1. Introduction
Part I of this study (Hua et al. 2003) has documented some generic properties of the equatorial subsurface countercurrents (SCCs) and of the equatorial thermostad present in numerical simulations. The general setup of these features corresponds to a large-scale meridional slope of the ventilated thermocline, which is responsible for a secondary meridional circulation in the lower equatorial thermocline. This causes a redistribution of angular momentum, creating eastward jets.1 Within these Hadley-like cells (Marin et al. 2000), homogenization of angular momentum leads to nearly uniform 0 PV. Moreover, for a closed basin, inertial recirculating gyres in a horizontal plane play a role comparable to the ventilation's one in the mass budget of near-equatorial dynamics and eventually sets the latitudinal scale of validity of ventilation theory near the equator in the surface layers. An analytic model has also been presented in Part I showing that the equatorward shoaling of the thermocline is controlled by the PV injection at subduction latitudes. This occurs only if interior ventilated pathways reach the equator in the thermocline layers and in presence of a large enough equatorial wind fetch, ensured either by strong winds or a large basin size.
Two independent sets of parameters can thus be distinguished that influence the local slope of the thermocline at the equator: (i) the PV injection mechanism, which in our primitive equation (PE) model is constrained by the imposed shape of the meridionally variable mixed layer depth, and (ii) the wind field structure in the immediate vicinity of the equator.
In the second part of this study, we document sensitivity results of the numerical simulations to the above two types of parameters. Section 2 explores the quantitative influence of the meridional large-scale slope of the thermocline on the SCCs/thermostad strength and on their latitudinal position/extent. The second section asseses the dynamical impact of more realistic features of the near-equatorial wind stress structure. Two cases are considered: (i) the effect of a weakening of the equatorial wind stress (section 3a) and (ii) the effect of the presence of a North Equatorial Countercurrent (NECC) raising a barrier to ventilation from higher latitudes (section 3b).
2. Large-scale ventilation
Both the analytical and the continuous PE models presented in Part I were focused on the control of the large-scale PV injection: this was schematically prescribed by fixing the lower boundary zf(y) of a meridionally varying finite depth “mixed layer.” The meridional slopes of the lower thermocline at the equator are linear functions of the PV source values Q2 and Q3 at subduction latitudes f2 and f3.2
In order to check if this large-scale thermocline slope has a direct impact on the strength and latitudinal position of the SCCs, we have performed two additional simulations (PIVOT2) and (PIVOT3) that, respectively, correspond to twice and three times shallower mixed layers than for the simulation (PIVOT) reported in Part I of this work (see Table 1 and Fig. 1). The vertical stratification, within the density-forced region and at the eastern boundary of the basin, and the definitions of the isopycnal layers in the analytical 3½-layer model, will be the same for all simulations.
For the first three simulations, the zonal wind stress structure is kept identical (Fig. 2a). In particular, the equatorial wind stress value τx(f = 0) is the same for the three first runs: this entails that the characteristics that delimit the ventilated zones of layers 2 and 3 will strike the equator at the same longitudes (in other words, the values xS1 and x
Figures 3b and 3c document the dynamical regions of the analytical ventilated 3½-layer model for runs PIVOT2 and PIVOT3 (continuous lines) while those of run PIVOT correspond to the dashed lines. The main difference between the three cases concerns the area covered by the ventilated zone in layer 3. For a shallower mixed layer depth, subduction occurs at higher latitudes and since the values xS1 at f = 0 are identical for all three runs, the characteristics xS1(y) will tend to be more meridionally oriented. The ventilated zonal velocity will decrease, therefore reducing the meridional slope of the thermocline due to thermal wind balance.
The density distribution at 10°E from the western boundary corresponds to the continuous lines of Figs. 4a,c,e for, respectively, the first three simulations of Table 1. Dotted lines correspond to the analytical 3½-layer model prediction that has been detailed in Part I of this study. As in the PIVOT case, the analytical model captures well the main features of the different regions.
There is a clear link between the slope of the mixed layer zf(y) depth and the actual slope of layer 3 between 2° and 6°N, which is parallel to the lower boundary zf(y) of the mixed layer. The strength of the SCCs and its latitudinal position increase with the meridional slope of layer 3.
Figure 5 shows the zonal evolution of the jet across the basin for the three runs as seen on the time-averaged zonal velocity field plotted on isopycnal surfaces in layer 3. (We recall that instantaneous zonal velocity fields for the PIVOT case can be found in Fig. 9 of Part I.) The ventilation dynamical boundaries are overlaid in white and confirm the tendencies for the jet core to remain zonally straight in the ventilated zone of layer 3, to shift both poleward as it enters the shadow zone of layer 3 and upward to lighter isopycnals downstream (not shown). Note also that the SCC cores are located on lighter isopycnal surfaces for PIVOT2 and PIVOT3 (Fig. 5).
In summary, the stronger the thermocline slope, the farther away from the equator the jet core will be and the stronger its inertial magnitude.
As a side comment, let us mention the formation of mode waters in PIVOT2 and PIVOT3 around 27°N in Figs. 4c,e, due to enhanced lateral PV injection favored by the stronger curvature of the base of the mixed layer zf(y) (Pedlosky and Robbins 1991). Thus, stronger mode water production coincides with weaker SCCs when comparing with the PIVOT case (Fig. 4a).
Besides, it must be noted that the strength of the barotropic gyre near the equator continuously decreases from ∼13 Sv (Sv = 106 m3 s−1) for the PIVOT case and ∼10 Sv for the PIVOT2 case to ∼8 Sv for the PIVOT3 case, as can be diagnosed from the time-average barotropic streamfunction for each simulation. This equatorial barotropic gyre is the combination (i) of a purely equatorial inertial gyre that takes place above and within the thermocline, and corresponds to the Cane's (1979a,b) gyre solution in a 1½-layer simulation of the equatorial undercurrent (EUC), and (ii) of the circulation of ventilated waters within the subtropical cell. According to the ventilation theory, the total amount of subtropical ventilated waters that reach the equator (i.e., the contribution of the subtropical cell to the barotropic equatorial gyre) only depends on the Ekman pumping at the bifurcation latitude, which divides northward and southward-flowing western boundary currents and is noticed to remain the same (∼12.5°N) for PIVOT, PIVOT2, and PIVOT3 simulations. This implies that the excitation of the resonant equatorial inertial gyre crucially depends on PV injection and on the thermocline slope.
We now turn to the influence of the equatorial wind field structure.
3. Wind forcing
a. Weak equatorial wind stress
The existence of inertial SCCs created by an angular momentum redistribution mechanism necessarily requires interior pathways that reach the equator. Such pathways within the lower thermocline force motion in the SCCs' layer and establish a meridional slope of that layer near the equator. This can occur through ventilated pathways only if the equatorial wind stress is strong enough.
We have therefore chosen to examine a counterexample situation, where the necessary condition for the existence of interior pathways is not satisfied in the lower thermocline. This has been tested by performing simulation LWIND, for which there is a substantial weakening of the wind stress near the equator (Fig. 2b and Table 1). For this run, the shape zf(y) of the mixed layer depth is kept identical to the central case PIVOT. When comparing the wind forcing in PIVOT and LWIND, the weakening of the equatorial wind stress could correspond to a situation where the ITCZ is located right at the equator. In our case, the wind curl changes sign at f = 9.5°N and the Sverdrup barotropic transport presents an additional cyclonic gyre (Fig. 6b). Note however that the Ekman pumping remains negative for all latitudes southward of f = 35°N so that the equator corresponds to a high pressure and the outcropping latitudes f2 and f3 are indeed prescribed in subduction regions as they should be in order for ventilation theory to apply.
Figure 6a shows the dynamical boundaries of the ventilation solution in this case. When compared with the PIVOT case, the modifications concern the shape of the characteristics delimiting the ventilated zones of layers 2 and 3 equatorward of 9.5°N. Interior ventilated pathways are still present in layer 2, while layer 3 equatorward of 5°N lies in the shadow zone and can be supplied with ventilated waters only via the western boundary. The base of the layer 3 should therefore be mostly flat for in the entire equatorial basin. Note that the characteristic x
Figure 7 shows that the time average density distributions at 10° and 20°E are well captured by the analytical solution away from the equator. The time-averaged zonal velocity shows that there is still a weak eastward velocity structure around 4.5°N at 20°E, which is quite broad and extends farther down in the water column than in the PIVOT case.
The instantaneous zonal velocity for the lower thermocline is shown in Fig. 7a: we no longer observe an eastward narrow inertial jet, but instead a track of eddies that present stronger eastward velocity values than westward ones. These eddies are linked to the so-called tropical instability waves. The bias toward eastward values within the eddies leads to a time-average eastward flow (Figs. 7c,d and 8b), where amplitude increases eastward and reaches its maximum eastward of 25°E. This time-average eastward flow is due to a nonlinear rectification of the tropical instability waves that are the strongest in the eastern part of the basin as observed in the ocean. In our numerical solutions these instability waves appear to be intrinsically tied to the existence of the strong PV spatial gradients inside the shadow zone of layers 2 and 3 that favor both barotropic and baroclinic instabilities. This rectification mechanism is somewhat reminiscent of the Manfroi and Young (1999) mechanism for the creation of eastward jets, which are nonlinear solutions forced by a small spatial-scale forcing (that mimics the small spatial scales forced by baroclinic instability in the idealized situation that is considered by the authors).
On average, this eddy track succeeds in somewhat mixing PV and in decreasing PV gradients in layer 3, but does not lead to a PV homogenization to near-zero values as in the case PIVOT. Moreover, the PV gradient near the eastward mean flow is less sharp than for the case of the strongly inertial jet of the PIVOT case (not shown). Properties along the core of the time-average eastward flow are given in Fig. 9. When contrasting them with the same diagnostics as for the PIVOT case (Fig. 10 of Part I), we note that the mean eastward jet lies farther away from the equator (at 4.2°N), and remains zonally straight throughout the whole basin, has a 2.5 times weaker amplitude, and that the current shifts upward vertically but remains roughly on the same isopycnal surface.
In the LWIND case, although layer 2 is directly fed via interior pathways, we do not get inertial SCCs in this layer in the western part of the basin that experiences interior ventilation, because the meridional slope in that layer is very weak (cf. Fig. 7a).
The case with a weaker equatorial wind stress thus leads only to a time-average eastward transport at the poleward limit of a broader, more diffuse thermostad. This occurs on lighter isopycnals than for the PIVOT case. The average eastward transport recirculates ventilated water that originates from the western boundary layer.
The barotropic streamfunction again departs from Sverdrup theory by developping an enhanced transport due to a horizontal inertial recirculation at the equator. (Figs. 6b,c).
b. Impact of the North Equatorial Countercurrent
The presence of a wind-forced North Equatorial Countercurrent (NECC), in case it extends throughout the whole basin,3 prevents the large-scale ventilation that occurs at higher latitudes from feeding equatorial regions and from building up the meridional thermocline slope necessary to trigger the secondary flow dynamics of the inertial SCCs. This is due to the inability of the geostrophic component of the Sverdrup flow to cross 0 Ekman pumping lines. Nevertheless, in the Pacific Ocean, in spite of the presence of such a strong countercurrent, the observed dynamical equatorial structure does not seem to be altered. One still observes PV fronts, Tsushiya jets, and an equatorward shoaling of the lower thermocline that is beast seen near 4°N and beneath 200 m (Fig. 1 of Part I). How can we then, in the framework of ventilation theory, recover the deeper layer large-scale density structure at the equator? Figure 2c shows the modified wind fields we shall use to illustrate the effect of a NECC with an ITCZ at 9°N as observed in reality. Note that the zonal wind stress value at f = 0 is identical for the two simulations PIVOT and NECC. As shown in Part I, the zonal dynamical structure of the thermocline right at the equator should not be altered by the existence of the NECC, because it depends solely on the equatorial wind fetch and on the stratification parameters at the eastern boundary. Therefore the limits of the different regions right at the equator, that is, the shadow and ventilated zones, are conserved and identical to the previous case. Where then is the origin of the water reaching the equator in layer 3 if ventilation of layer 3 is prohibited?
We see in Fig. 2c that the negative Ekman pumping reverses its sign between 9.5° and 13°N generating two latitudinal barriers fw1 and fw2 forbidding net meridional geostrophic Sverdrup flows.4 The outcropping latitudes are the same as in the previous cases and are located in regions where the Ekman pumping is negative. Figure 10a shows the different dynamical zones appearing in this case. Notations and analytical developments are given in the appendix and Fig. 14. Streamlines in layer 3 subduct at f3 under layer 2, which is forced and hit the western boundary before reaching the fw2 line, dividing the basin into a ventilated zone (VZ), and a shadow zone (SZ) extending up to the western boundary. Therefore layer 3 should be motionless south of fw2. However the key point is that potential vorticity pools are able to be set up in regions where the PV isolines in layer 3, which are deduced from the analytical ventilation model, are connected to the western boundary layers (Rhines and Young 1982). This occurs at locations where zonal mean velocities carry long Rossby waves eastward, that is, near the fw1 line where the wind imparts strong meridional geostrophic velocity divergences to the ocean (Fig. 10a). The size of this pool, controlled by the blocking long Rossby wave condition (Rhines and Schopp 1991), in our case extends zonally up to the eastern boundary and crosses the fw1 line reaching the equator on its eastern part. A second pool (PZ2) appears in layer 2 while subducting under layer 1 at f2 and also has a large zonal extension. Here S and R are the classical shadow and ventilated zones with one or two layers in motion, QZ3 is identical to R with streamlines originating from the PZ zone, with QZ2 is the pool in layer 2 with layer 3 motionless.
Therefore in the presence of an NECC, one is again able to build up a large-scale current field in the deeper layer that reaches the equator in case the dynamics of PV pools are taken into account. Nevertheless, fluid reaching the equator originates from the western boundary and not from high-latitude subducted water as in the PIVOT case. The strength and the northward extent of this pool depends on the position of the fw1 line and the magnitude of the wind field. The meridional shoaling of the thermocline, motor of the Hadley cell mechanism, is again, in the presence of a NECC, able to take place and to generate PV fronts and Tsuchiya jets (TJ).
The distribution of density fields at 10° and 20°E are given in Figs. 11a and 11c: the most important result for what concerns the SCCs dynamics is that the meridional slope of layer 3 is again parallel to the base zf(y) of the mixed layer equatorward of 6°N in the western part of the basin. Actually it is almost identical to the slope of layer 3 found in the PIVOT run (Fig. 4a).
As noted by a reviewer, this thermocline structure differs from the observations in the Northern Hemisphere of the western Pacific Ocean (Fig. 1b of Part I), where there is a meridional shoaling (instead of deepening) of the thermocline from 4° to 8°N. An additional simulation (not shown) has thus been performed with an ITCZ in the wind field that lies closer to the equator, thus yielding a more realistic-looking thermocline structure in the equatorial region. The pool mechanism still applies, but then requires a different calibration for the 3½-layer ventilation model. For the sake of simplicity, we will not present this case of an ITCZ lying closer to the equator.
An intercomparison of Figs. 11a,b and Figs. 4a,b shows that there is little difference between both runs for latitudes equatorward of 5°N both in terms of the density field and of the zonal velocity field: the NECC simulation also displays a well-defined eastward countercurrent at about 3°N. The largest differences between simulation PIVOT and NECC occur for the density distribution in the we > 0 region between fw1 and fw2 (9.5° and 13°N), where isopycnals are lifted upward, and between 7° and 9.5°N where an intense front in both layers 1 and 2 occurs because of the existence of a quite strong NECC in the surface layers. We note that in this simulation the eastward zonal velocity present in the surface layers due to the NECC and at depth due to the SCCs covers a continuous region, while in the PIVOT case, these two eastward currents were separated by westward flow near 180-m depth and between 4° and 6° in latitude. The numerical simulation displays a much stronger eastward NECC flow than predicted by the ventilated theory and this causes such a strong tightening of the density surfaces between 7° and 9.5°N that layers 1 and 2 are very strongly coupled. This tightening also make our numerical simulation depart from observations where the diffuse NECC extends farther to the equator masking the equatorward shoaling of the thermocline. The numerical solution at 10°E behaves more like a 2½-layer system where layers 1 and 2 are directly forced there, while only layer 3 could be considered as shielded from direct wind forcing. We shall come back to this point further below in the discussion of the PV distribution.
Overall the analytical prediction for the behavior of the base of layer 3 can be identified as the deepest moving layer of the numerical solution in both Figs. 11a and 11c. A detailed comparison with the various dynamical regimes PZ, VZ, SZ, and so on, appears to be valid in the numerical solution behavior.
Both the time-average and instantaneous distribution of the zonal velocity fields are given in Figs. 12a,b, and c, respectively. Again an inertial SCC is observed to occur in the western part of the basin as for the PIVOT case and to remain straight within the PV pool PZ3, and to shift poleward and reach lighter isopycnal surfaces as it moves into the shadow zone of layer 3.
In terms of PV pools, Fig. 13 presents instantaneous distribution of PV on two isopycnal surfaces that lie, respectively, in layers 2 and 3.
For layer 2, Fig. 13a shows that, as expected, the westward flow near 13°N is the location of strong flow instability. For latitudes between f3 and f2 layer 2 is directly forced by the wind. Farther south, the eastward limit of the PV pool PZ2 broadly agrees with the instantaneous PV distribution only for longitudes that are east of 15°E, with rather well mixed values of PV close to 3.5 × 10−7 PV units. West of 15°E and south of f2, we obviously do not observe PV homogenization in our numerical solution: this is due to the fact that the numerical solution has such a strong NECC that both layers 2 and 1 appear to be strongly coupled and PV forcing occurs in both these layers. A 3½-layer representation is no longer appropriate in this limited region that behaves more like a 2½ layer, where both our present layers 1 and 2 are forced so that PV conservation is not verified in layer 2. This direct forcing reinforces the vertical stratification ∂ρ/∂z along the surface eastward NECC flow, and this explains the PV maximum found near 7°N in the western part of the basin in Fig. 13a.
In contrast, the PV distribution in our layer 3 appears to overall agree with the analytical prediction at all latitudes except for the equatorial area south of 5°N. Explicitly, the ventilated zone VZ and the PV pool PZ are well captured by the numerical simulation in terms of both longitude and latitude positions. We observe a well-mixed value of PV around a value of 2 10−7 PV units in both the instantaneous PV distribution (Fig. 13) and the time-averaged one (not shown). Note that PV homogenization to a common value on both sides of fw1 within PZ3 is analogous to what happens for the inertial eastward-flowing Gulf Stream, where PV is homogenized to a common value on both sides of the eastward jet (Rhines and Holland 1979).
The main departure from ventilation theory occurs at the strong PV front that starts at 3°N in the western part of the basin, with a southward limit of this front, which is zonally straight within the PZ3 region, and gradually shifts poleward in the VZ3 region. The latter result is quite analogous to what was found in the PIVOT case. Equatorward of 3°N, the numerical solution presents a strong PV homogenization to near-0 values as for the PIVOT case and thus we are again in the situation where angular momentum redistribution could be a candidate leading to near-0 PV values, equatorward of an inertial SCC.
Figures 10b and 10c display the barotropic Sverdrup solution and the barotropic streamfunction in the numerical solution. The NECC case corresponds to a case in which we have four gyres south of 35°N, and again a barotropic cyclonic equatorial inertial recirculating gyre is observed between 0° and 5°N.
4. Discussion
The overall objective of this study has been to reconcile in a common dynamical framework a diverse set of observations:
a basin-scale continuous inertial SCC that is quite narrow and strongly nonlinear,
the near-0 PV value in the lower thermocline, equatorward of the SSC's position,
the sharp frontal character of the PV front that coincides with the SCC's position, and
the large-scale thermocline structure.
Constructing a rationale for those observations obviously requires a “matching” between the tropical/subtropical and equatorial thermoclines; in this study, we have retained the ventilation theory to explain the extra-equatorial thermocline structure and we have searched for its equatorward extension, as was done by Pedlosky (1987) for the EUC. However, our present approach takes into account two novel additional constraints in this “matching.” The first one is the possibility of an equatorial partial closure of the mass budget through horizontally recirculating gyres whose contribution may be comparable to the ventilation's one. The second, more important, one is to allow flow transitions due to flow instabilities that are completely excised by the Sverdrupian ventilation approach. Explicitly, meridional secondary recirculations that redistribute angular momentum are deemed important in a 3°-wide equatorial area and shear instabilities (both barotropic and baroclinic) that reach their maximum expression in the surface equatorial layers are believed to be ubiquituous in the eastern part of the basin, entailing substantial rectification effects on the time-average flow.
In this second part of our study, we have addressed the impact on the equatorial inertial dynamics of the SCCs/thermostad of two major groups of dynamical factors:
the large-scale PV injection mechanism through the imposition of the shape of a meridionally varying finite mixed layer depth, as well as fixing the stratification at the eastern boundary;
the impact of major modifications of water masses pathways in the lower thermocline, obtained by varying the latitudinal distribution of the Ekman pumping distribution. In particular, the case in which the only possible pathways that reach the equator in the lower thermocline occur within the western boundary layer has been considered, as well as the case of a drastic upheaval of the basin-scale PV distribution caused by the existence of a strong basinwide NECC.
A common result that holds for all the runs is that the zonal structure of the thermocline right at the equator only depends at first order on the equatorial wind fetch, provided the stratification at the eastern boundary is unchanged.
The PIVOT, PIVOT2, and PIVOT3 runs have confirmed the quantitative relationship between the meridional slope of the lower thermocline and the strength and position of the SCCs.
In the case of a too-weak equatorial wind stress, the LWIND simulation corresponds to a case where the lower thermocline lies in the shadow zone. The density jump Δρ as well as the meridional slope of the midthermocline are too weak to enable the creation of inertial SCCs in the midthermocline. Only a time-mean eastward current that has an amplitude that is at least 2 times as weak as in the PIVOT case is observed in the LWIND simulation. This eastward current is created by a downward penetration of rectification effects of tropical instability waves, possibly by a mechanism such as the one proposed by Manfroi and Young (1999).
The overall results in the case of the existence of an NECC show that it acts as a barrier only for the two upper-thermocline layers, while the lower thermocline, through the appearance of a PV pool whose longitudinal extent is comparable to the basin size, is successfully set into motion causing a sizable meridional slope of the lower thermocline. In consequence, SCCs appear and can be created by angular redistribution within meridional secondary cells. A somewhat surprising result is that the near-equatorial meridional slope of the thermocline is quantitatively little changed when compared to its value for the central PIVOT case. In other words, the carving out of a shadow zone (SZ) between f3 and fw2 that reaches the western boundary in layer 3 has had almost no quantitative impact on the ventilated solution near the equator for the lower thermocline (Fig. 10a). What happens in the numerical model, as far as the large-scale meridional slope of the thermocline is concerned [Eqs. (A12) or (A13) of the appendix of Part I], is that the decrease in Q3 is almost totally compensated for by an increase in Q2 within the PV pool PZ2. The major differences between the solutions of the PIVOT and NECC cases are therefore confined to the upper thermocline.
Let us discuss the various types of PV mixing mechanisms that can occur in our numerical simulations.
The clearest case of near-0 PV values occurs in the PIVOT case; we documented in Part I that 0-PV values are actually observed at depths (180 m) where a strong vertical stratification is still present (the vertical position of the 0-PV region is thus somewhat shallower than the thermostad's vertical extent). An essential ingredient is the homogenization of angular momentum within secondary meridional cells: this is the only way we can obtain 0-PV in a strongly stratified fluid and this occurs within Hadley-like cells as in the paradigm model of Held and Hou (1980).
Another well-studied lateral PV homogenization mechanism occurs in horizontal recirculating gyres as shown by Rhines and Young (1982), away from the influence of direct external forcings. If we consider the horizontal recirculation within layer 3 between the SCCs latitude and the westward flow at 1.5°N, the expected constant PV value, which is the arithmetical mean of the planetary vorticity values at the northern and southern boundaries of the recirculating gyre, is larger by a factor of at least 3 than the value found in the numerical simulation. In summary, within the western part of the basin and in the lower thermocline, the quite small values of PV require mechanisms other than that of Rhines and Young.
A third possibility concerns diapycnal fluxes by shear instability waves that can create low stratification and weak thermostad-like structure: this occurs in the eastern part of the basin, and is the most clearly illustrated in the LWIND case.
In order to limit these sensitivity studies to a reasonable amount of numerical simulations, we have only varied one parameter at a time in a rather idealized way, for example, we have everywhere kept zonally invariant forcing fields. Although the actual forcings do vary zonally in reality, we suspect that our broad conclusions should apply to the large zonal-scale observations.
A large number of open issues remain, and among them let us cite three. (i) We do not solve the dynamics that sets the vertical stratification at the eastern boundary, since we impose it in our model. (ii) We still do not understand what controls the vertical extent of the SCCs. (iii) Presently, some of the simulations that have been performed for wider basins and are not shown here exhibit a stronger continuous secondary TJ than in the PIVOT case, but this occurs together with primary TJs that are disrupted by too-strong instability waves. In reality, these instability waves remain confined in the eastern part of the basin and play an important role in the local thermodynamic air–sea budget. Our wind-only configuration does not take such thermodynamic effects into account that may curb their spurious excitation within the shadow zone of the equatorial lower 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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APPENDIX
Analytical Model
The analytical 3½-layer model of the ventilated thermocline, which was described in the appendix of Part I, is modified to take into account the existence of a region with positive Ekman velocities in the tropical region producing a NECC (Fig. A1). At the limits f = fw1 and f = fw2, the Ekman vertical velocity and thus the net meridional geostrophic transport vanish. The two subduction latitudes f2 and f3 are located outside this region of Ekman suction.
For f2 ≤ y ≤ f3, the analytical solution of Part I predicts that a line xs(y) delimits the ventilated zone (VZ) westward and the shadow zone (SZ) eastward. Because
Nevertheless, in the presence of the NECC, with Sverdrup velocities directed to the east (near the fw1 line), PV isocontours in layer 3 can emanate from the western boundary layer and isolate a pool region shielded from the eastern boundary. Mixing of PV (Rhines and Young 1982) in this pool will lead to a flow field in layer 3, which can reach the equator.
Equatorward of f1, six different dynamical regions may coexist. The solution in each region is obtained by expressing z1 and z3 as functions of z2; injecting these expressions in (A1) then leads to a quadratic equation for z2.
(i) The shadow zone S and (ii) the semiventilated region R, which are the easternmost dynamical regions, have been described in Part I. Note that, unlike the limit xs2(y) between regions S and R, the western limit xR(y) of region R will have a different expression here.
(vi) An additional region QZ2 occurs when the streamline of layer 2, which originates from the western boundary at f = f2 penetrates into region QZ3. Layer 3 lies in the shadow zone in this region (z3 = Z3), and potential vorticity is homegeneous in layer 2, leading to (A4).
As in Part I, the meridional slopes of the thermocline layers at the equator are linear functions of the PV source values Q2 and Q3 [Eqs. (A12) or (A13) of the appendix in Part I, according to the dynamical regions]. Nevertheless, the values of PV are no longer set at subduction latitudes, but in the western PV-homogenized regions. For instance, the values of Q2 and Q3 in region PZ3 at the longitude x at the equator are, respectively, given by
Subducting lines zf(y) delimiting the forced region, where density is restored, and the evolving region, respectively, for the PIVOT (thick continuous line), PIVOT2 (thick dashed line), and PIVOT3 (thin continuous line) cases. The mixed layer depths are, respectively, 200 and 500 m, 100 and 250 m, and 70 and 170 m at 26° and 35°N
Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2610:TDOTSC>2.0.CO;2
Latitudinal dependence of zonal wind (continuous line), wind curl (dashed line), and “Ekman pumping” ∂
Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2610:TDOTSC>2.0.CO;2
Dynamical zones for the 3½-layer model for the (a) PIVOT, (b) PIVOT2, and (c) PIVOT3 cases. Here xs(y) separates the ventilated zone (VZ) of layer 3 from its shadow zone (SZ). 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 either from VZ (M) or SZ (R); in the shadow zone (S), both layers 2 and 3 are motionless. These regions are separated 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 via the basin interior. Dashed lines in (b) and (c) correspond to the PIVOT case
Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2610:TDOTSC>2.0.CO;2
Meridional sections of (a), (c), (e) density and (b), (d), (f) zonal velocity at 10° from the western boundary for simulations (a), (b) PIVOT, (c), (d) PIVOT2, and (e),(f) PIVOT3. The thick solid line is the equatorward limit of the density-forced region. The thick dashed lines are the interfaces predicted by the analytical 3½-layer model. Contour intervals are 5 cm s−1 for velocity and 0.2 kg m−3 for density. Eastward velocities are shaded. Layers 2 and 3 (as defined in the 3½-layer model) are represented with two different grays (layer 2 is dark; layer 3 is light)
Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2610:TDOTSC>2.0.CO;2
One year-average zonal velocity (cm s−1) on isopycnal surfaces in the lower thermocline for the simulations (a) PIVOT, (b) PIVOT2, and (c) PIVOT3. Note that the jet core is located on lighter isopycnal surfaces (26.25 instead of 26.50) for PIVOT2 and PIVOT3. Limits of the dynamical regions computed with the 3½-layer model are in white
Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2610:TDOTSC>2.0.CO;2
Simulation LWIND: (a) dynamical zones for the 3½-layers model; (b) analytical Sverdrup transport streamfunction; (c) 1-yr-averaged barotropic streamfunction. Contour interval is 2.5 Sv for streamfunction
Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2610:TDOTSC>2.0.CO;2
Simulation LWIND: meridional sections of (a),(c) density and (b),(d) zonal velocity at, respectively, 10° and 20° from the western boundary. The thick solid line is the equatorward limit of the density-forced region. The thick dashed lines are the interfaces predicted by the analytical 3½-layer model. Contour intervals are 5 cm s−1 for velocity and 0.2 kg m−3 for density. Eastward velocities are shaded. Layers 2 and 3 (as defined in the 3½-layer model) are represented with two different grays as in Fig. 4
Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2610:TDOTSC>2.0.CO;2
Simulation LWIND: (a) instantaneous and (b) 1-yr-average distribution of zonal velocity (cm s−1) on isopycnal surface ρ = 26.00 kg m−3 (equatorial thermostad). Limits of the dynamical regions computed with the 3½-layer model are in white
Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2610:TDOTSC>2.0.CO;2
Simulation LWIND: zonal evolution of 1-yr-average properties of the velocity maximum core for the subsurface countercurrent from 5° to 35°: (a) latitude, (b) density (kg m−3), (c) depth (m), and (d) velocity (cm s−1).
Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2610:TDOTSC>2.0.CO;2
Simulation NECC: (a) Dynamical zones for the 3½-layer model (see appendix for details); (b) Sverdrup transport streamfunction, and (c) 1-yr-averaged barotropic streamfunction (contour interval is 2.5 Sv)
Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2610:TDOTSC>2.0.CO;2
Same as for Fig. 7, but for simulation NECC.
Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2610:TDOTSC>2.0.CO;2
Simulation NECC: Distribution of zonal velocity (cm s−1) for the thermostad on isopycnal surfaces: 1-yr average on ρ = (a) 26.25 and (b) 26.50, and (c) instantaneous distribution on ρ = 26.50. Limits of the dynamical regions computed with the 3½-layer model are in white.
Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2610:TDOTSC>2.0.CO;2
Simulation NECC: instantaneous isopycnal distribution of potential vorticity on isopycnal surfaces ρ = (a) 25.50 and (b) 26.50 kg m−3. Limits of the dynamical regions computed with the 3½-layer model are in white
Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2610:TDOTSC>2.0.CO;2
Fig. A1. Notations for the analytical ventilated model in presence of an NECC
Citation: Journal of Physical Oceanography 33, 12; 10.1175/1520-0485(2003)033<2610:TDOTSC>2.0.CO;2
Parameters for the various runs
By thermal wind, the equatorial uplift of the thermocline induces a westward shear that is surface-intensified: at the South Equatorial Current (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.
See Eqs. (A12) or (A13) in the appendix of Part I, according to the dynamical regions. These PV values are controlled by Z3 − Z2 and Z2 − Z1, so that the slope is roughly a decreasing function of the depths Z2 and Z3 of layers 2 and 3 specified at the eastern boundary. This slope will be thus smaller for a shallower mixed layer profile zf(y).
Lu and McCreary (1995), Liu and Huang (1998), and Huang and Wang (2001) have indeed shown for the Pacific and Atlantic Oceans that the zonal extension of the NECC is limited eastward.
A possible alternative could be a geostrophic cross-gyre flow, based on blocking long baroclinic waves with eastward mean velocities (Pedlosky 1984; Schopp 1988). Nevertheless even if it permits ventilation to cross the f
