within the ventilation framework, which is intrinsically geostrophic and conservative. We therefore need a primitive equation (PE) model that is capable of reproducing both the large-scale ventilated thermocline and the local ageostrophic dynamics near the equator. We have opted to be as faithful as possible to our 3½-layer formulation for PV forcing, in order to have an analytical handle on the meridional slope of the thermocline.

The prescription of the subduction latitudes in the PE model strictly follows their prescription in the layered model (Fig. 5a). The subduction latitudes are again defined as the equatorward limit of a region where the isopycnals are forced to remain flat, with a Rayleigh damping toward a prescribed density profile ρ̃(z). In a PE configuration, the subduction latitudes are thus continuously defined once the limit zf(y) of the density-forced region is prescribed. Equatorward of this density-forced region, the model dynamics is free to adjust. The equatorward limit of the density region is the analog of the variable mixed layer depth in the analytical model. In this view, the subduction latitude for a given layer is at the intersection of the density-forced surface with the zf(y) line. It should be kept in mind that the calibration of our PE model to the previous analytical model will be performed through the prescription of the zf(y) line. However, our PE model is not a layered model, but has a continuous density stratification in the gray-shaded region of Fig. 5a.

We will present numerical PE simulations of the ventilated thermocline for a flat, rectangular Northern Hemisphere basin, with symmetric conditions with respect to the equator. The basin has a zonal extension of 40°, which is comparable to the Atlantic Ocean width, and extends meridionally to 40°N, with a constant depth H = 5000 m. The PE equations are solved with the S-Coordinate Primitive Equation Model (SPEM) (Haidvogel et al. 1991).

The forcing of this model is provided by imposing a zonal wind stress (Fig. 6) in a surface layer of constant thickness (Z0 = 35 m). This wind stress is similar to Liu's (1994): it has no zonal dependence and induces a negative Ekman velocity from 35°N to the equator. The density profile ρ̃(z) is chosen to be piecewise linear (Fig. 5b). The equatorward limit zf(y) of the density-forced region is piecewise linear too (Fig. 5), and the restoring time is 10 days in the density-forced region. Note that our vertically continuous configuration allows an easy comparison to the layered model, since there is a direct correspondance between the density, the depth, and the latitude along the equatorward limit zf(y) of the density-forced region: once a layer is defined by the respective densities of its upper and lower interfaces, the mean density of this layer can be easily deduced, and the subduction latitude for this layer is the latitude at which the upper isopycnal surface intersects the zf(y) line.

The boundary conditions at the western, northern, and eastern boundaries are no heat flux and a slip condition. In order to conserve PV, we have no explicit vertical diffusion and dissipation in the model. Small biharmonic horizontal dissipation and diffusion are used, which require the following boundary conditions:
i1520-0485-33-12-2588-eq3
Note that the explicit horizontal dissipation and diffusion can cause cross-isopycnal mixing since isopycnal surfaces are not flat. The boundary conditions differ from the analytical model at the eastern boundary. Indeed, in a primitive equation model, the total zonal velocity, to which both geostrophic and ageostrophic components contribute, must vanish at the eastern boundary. In the ventilation theory, the geostrophic approximation is used, so that the geostrophic zonal velocity then vanishes. In order to faithfully simulate the ventilated thermocline in our PE model, we chose to apply an additional restoring toward ρ̃(z) in a zonally thin layer at the eastern boundary, with a time constant equal to 10 days. Besides, an additional Laplacian dissipation of momentum is imposed in western, northern, and eastern boundary layers. The maximum value for the viscosity coefficient is νmax = 10 000 m2 s−1 and varies as an hyperbolic tangent away from the boundary. For example, at the western boundary,
i1520-0485-33-12-2588-eq4
These boundary layers are centered at xWB = 2.5° at the western boundary, xEB = 35° at the eastern boundary, and at yNB = 35°N at the northern boundary. The characteristic width Δx (or Δy at the northern boundary) is chosen to be the same for all the boundaries, equal to 1°.

For each of the simulations presented, the model is integrated 24 yr with a resolution of ⅔° in longitudes and latitudes, then 6 yr with a resolution of ⅓°, finally 2 yr with a resolution of ⅙°. The constant dissipation and diffusion biharmonic coefficients are adapted to the different horizontal resolutions, and are equal to 1013 m4 s−1 first, then 3 × 1011 m4 s−1, and finally 3 × 1010 m4 s−1. The initial condition is a rest state with the vertical stratification, which is prescribed in the density-forced region. The vertical grid has 32 points, with a vertical resolution of 25 m in the upper 600 m.

4. Numerical simulation for the SCCs

a. Large-scale meridional structure of the thermocline

The resulting PE run density distributions (continuous lines) at 15° and 30° in longitude from the western boundary are shown in Figs. 7a,b. They reveal meridional slopes of opposite signs at the base and the top of the equatorial thermocline, with the largest slopes in the western part of the basin. These features are consistent with the analytical 3½-layer model. The parameters calibration (Table 1) has been performed using the following rules: the base of the third layer is chosen such that xs2 > 0, that is, there is an interior ventilation of the third layer at the equator (Fig. 3). The interfaces between layers 1 and 2 and between 2 and 3 are such that γ1γ2 approximately, where ρ1, ρ2, and ρ3 are the depth average density value of the prescribed stratification for each layer in the density-forced region. We moreover assume that the density of the motionless deep layer ρ4 is given by the density of the base of layer 3. This actually amounts to calibrate our continuous model mostly for the vicinity of the equator, where the SCCs (third) layer is assumed to be the deepest moving layer: it is well known that the analytical solutions of an N-½-layer model (for large N values) will exactly coincide with those of a 3½-layer one in dynamical regions where there are only three moving layers. We have empirically checked that it ensures the best match between the PE and ventilation solutions in terms of the horizontal structure of the dynamical regions of ventilation near the equator (Fig. 3).

The dotted lines in Figs. 7a,b are the analytical solutions provided by the 3½-layer model. There is a very good agreement between the overall meridional shape of the first two layers identified by different shading, while the agreement is good for the third layer only between the equator and 10°N. This can be easily understood since a 3½-layer model cannot fully correspond to a continuous problem, and we would obviously need more layers in order to represent the behavior of the deepest isopycnal layers in the subtropics.

Moreover, the meridional slope of the thermocline is seen to decrease from west to east, as predicted by our analytical model (Figs. 7a,b). The bowl-shape of the deepest moving layers and its variations from west to east behave as expected in the ventilated theory.

The large-scale zonal shape of the thermocline near the equator (3°N) is in agreement with the analytical model (Fig. 8). The zonal slope is the most pronounced in the eastern basin and is weaker in the western part. The flattening of the deepest isopycnals is also observed.

b. Characteristics of the SCCs

The local equatorial response is illustrated in Fig. 7c, that is a zoom of Fig. 7a between 0° and 10°N and 0 and 400 m. In the vicinity of the equator, the solution obviously departs from the ventilated solution in a region of about 5° width for the entire thermocline and upper subthermocline. A splitting of the isopycnals near 150 m right at the equator is produced and is the geostrophic signature of the equatorial undercurrent. In the lower thermocline and in the layers just beneath, a pycnostad is present. According to this PE model, the latitudinal limit of validity of the ventilation theory is significantly larger than the inertial scale of the equatorial undercurrent, which has been proposed by Pedlosky (1987). This suggests that the dynamics, which is responsible for the thermostad, has a strong impact on all the layers above, implying interactions between pycnostad and thermocline. A second point to note concerns the theoretical depth of the thermocline at the equator [Z(15°) = 170 m, see appendix], which is located in the lower part of the thermocline, while the EUC core is close to 100 m and lies in the upper part of the thermocline and the position of the midthermocline is 150 m. These differences in depth reveal that there is a large ageostrophic component for the EUC and moreover that the main EUC transport does not occur in layer 2. Our numerical simulation of the EUC is therefore a mixture of the ventilated EUC solution obtained in a 2½-layer model by Pedlosky (1987) and of a 1½-layer numerical simulation of Cane (1979a,b) where the EUC constitutes the eastward branch of an equatorial gyre. In the latter paper, the entire EUC transport recirculates westward in a meridionally tight equatorial version of a Fofonoff-like inertial gyre.

The subsurface countercurrents in our simulation have a velocity maximum close to 20 cm s−1 and their cores are quite distinct from the EUC, separated from it by a westward-flowing structure. The meridional scale of the core (≈50 km half-width) is compatible with Rowe et al. (2000) and the 2D model (Marin et al. 2000), but the downward extent of the SCCs is not deep enough, leading to a too weak transport. At this point, we do not yet fully understand which parameters govern the vertical extension of the SCCs.

Another eastward current occurs near the surface at 7°N, although not linked to the Sverdrup theory. It has a geostrophic nature that is due to the upward and poleward slope of the upper thermocline. The strength of this “geostrophic NECC” is controlled by the choice of zf(y), in our model.

The zonal evolution of SSCs can be infered from Fig. 9, which presents the instantaneous distribution of zonal velocity for three isopycnal surfaces that bracket the thermostad layer. A narrow, intense, and continuous jet, centered around 3°N is seen throughout the basin. It is essentially zonal between 5° and ≈17°E, that is, in the ventilated region V, whereas it shifts poleward from 17° to 35°E. This behavior is compatible with the zonal slope of the thermocline at 3°N (Fig. 8), and with a poleward shift that is only present in the eastern half of the basin where the zonal slope of the thermocline is the largest (Johnson and Moore 1997). The velocity maximum shifts from the base of the thermostad (ρ = 26.50) in the western part to ρ = 26.0 in the eastern basin, showing that the SCC core crosses the isopycnal surfaces from west to east, as in the observations of Rowe et al. (2000).

In Figs. 9b,d the theoretical separation lines of the different dynamical regions (white continuous lines) is overlaid on the instantaneous zonal velocity field, revealing a clear correspondence between region V and the region where the SCC is strictly zonal. Eastward of region V, strong meanders are present along the jet axis. We want to emphasize that there is a strong temporal variability in the solution, as seen in Fig. 9a that presents the instantaneous distribution of velocity on ρ = 26.25 kg m−3. However, as corroborated by Figs. 9b,d, the zonal component u remains eastward throughout the basin along the jet axis and the strong variability thus mostly concerns the meridional component. Our simulations differ from Ishida et al. (1998) and Donohue et al. (2002), whose instantaneous velocity fields exhibit neither continuous eastward jet nor poleward shift of the primary SSC.

The eastward poleward shift and lightening of the SCC core seen in the instantaneous fields are still present in time average fields (Figs. 10a,b), concomitantly with an eastward shoaling (Fig. 10c). The lightening is the most important in the first third of the basin, while the jet core has a quasi-constant density in the middle of the basin, suggesting that the diapycnal mixing within the jet core occurs preferentially in the region where layer 3 is directly supplied with subtropical ventilated waters in the basin interior. In the vicinity of the eastern boundary, both the intense instability waves and the density restoring toward a flat density structure may explain the large variation in density in the jet core. The velocity maximum (Fig. 10d) remains fairly constant through the basin, in agreement with observations of Rowe et al. (2000); this result is however at variance with Johnson and Moore's (1997) prediction of a downstream acceleration of SCCs in their strictly PV conservative model applied to near-equatorial dynamics.

The SCC is the location of an abrupt PV front (thick line) that results from the combined effects of planetary (thin continuous line) and relative (dotted line) components of PV diagnosed on an isopycnal surface (Fig. 11b). A meridional homogenization of PV occurs equatorward of the jet, in a 2°-wide region. PV homogenization is due to the compensating effects of the planetary and relative vorticity components, while on the contrary both terms contribute additively to the enhancement of the front at 3°N. A typical meridional scale for this front is less than ½° half-width. In parallel, a homogenization of PV toward a near-zero value is produced. The distribution of Figs. 11a and 11c for the two isopycnal surfaces, which bracket the thermostad give an indication of the vertical extent of the PV-homogenized region and of the jet core. All the above results are compatible with the observations of Rowe et al. (2000) (e.g., their Fig. 8) and also with the 2D simulations of Marin et al. (2000) (their Figs. 6c,d and 12c,d). A quantitative intercomparison shows that our simulated jet is about twice weaker than in the observations of Rowe et al., but it should be kept in mind that our quoted values correspond to an Eulerian average while an SCC stream-coordinate average was used by Rowe et al. (2000). Our simulated jet is too weak when compared with the 2D model of Marin et al. (2000), but it is well known that 2D models overestimate inertial dynamics when compared with 3D models, which allow other types of instabilities (Lindzen 1990).

To summarize, despite its quite idealized configuration, our PE model thus succeeds in reproducing the main characteristics of the equatorial thermostad and its flanking SCCs: (i) the SCCs position in latitude, (ii) the detailed PV budget leading to its meridional homogenization to near-zero values within the thermostad, and (iii) their eastward evolution (lightening of the SCCs core and widening of the thermostad). We suspect that quantitatively stronger jets would require higher resolutions than the ⅙° resolution used in the present numerical solution.

c. Secondary meridional circulation

In a stationary framework, the SCCs generating mechanism put forward in the 2D model of Marin et al. (2000) is based on the existence of secondary meridional circulations (oceanic Hadley-like cells), which (i) redistribute angular momentum, leading to eastward jets (Held and Hou 1980), and (ii) homogenize angular momentum creating a uniform zero-PV pool.

To verify if this mechanism operates in the 3D simulations, we performed diagnostics based on time-average fields. Figures 12a,b present the latitude-depth distributions of zonal velocity and density averaged over 1 yr. The corresponding meridional circulation is shown in Figs. 12c–e, respectively, for the meridional velocity component υ, the zonal vorticity (which hydrostatic value is −υz), and vertical velocity. Figure 12c for the meridional velocity shows the presence of (i) the well-known geostrophic equatorward convergence within the thermocline and (ii) a poleward divergence at the top of the thermostad. This distribution of the time-averaged meridional velocity is similar to the observations of Johnson et al. (2001) (see their Fig. 5a). We need additional information in order to diagnose the existence of secondary meridional circulations. This evidence is partly provided by the diagnostic of zonal vorticity (which provides a local measure of the overturning meridional circulation: in a 2D formulation, its expression is ∇2Ψ where Ψ is the meridional streamfunction). We observe in Fig. 12d near the equator two opposite-signed meridional cells of unequal strength: the upper positive-sign one is the strongest and is located in the lower thermocline, implying downwelling at about 2°N and upwelling at the latitude of the jet. These two cells are quite compatible with the meridional circulation found in the 2D model of Marin et al. (2000), although again the 3D simulation is weaker, with average poleward meridional velocities that do not exceed 2 cm s−1. The direction of the two cells is confirmed by the meridional distribution of the time-averaged vertical velocity (Fig. 12e), with amplitudes up to 0.2 m day−1 around 200-m depth. In particular, the location of downward and upward motions implied by the zonal vorticity diagnostic is in complete agreement with the location of negative and positive vertical velocities between 2° and 4°N. We should stress that these secondary motion diagnostics require time-averaged fields to filter out the strong gravity wave signal present in the simulations near the equator, which might otherwise completely dominate the vertical velocity field.

The meridional extent and depth position of the main positive zonal vorticity cell is consistent with a redistribution of angular momentum responsible for the creation of eastward SCCs (Figs. 12a and 12d). Such a diagnostic of zonal vorticity has been performed on the data of Fig. 5 of Johnson et al. (2001) and leads also to to a positive vorticity cell. Its relative position in latitude and depth with respect to the northern equatorial Pacific SCC is rather similar to our present numerical result (G. Johnson 2002, personal communication). Despite large observational error levels for the latter diagnostic, this experimental result suggests that angular momentum redistribution could operate in the northern equatorial Pacific as well.

It must be noted that no statically unstable convection process is occuring in the thermostad in our simulations, and even the strongest branch of the upper vorticity cell lies at a depth range where the stratification is still important (see Fig. 12b at 180 m). This suggests that homogenization of angular momentum (rather than density mixing by overturning motion) is at the origin of the near-zero values for potential vorticity.

There is thus a strong similarity between our fully 3D PE model results and the 2D model of Marin et al. (2000) for what concerns the characteristics of the secondary meridional circulation that occurs equatorward and upward of the jets location.

d. What about lateral eddies?

Figure 9a reveals a strong eddy activity that is tied to surface-intensified instability waves that are expressed the strongest in the eastern part of the basin. Thus, a question rightfully asked by one of the referees was what is the impact of such eddies on the SCCs dynamics?

It is not straightforward to curb the eddy activity in such a simulation. One possible option would be to attempt a simulation with a larger β effect, since on the one hand β is known to stabilize rotating stratified flows with respect to baroclinic instability, while on the other hand the thermocline structure of the ventilation solution is independent of β (see appendix). We have thus performed another simulation while artificially doubling the value of β. Unexpectedly the opposite effect is found: instability waves activity increases even further mainly due to a tightening of the equatorial recirculation gyre in the surface layers (its meridional width is proportional to 1/β1/2), which causes an increase of lateral shear by the too vigorous eddies and the SCCS are no longer continuous.

Another possible option for curbing eddy activity is to take advantage of the fact that the eddy activity at the SCCs depth is mostly due to the form-drag exerted at deeper levels by the surface-intensified instability waves. An additional “eddy-damped simulation” has thus been performed with an explicit dissipation operator chosen such that it has no impact at the SCCs level (≈200 m). This was done by repeating the 2 yr and ⅙° resolution part of the simulation with a Laplacian operator damping KH = 5000 m2 s−1 in both momentum and temperature equations, which is acting only in the surface-most 75 m. (The span of 2 yr is long enough for the adjustment of the top 300 m of the equatorial ocean, while short enough for the explicit damping not to have had enough time to modify the general circulation ventilation dynamics.)

The resulting velocity field at the SCCs level for this “eddy-damped simulation” (cf. Fig. 13a with Fig. 9a) indeed displays a considerably lessened eddy activity, while we observe that the SCCs keep the same overall structure with even an increase in its strength in the western part of the basin for the “eddy damped” case (compare Fig. 13b with Fig. 9c). Therefore strong lateral eddies are not necessary for the existence of inertial SCCs.

We then performed a budget of the zonal momentum equation for this case based on a spatial average over the longitudinal band 7°–20°E from the western boundary (see Fig. 13b). The main balance (in the immediate vicinity of the SCCs core) is found to obey
i1520-0485-33-12-2588-eq5
other terms in the momentum equation being much smaller at that location.

The latitude-depth distribution of the zonal pressure gradient force (ZPGF) −(1/ρ0)(∂p/∂x) is displayed in Fig. 14a. The dark gray overlaid isolines correspond to contours of average zonal velocity in order to locate the SCCs core position (200-m depth, 2.7°N). As expected, the ZPGF is positive and accelerates the flow in the upper thermocline for the EUC while it changes sign in the lower thermocline. We want to draw attention to the fact that the ZPGF sign is negative at the SCCs core level and the ZPGF thus cannot be be invoked for accelerating the eastward flowing SCCs. Moreover, its magnitude is considerably smaller than in the upper thermocline: indeed the jet core lies just beneath the zero crossing of the ZPGF.

The Coriolis acceleration − field (not shown) closely resembles the ZPGF field in the lower thermocline at the largest meridional scales. Therefore the lower thermocline at these largest scales is in geostrophic balance at zeroth order and this is compatible with ventilation dynamics. Such a large-scale geostrophic balance, which is the leading order in the 3D PE model, is completely excised by construction in a 2D formulation such as Marin et al. (2000), which only contains an ageostrophic meridional flow. Let us check that such ageostrophic dynamics are important for the small meridional scales that characterize the narrow eastward jet at 2.7°. One can indeed see in Fig. 14b, which presents the “geostrophic unbalance” −(1/ρ0)(∂p/∂x) + fυ, that there is a quite distinct extremum in the immediate vicinity of the SCCs core. Note that this local extremum is positive, implying that the Coriolis force dominates over the pressure gradient force: the Coriolis force is thus responsible for the jet eastward acceleration. The field of υ(∂u/∂y) (Fig. 14c) equilibrates most of the “geostrophic unbalance” at the jet location. In principle, the eastward acceleration of the jet can be balanced by either the mean meridional redistribution of zonally averaged velocity 〈υ〉(∂〈u〉/∂y) or by the eddy flux υ′(∂u′/∂y). The latter field is shown in Fig. 14d and its intercomparison with Fig. 14c implies that the eddy flux plays a significantly lesser role than the zonally averaged meridional redistribution near the SCCs core.

One cannot of course expect angular momentum conservation in a 3D model, and we indeed find a primary geostrophic balance for the largest scales in the zonal momentum equation for the lower thermocline. However for the narrow meridional scales near the SCCs core a secondary ageostrophic circulation exists. The above detailed budget of the zonal momentum points out that the eastward acceleration of the SCCs results from an ageostrophic force whose main component is the Coriolis force and is equilibrated by 〈υ〉(∂〈u〉/∂y): such a balance precisely corresponds to what happens in a 2D model. These results joined to the 0 PV evidence of section 4b, where PV ≈ (fuy)ρz with ρz ≠ 0 implies (fuy) ≈ 0 (i.e., to say nearly homogeneous angular momentum), are compatible with the interpretation that the eastward jets result from angular momentum redistribution like in Marin et al. (2000).

Finally let us contrast the prevailing zonal momentum balances for the EUC and the SCCs. The EUC is accelerated by −(1/ρ0)(∂p/∂x) > 0 and is centered at the equator. This eastward current may be explained by potential vorticity conservation (Pedlosky 1996). SCCs are instead decelerated by −(1/ρ0)(∂p/∂x) < 0, accelerated by the Coriolis force, are extra-equatorial, and the above results are quite compatible with a creation mechanism by angular momentum redistribution. At last, both the EUC and SCCs require the existence of extratropical ventilated water masses reaching the equatorial region.

e. General circulation involved by SCCs

The secondary meridional circulation documented in the last sections has been shown in the 2D model of Marin et al. (2000) to be triggered by the large-scale shoaling of the thermocline, which results itself from the conservative advection of PV toward the equator. The time-averaged PV distribution along an isopycnal surface that corresponds to the midthermostad is overall consistent with ventilation theory, with a direct pathway from the subduction latitude at 26°N to about 5°N (Fig. 15). South of 5°N, there is a sharp PV front through the whole basin, equatorward of which lies a uniform nearly zero PV region. This demonstrates that our previous discussion about the latitudinal limit for the validity of ventilation theory is valid over the whole width of the basin. Furthermore, the PV front has a straight zonal path in the western region V, with a sharp poleward shift in its position at the eastward limit of this region. The corresponding velocity distribution (Fig. 15b) shows that the PV front coincides with the SCC position. These jets are the eastward branch of three different circulations: (i) a strong equatorial anticyclonic gyre whose westward branch is provided by the lower part of the South Equatorial Current, (ii) a tropical cyclonic gyre whose center coincides with the PV maximum, and (iii) a large-scale circulation that flows northward near the eastern boundary of the basin. The latter circulation could constitute the deepest part of the sub tropical cell (STC; McCreary and Lu 1994), suggesting that SCCs are another possible eastward route to close the ventilated circulation in the vicinity of the equator.

A rather weak secondary SCC located between 6° and 7°N is also present in the simulation (Fig. 15b) and is reminiscent of the secondary subsurface countercurrents documented for the South Pacific by Rowe et al. (2001) and also quite recently for the North Pacific by Y. Gouriou (2002, personal communication). These secondary countercurrents are seen to contribute to the tropical cyclonic gyre and to the presence of the PV maximum in the eastern part of the basin mentioned above.

In the subtropical area, the time-averaged circulation is seen to follow isolines of potential vorticity, consistent with ventilation theory.

5. Discussion

We have presented a PE numerical simulation where an equatorward shoaling of the thermocline is observed and the equatorial thermostad and SCCs are present. The simulated large-scale thermocline structure is consistent with the results of a 3½-layer model of the ventilation. This analytical model has been built to provide new insights on what sets the large-scale meridional slope of the thermocline, focusing on the quantitative importance of he entry function that sets the PV distribution. It is shown that the equatorward shoaling of the thermocline is controlled by the PV injection at subduction latitudes. This happens only if interior pathways reach the equator in the thermocline layers, requiring strong enough equatorial winds.

In the lower equatorial thermocline of the PE simulation, a meridional circulation develops. At large spatial scales this meridional flow is in geostrophic balance and is compatible with ventilation theory. At the narrow scales of the SCCs, there is a net geostrophic eastward acceleration due to the Coriolis force, which is mainly balanced by the meridional mean advection of mean zonal velocity: this is consistent with a 2D angular momentum redistribution. The jet core indeed lies just beneath the zero crossing of the zonal pressure gradient force, which is therefore too weak to modify the angular momentum. The main difference between the 2D model of Marin et al. (2000) and the present 3D model therefore lies in the existence of a zeroth order large-scale geostrophic meridional flow.

Evidence will be given in Part II of this study (Marin et al. 2003) that the strength of this secondary ageostrophic circulation is controlled by the large-scale meridional slope of the thermocline.

This secondary motion redistributes angular momentum, creating eastward jets: the SCCs. Within these Hadley-like cells, homogenization of angular momentum leads to uniform near-zero PV. Our results are thus consistent with the 2D model of Marin et al. (2000), albeit the 3D simulations present stronger levels of temporal and spatial variability (meanders, etc.), and weaker amplitude jets, closer to the observations. Another favorable difference concerns the zonal mass budget. In a 3D framework, inertial eastward jets require westward flows (which are observed): such a consistent does not exist in a 2D formulation, thus explaining why there is no wastward flow separating the core of the EUC and the SCCs in the 2D simulations. Our 3D model thus supports the 2D mechanism proposed by Marin et al. (2000) and yields more realistic results than the 2D ones. The PE simulations also showed that both eddy activity possibly leading to homogenized pools (Rhines and Young 1982) and zonal pressure gradients effects in the high-order cell dynamics only play a minor role in comparison with the Coriolis and mean advective terms.

Our mechanism is therefore essentially a local, equatorially confined one, but needs to be remotely forced by PV injection at higher latitudes and strong equatorial winds.

Such a distant forcing for the thermostad was originally proposed by Tsuchiya (1981, 1986), who advocated that thermostad waters were formed by convection at a distant location (e.g., the Tasmania Sea for the Pacific), before being advected to the equator along a large-scale isopycnal route characterized by a minimum of PV. Nevertheless, for Tsuchiya (1981, 1986), the origin of the thermostad is distant (in the subtropics), whereas in our case the origin of the thermostad is local but triggered at distance.

Another plausible explanation for the equatorial PV homogenization in the lower thermocline could have been the Rhines and Young's (1982) mechanism of lateral homogenization within closed streamlines through eddy activity. However, (i) such a mechanism can occur only once closed contours, which are not predicted by the ventilation theory, take place in the vicinity of the equator, that is, only once equatorial dynamics has generated the equatorial recirculation gyres and, in particular, the SCCs. (ii) Lateral eddy fluxes are required for such a mechanism, but such fluxes play a minor role in our numerical simulations at the level of the SCCs. (iii) The expected homogenized PV value that would be obtained by such a mechanism is not 0, but an average value of PV between the SCC latitude (∼3°N) and the westward flow at 1.5°N (Fig. 7d), that is to say 0.5(f1.5°N + f3°N)(∂ρ̃/∂z) ∼ 9 × 10−8 PV units; this value is three times greater than the PV value produced in the lower thermocline by the numerical simulation (Fig. 11b). For all these reasons, we do not think that the Rhines and Young's (1982) mechanism is the first-order mechanism to be invoked to explain the SCCs creation and the equatorial PV homogenization in the lower thermocline.

The PE model used in this study is a vertically continuous extension of the analytical model of the ventilation, with the utmost possible care given to PV conservative dynamics (no explicit vertical dissipation/diffusion, horizontal biharmonic operators). This model can thus simulate both the large-scale ventilated thermocline and local equatorial dynamics, providing a framework for objectively assessing the latitudinal limit of validity of ventilation theory near the equator. We find that this latitudinal limit coincides with the zero streamfunction (at about 5°N) of an equatorial inertial gyre [Fig. 16 is quite akin to that of Cane (1979a,b)]. This latitudinal width is at least 2 times the meridional extent of the boundary-layer scale predicted by Pedlosky (1987) to explain the equatorial undercurrent. Our simulations show that this inertial equatorial region comprises both the equatorial undercurrent and the subsurface countercurrents as well as part of their westward recirculating flow. In terms of mass budget, let us distinguish the contributions to the net transport due to ventilation and to purely equatorial recirculation. (i) Liu (1994) has advocated that the amount of subtropical waters reaching the equatorial region is set at the bifurcation latitude (which divides northward and southward flowing western boundary currents). In our simulation, the bifurcation latitude lies at about 12°N, leading to a net meridional equatorward geostrophic transport of ∼8 Sv (Sv ≡ 106 m3 s−1) according to the ventilation theory. (ii) In the equatorial region, the transport of the equatorial gyre varies from 10 to 14 Sv (Fig. 16) along the equator. This net equatorial transport has a component from the subtropical cell (the 8 Sv mentioned above) and an estimate of the recirculating equatorial gyre thus comprises between 2 and 6 Sv: both ventilation and recirculating gyres therefore play an important role in the equatorial eastward jets dynamics. Let us contrast the EUC dynamics and the SCCs dynamics. A key idea to keep in mind is that the SCCs are necessarily confined to the lowest part of the thermocline, where the meridional slope is the largest. Thus a water mass that is advected equatorward within the lower thermocline in the basin interior will encounter the PV barrier of the SCCs where it must flow eastward. Consequently, the part of the EUC that lies in the lowest part of the thermocline can only be supplied with ventilated waters via the western boundary and by the inertial recirculating equatorial gyre.

Our mechanism provides an explanation for the formation of SCCs from the westernmost part of the equatorial basin. These jets are seen to lighten from west to east, due to the presence of a secondary diapycnal circulation in the meridional plane, and experience an abrupt poleward shift once they penetrate into the shadow zone, which is no longer motionless and where the zonal slope of the thermocline is the strongest. Unlike Johnson and Moore's (1997) model, ours does not presuppose eastward flow in the western basin. Nevertheless, in the eastern basin, our analytical model supports their rationale for the poleward shift of the SCCs by pointing out the enhancement of the zonal slope of the thermocline above the shadow zone. We want to stress another difference between our model and theirs that precludes the existence of westard recirculation by discarding such solutions. Indeed, their prescribed velocity profile in the western part of the basin with no westward velocities implies a mass budget closure far away from the equatorial region.

We have checked with Lagrangian diagnostics along particle trajectories (not shown) that the density is not conserved for particles launched in the vicinity of the jet (more generally, this result holds for all particles trajectories equatorward of 5°N), and density variations are the largest in the upper thermocline and weaken with depth. In our model, the time-averaged zonal circulation is at least five times larger than the secondary meridional velocity. Therefore, the primary zonal circulation can mostly be PV conservative as in Johnson and Moore (1997), while the secondary meridional circulation implies diapycnal mixing. The latter mechanism is consistent with the lightening of the jet core eastward and is therefore an internal obduction mechanism (Qiu and Huang 1995). The mass budget of the pycnostad layers corresponds to a net input at high latitudes (PV injection) and internal obduction in the equatorial eastern basin. We are aware that our eastern boundary condition, which is restoring toward the analytical ventilation solution, may appear contrived and further studies are required to definitively determine the actual mass closure for the pycnostad water masses. A quite different obduction mechanism is proposed by McCreary et al. (2002), where an eastern boundary upwelling, induced by a meridional wind stress, forces a rather broad current. This mechanism is advocated by the authors to be at the origin of the SCCs. In contrast, our modeled SCCs and the underlying theory concern a quite narrow, intense eastward jet centered around 3°N at its creation. As remarked by Donohue et al. (2002), McCreary et al.'s (2002) mechanism could correspond to Johnson and Moore's (1997) mechanism where the roles of the western and eastern basins are reversed. Similar comments pertaining to the mass budget that have been given above for Johnson and Moore's (1997) model apply here, and might explain the need for an Indonesian Throughflow in McCreary et al.'s solution. Furthermore, McCreary et al. (2002) invoke the existence of shocks in the solution characteristics along the SCCs position. In contrast, our ventilated analytic solution predicts no shock in our solution and the imposed wind stress is strictly zonal.

Despite the quite idealized character of our setup, there are many contact points between our model results and actual observations. (i) The jets are predicted at the right latitude and capture the inertial character of the observed SCCs. (ii) We provide a rationale to explain why the SCCs constitute the poleward limit of the thermostad and near-0-PV region. (iii) The Pacific SCCs start with a strictly zonal path in the western basin and markedly shift poleward in the eastern basin (Rowe et al. 2001), just like in our numerical solutions. We therefore think that our mechanism can operate in the North and South Pacific, and South Atlantic where there is evidence of interior pathways within the thermocline. The strong temporal variability of the North Atlantic countercurrent suggests additional mechanisms at work. (iv) Both the simulated large-scale and near-equatorial PV distributions are compatible with the observations [e.g., the existence of a nearly uniform 0-PV region and also the local PV maximum around 7°N in the eastern basin is quite compatible with the observations of Johnson and McPhaden (1999) in the eastern Pacific lower thermocline].

The overall characteristics of both the lower thermocline and upper subthermocline documented in the present study suggest that the SCCs may participate to the deeper limb of the equatorial STC.

Among obvious criticisms of the present study is the rather short longitudinal extent of our basin, but a larger zonal extent would favor even more the possibility of interior pathways for ventilation. More important, the observed thermocline presents an interhemispheric assymetry due to the presence of the North Equatorial Countercurrent (Fig. 1). The study of such a case is presented in Part II of this work, along with numerical evidence of the dependence of SCCs dynamics upon the strength of the meridional slope of the thermocline.

Acknowledgments

Support from the Institut du Dévelopment et des Ressources en Informatique Scientifique with Grant 21299 is gratefully acknowledged. Author FM received support from AOS Program of Princeton University during part of this work. We thank Sophie Wacongne for many interesting discussions. The manuscript benefited from the valuable comments of two anonymous reviewers.

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  • Rhines, P. B., and W. R. Young, 1982: Homogenization of Potential Vorticity in planetary gyres. J. Fluid Mech., 122 , 347367.

  • Rowe, G. D., E. Firing, and G. C. Johnson, 2000: Pacific Equatorial Subsurface Countercurrent velocity, transport, and potential vorticity. J. Phys. Oceanogr., 30 , 11721187.

    • Search Google Scholar
    • Export Citation
  • Stramma, L., and F. Schott, 1999: The mean flow field of the tropical Atlantic Ocean. Deep-Sea Res., 42 , 773795.

  • Tsuchiya, M., 1981: The origin of the Pacific equatorial 13°C water. J. Phys. Oceanogr., 11 , 794812.

  • Tsuchiya, M., 1986: Thermostads and circulation in the upper layer of the Atlantic Ocean. Progress in Oceanography, Vol. 23, Pergamon, 101–147.

    • Search Google Scholar
    • Export Citation

APPENDIX

Analytical Model

The analytical model used to explore the numerical PE model is based on a 3-layer Luyten et al. (1983) model above a resting ocean (3½-layer model). In this model, the wind stress is imposed as a body force in an additional surface layer of constant thickness Z0 (Liu 1994). The subduction latitudes where we specify potential vorticity are f2 and f3 where f represents the Coriolis parameter. Subduction occurs at depths Z1 for latitude f2 and Z2 for latitude f3 for a subtropical gyre. The flow being geostrophic, hydrostatic, and incompressible, the velocities are given by
i1520-0485-33-12-2588-ea1
The derivation follows Luyten et al. (1983), Liu (1994), or McCreary and Lu (1994). The net meridional geostrophic transport is obtained from the Sverdrup relation β Σi=0,3(zizi−1)υi = fwe, which integrated from the eastern boundary (x = L) leads to
i1520-0485-33-12-2588-ea2
where γi = g(ρi+1ρi)/ρ is the reduced gravity between layers i and i + 1, Zi are the layer depths along the eastern boundary, and
i1520-0485-33-12-2588-eq6
the Ekman we pumping being
i1520-0485-33-12-2588-eq7

Despite the fact that the Ekman pumping we is singular at f = 0, D20 = −2Lx(τx/ρ0)dx′ is well defined at the equator. We assume in the following that the Ekman velocity is negative everywhere over the basin, so that a net equatorward geostrophic transport occurs from the subtropics up to the equator.

Poleward of f3, only z3 varies spatially. Injecting z1 = Z1 and z2 = Z2 in (A2) leads to
i1520-0485-33-12-2588-eq8
For f2 < y < f3, in the ventilated zone (VZ), both z3 and z2 can vary spatially. Potential vorticity (f/h3) must be conserved along streamlines (i.e., pressure lines γ3z3), yielding:
i1520-0485-33-12-2588-eq9
leading to the relation z2 = (1 − f/f3)z3 + f/f3Z3. Replacing this relation into (A2), with z1 = Z1, gives a quadratic equation for z3:
i1520-0485-33-12-2588-ea3
In the shadow zone (SZ), separated from the ventilated zone by xs(y), layer 3 is motionless, z3 = Z3, with z2 given by
i1520-0485-33-12-2588-eq10
The limit xS(y) is obtained by fixing z3[xS(y), y] = Z3 in (A3), that is,
i1520-0485-33-12-2588-ea4
We do not take into account the homogeneous western potential vorticity pools that can originate from the western boundary at subduction latitudes, since we are mainly interested in the equatorial mean westward-flowing motions.

South of f2, four different dynamical regions are present.

(i) In the ventilated region (V), both layers 2 and 3 are ventilated. The flow in layer 3 conserves the potential vorticity it has acquired at f = f3, so that
i1520-0485-33-12-2588-ea5
whereas the flow in layer 2 conserves the one originating at f = f2, leading to
i1520-0485-33-12-2588-ea6
where
i1520-0485-33-12-2588-eq11

Replacing z2 and z3 in (A2) leads again to a quadratic equation for z3 that can be easily solved. The isoline xS1(y) emanating from x = xs(f2) at f = f2 in layer 3 constitutes the eastward limit of this region, obtained by setting z3 = Z3 in (A5), (A6), and (A2).

(ii) In the semiventilated region (M), layer 3 is motionless, lying in the shadow zone where z3 = Z3. Layer 2 is still ventilated and originates from the ventilated region, and conservation of potential vorticity along streamlines in layer 2 implies
i1520-0485-33-12-2588-ea7
where
i1520-0485-33-12-2588-eq12
Injecting (A7) into (A2) yields a quadratic equation for z2. The eastward limit of this region corresponds to the streamline xR(y), which originates from x = xs(f2) at f = f2 in layer 2; it can be determined by matching the formulations of z2 between this region and the region R, which is described hereinafter.
(iii) In the semiventilated region (R), layer 3 is also motionless, with z3 = Z3. Layer 2 is ventilated, but now the flow comes from the northward shadow zone, where z3 = Z3. Under these conditions, the conservation of the potential vorticity in layer 2 implies:
i1520-0485-33-12-2588-ea8
After replacing (A8) in (A2), z2 is solution of the following equation:
i1520-0485-33-12-2588-ea9
This region is delimited eastward by the isoline xS2(y), which originates from the eastern boundary at f = f2 and is characterized by z2[xS2(y), y] = Z2; this streamline is given by
i1520-0485-33-12-2588-ea10
(iv) The easternmost region (S) is a motionless shadow zone for both layers 2 and 3, with z2 = Z2 and z3(S) = Z3. Only z1 departs from its value at the eastern boundary, so that, according to (A2):
i1520-0485-33-12-2588-ea11

The meridional slopes of the equatorial thermocline can be computed from the Sverdrup relation (A2) by retaining the first order terms in f. In each dynamical region (Fig. 3), the relations between z1, z2, and z3 from PV conservation are used. Because ∂D20/∂f = 2Lxf2τx/∂f2 at the equator, the contribution of wek in the Sverdrup relation (A2) is zero at first order in f in the vicinity of the equator.

In the fully ventilated region V (i.e., for x < xS1), these slopes are given by
i1520-0485-33-12-2588-ea12
where
i1520-0485-33-12-2588-eq13

In the above equations, z(x) is the depth of the equatorial thermocline and Γ3 = γ1 + γ2 + γ3 is the total reduced gravity g(ρ4ρ1)/ρ for the equatorial thermocline. Here Q2(x < xS1) and Q3(x < xS1) are the potential vorticities in layers 2 and 3 acquired, respectively, at the subduction latitudes f2 and f3.

In the semiventilated regions M and R (i.e., for xS1 < x < xS2), comparable calculations yield
i1520-0485-33-12-2588-ea13
Again, the meridional slopes in these regions depend upon the reduced gravity (Γ2 = γ1 + γ2), and on the potential vorticity Q2 that the streamline reaching the equator at the longitude x has acquired at the subduction latitude f2. The potential vorticity Q2 is defined, in regions M and R, respectively, by
i1520-0485-33-12-2588-eq14
In the shadow zone S (i.e., for x > xS2), the only moving layer is layer 1, and the base of layer 2 is flat, that is,
z2f

Apart from the shadow zone, the common feature between the dynamical regions is that the base of the thermocline (z3 in region V, z2 in regions M and R) deepens poleward, whereas the top of the thermocline (z1 for all these regions) shoals poleward. The meridional slope of the thermocline depends upon the reduced gravities of the different layers and of the injected potential vorticity at the subduction latitudes. In particular, a change in the subduction latitudes f2 and f3 has a significant impact on the meridional slope of the equatorial thermocline.

Fig. 1.
Fig. 1.

Mean meridional distributions of (a) zonal velocity and (b) temperature at 165°E in the western Pacific Ocean, from SURTROPAC cruises (1984–92) (Delcroix et al. 1992). The lower thermocline, with temperatures between 10° and 15°C, as well as eastward velocities, are shaded. Contour intervals are, respectively, 1°C and 5 cm s−1

Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2588:TDOTSC>2.0.CO;2

Fig. 2.
Fig. 2.

Schematic meridional section of the 3½-layer model of the ventilated thermocline. Here ρi is the density of layer i, Zi is its depth at the eastern boundary, and zi is its spatially varying depth in the basin interior. The originality of this model lies in the definition of the subduction latitudes: fi is defined as the latitude between an unforced layer i equatorward and an imposed flat upper interface poleward. The forcing of the model is provided by an analytical longitude-independent zonal wind stress that acts as a body force in the constant-depth layer 0

Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2588:TDOTSC>2.0.CO;2

Fig. 3.
Fig. 3.

Spatial locations of the different dynamical regions obtained for the 3½-layer model. For f2 < f < f3, xs(y) separates the ventilated zone (VZ) of layer 3 from its shadow zone (SZ). Equatorward of f2, layers 2 and 3 are ventilated in region (V); in the semiventilated regions (M) and (R), layer 3 is motionless and layer 2 is ventilated with waters coming either from VZ (M) or SZ (R); in the shadow zone (S), both layers 2 and 3 are motionless. These regions are delimited from west to east by the lines xS1(y), xR(y), and xS2(y). The values of xS1(0), xR(0), and xS2(0) determine whether the equatorial region is supplied by subtropical ventilated waters

Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2588:TDOTSC>2.0.CO;2

Fig. 4.
Fig. 4.

Equatorial thermocline as predicted by the 3½-layer model, in case ventilation of layers 2 and 3 reaches the equator. Because the PV-conserving moving layers have zero thickness at the equator, the depth z(x) of the thermocline at the equator is equal to the depth of all moving layers supplied by subtropical ventilated waters

Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2588:TDOTSC>2.0.CO;2

Fig. 5.
Fig. 5.

Configuration of the 3D primitive equation model. (a) Schematic meridional section of density; the bold line is the limit zf(y) between a forced region (in gray), where density is restored to remain flat, and a freely evolving region equatorward. (b) Vertical density ρ̃(z) distribution in the density-forced region having a piecewise linear shape; density is taken equal to 29.5 kg m−3 at the ocean bottom (H = 5000 m). Note that there is a direct correspondence between the density ρ, the depth Z, and the latitude Y along the line zf(y).

Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2588:TDOTSC>2.0.CO;2

Fig. 6.
Fig. 6.

Meridional distribution of zonal wind (continuous line), wind curl (dashed line), and “Ekman pumping” ∂D20/∂x = 2f2we/β (dotted line); units are, respectively, 10−1 N m−2, 10−7 N m−3, and 10−3 m2 s−2

Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2588:TDOTSC>2.0.CO;2

Fig. 7.
Fig. 7.

Meridional instantaneous sections of density at (a) 15° and (b) 30° from the western boundary with (c) an equatorial closeup of density and (d) zonal velocity at 15°. The thick solid line is the equatorward limit of the density-forced region. The thick dashed lines are the meridional slopes predicted by the analytical 3½-layer model, capturing the main features of the numerical model. Contour intervals are 5 cm s−1 for velocity and 0.2 kg m−3 for density. Eastward velocities and lower thermocline (25.90 ≤ ρ ≤ 26.50) are shaded

Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2588:TDOTSC>2.0.CO;2

Fig. 8.
Fig. 8.

Instantaneous zonal section of density at 3.5°N with analytically predicted interfaces superposed. Contour interval is 0.2 kg m−3

Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2588:TDOTSC>2.0.CO;2

Fig. 9.
Fig. 9.

Instantaneous isopycnal distribution of (a) velocity vectors for the midthermostad. Instantaneous zonal velocity (cm s−1) of the equatorial thermostad on three isopycnal surfaces: (b) ρ = 26.00, (c) 26.25, and (d) 26.50. Jumps of the jet position are well captured by the different dynamical transition zones of the 3½-layer model.

Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2588:TDOTSC>2.0.CO;2

Fig. 10.
Fig. 10.

Eastward zonal evolution of the time-averaged properties of the SSC's core (velocity maximum): (a) latitude, (b) density (kg m−3), (c) depth (m), and (d) velocity (cm s−1). The SCC is straight in VZ and shifts poleward within SZ, while largest diapycnal effects take place within VZ. The velocity maximum does not increase downstream. All these results are consistent with the observations of Rowe et al. (2000)

Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2588:TDOTSC>2.0.CO;2

Fig. 11.
Fig. 11.

Instantaneous meridional distribution of potential vorticity at the midbasin and in the lower thermocline, for isopycnal surfaces ρ = (a) 26.00, (b) 26.25, and (c) 26.50. The solid thick line is the total potential vorticity, while the solid thin line and the dashed line are, respectively, its planetary and relative components. The 3° latitude corresponds to the jet latitude

Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2588:TDOTSC>2.0.CO;2

Fig. 12.
Fig. 12.

Time-averaged meridional section of zonal (a) velocity, (b) density, (c) meridional velocity, (d) zonal vorticity, and (e) vertical velocity at 15° from the western boundary. These plots demonstrate that a meridional cell is present in the lower thermocline, implying downwelling at the equator and upwelling near 4° in latitude between 150 and 200 m. Contour intervals are, respectively, 5 cm s−1, 0.2 kg m−3, 0.5 cm s−1, 5 × 10−5 cm s−1, and 10−4 for the zonal velocity, density, meridional velocity, vertical velocity, and zonal vorticity. Positive values are shaded for the velocity components and the zonal vorticity

Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2588:TDOTSC>2.0.CO;2

Fig. 13.
Fig. 13.

“Eddy-damped” simulation: instantaneous isopycnal distribution of (a) velocity vectors and (b) zonal velocity (cm s−1) on the isopycnal surface ρ = 26.25. White isolines indicate the different dynamical transition zones of the 3½-layer model.

Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2588:TDOTSC>2.0.CO;2

Fig. 14.
Fig. 14.

“Eddy-damped” simulation: instantaneous zonal momentum balance between 7° and 20° in longitude from the western boundary. (a) Zonal pressure gradient force −(1/ρ0)(∂p/∂x); (b) geostrophic unbalance −(1/ρ0)(∂p/∂x) + ; (c) total field υ(∂u/∂y); (d) eddy flux υ′(∂u′/∂y). The contour interval is 10−8 m s−2, and positive values are shaded. Contours of zonal velocity (contour interval of 10 cm s−1) are superimposed in dark gray.

Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2588:TDOTSC>2.0.CO;2

Fig. 15.
Fig. 15.

(a) One-year-average isopycnal distribution of potential vorticity and (b) velocity vectors within the thermostad, for the isopycnal surface ρ = 26.25 kg m−3. Near-zero-PV values are found near 20°E on this particular isopycnal surface. The sharp PV front clearly extends throughout the basin, and the SCC inertial velocities are clearly identifiable everywhere

Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2588:TDOTSC>2.0.CO;2

Fig. 16.
Fig. 16.

(a) Analytical Sverdrup transport streamfunction. (b) One-year-averaged barotropic streamfunction. Contour interval is 2.5 Sv; negative values are shaded

Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2588:TDOTSC>2.0.CO;2

Table 1.

Values for the parameters of the 3½-layer ventilation model, which have been calibrated in order to be compared with the primitive equations model: Zi, ρ i, and γ i are, respectively, the constant depth (in the density-forced region; m), the mean density (kg m−3), and the reduced gravity (m s−2) for layer i . Here fi is the latitude where the top of layer i intersects the zf (y ) line. Therefore, f 2 and f 3 are respectively the subduction latitudes of layers 2 and 3

Table 1.
Save
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  • Fig. 1.

    Mean meridional distributions of (a) zonal velocity and (b) temperature at 165°E in the western Pacific Ocean, from SURTROPAC cruises (1984–92) (Delcroix et al. 1992). The lower thermocline, with temperatures between 10° and 15°C, as well as eastward velocities, are shaded. Contour intervals are, respectively, 1°C and 5 cm s−1

  • Fig. 2.

    Schematic meridional section of the 3½-layer model of the ventilated thermocline. Here ρi is the density of layer i, Zi is its depth at the eastern boundary, and zi is its spatially varying depth in the basin interior. The originality of this model lies in the definition of the subduction latitudes: fi is defined as the latitude between an unforced layer i equatorward and an imposed flat upper interface poleward. The forcing of the model is provided by an analytical longitude-independent zonal wind stress that acts as a body force in the constant-depth layer 0

  • Fig. 3.

    Spatial locations of the different dynamical regions obtained for the 3½-layer model. For f2 < f < f3, xs(y) separates the ventilated zone (VZ) of layer 3 from its shadow zone (SZ). Equatorward of f2, layers 2 and 3 are ventilated in region (V); in the semiventilated regions (M) and (R), layer 3 is motionless and layer 2 is ventilated with waters coming either from VZ (M) or SZ (R); in the shadow zone (S), both layers 2 and 3 are motionless. These regions are delimited from west to east by the lines xS1(y), xR(y), and xS2(y). The values of xS1(0), xR(0), and xS2(0) determine whether the equatorial region is supplied by subtropical ventilated waters

  • Fig. 4.

    Equatorial thermocline as predicted by the 3½-layer model, in case ventilation of layers 2 and 3 reaches the equator. Because the PV-conserving moving layers have zero thickness at the equator, the depth z(x) of the thermocline at the equator is equal to the depth of all moving layers supplied by subtropical ventilated waters

  • Fig. 5.

    Configuration of the 3D primitive equation model. (a) Schematic meridional section of density; the bold line is the limit zf(y) between a forced region (in gray), where density is restored to remain flat, and a freely evolving region equatorward. (b) Vertical density ρ̃(z) distribution in the density-forced region having a piecewise linear shape; density is taken equal to 29.5 kg m−3 at the ocean bottom (H = 5000 m). Note that there is a direct correspondence between the density ρ, the depth Z, and the latitude Y along the line zf(y).

  • Fig. 6.

    Meridional distribution of zonal wind (continuous line), wind curl (dashed line), and “Ekman pumping” ∂D20/∂x = 2f2we/β (dotted line); units are, respectively, 10−1 N m−2, 10−7 N m−3, and 10−3 m2 s−2

  • Fig. 7.

    Meridional instantaneous sections of density at (a) 15° and (b) 30° from the western boundary with (c) an equatorial closeup of density and (d) zonal velocity at 15°. The thick solid line is the equatorward limit of the density-forced region. The thick dashed lines are the meridional slopes predicted by the analytical 3½-layer model, capturing the main features of the numerical model. Contour intervals are 5 cm s−1 for velocity and 0.2 kg m−3 for density. Eastward velocities and lower thermocline (25.90 ≤ ρ ≤ 26.50) are shaded

  • Fig. 8.

    Instantaneous zonal section of density at 3.5°N with analytically predicted interfaces superposed. Contour interval is 0.2 kg m−3

  • Fig. 9.

    Instantaneous isopycnal distribution of (a) velocity vectors for the midthermostad. Instantaneous zonal velocity (cm s−1) of the equatorial thermostad on three isopycnal surfaces: (b) ρ = 26.00, (c) 26.25, and (d) 26.50. Jumps of the jet position are well captured by the different dynamical transition zones of the 3½-layer model.

  • Fig. 10.

    Eastward zonal evolution of the time-averaged properties of the SSC's core (velocity maximum): (a) latitude, (b) density (kg m−3), (c) depth (m), and (d) velocity (cm s−1). The SCC is straight in VZ and shifts poleward within SZ, while largest diapycnal effects take place within VZ. The velocity maximum does not increase downstream. All these results are consistent with the observations of Rowe et al. (2000)

  • Fig. 11.

    Instantaneous meridional distribution of potential vorticity at the midbasin and in the lower thermocline, for isopycnal surfaces ρ = (a) 26.00, (b) 26.25, and (c) 26.50. The solid thick line is the total potential vorticity, while the solid thin line and the dashed line are, respectively, its planetary and relative components. The 3° latitude corresponds to the jet latitude

  • Fig. 12.

    Time-averaged meridional section of zonal (a) velocity, (b) density, (c) meridional velocity, (d) zonal vorticity, and (e) vertical velocity at 15° from the western boundary. These plots demonstrate that a meridional cell is present in the lower thermocline, implying downwelling at the equator and upwelling near 4° in latitude between 150 and 200 m. Contour intervals are, respectively, 5 cm s−1, 0.2 kg m−3, 0.5 cm s−1, 5 × 10−5 cm s−1, and 10−4 for the zonal velocity, density, meridional velocity, vertical velocity, and zonal vorticity. Positive values are shaded for the velocity components and the zonal vorticity

  • Fig. 13.

    “Eddy-damped” simulation: instantaneous isopycnal distribution of (a) velocity vectors and (b) zonal velocity (cm s−1) on the isopycnal surface ρ = 26.25. White isolines indicate the different dynamical transition zones of the 3½-layer model.

  • Fig. 14.

    “Eddy-damped” simulation: instantaneous zonal momentum balance between 7° and 20° in longitude from the western boundary. (a) Zonal pressure gradient force −(1/ρ0)(∂p/∂x); (b) geostrophic unbalance −(1/ρ0)(∂p/∂x) + ; (c) total field υ(∂u/∂y); (d) eddy flux υ′(∂u′/∂y). The contour interval is 10−8 m s−2, and positive values are shaded. Contours of zonal velocity (contour interval of 10 cm s−1) are superimposed in dark gray.

  • Fig. 15.

    (a) One-year-average isopycnal distribution of potential vorticity and (b) velocity vectors within the thermostad, for the isopycnal surface ρ = 26.25 kg m−3. Near-zero-PV values are found near 20°E on this particular isopycnal surface. The sharp PV front clearly extends throughout the basin, and the SCC inertial velocities are clearly identifiable everywhere

  • Fig. 16.

    (a) Analytical Sverdrup transport streamfunction. (b) One-year-averaged barotropic streamfunction. Contour interval is 2.5 Sv; negative values are shaded

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