1. Introduction
There has been much recent debate concerning the dynamical balance of the Antarctic Circumpolar Current (ACC) and in particular the issue of what determines the ACC transport. There are two prevailing viewpoints. Stommel (1957), and most recently Warren et al. (1996), have suggested that the ACC transport is controlled by Sverdrup balance (Sverdrup 1947). The wind stress curl to the north of Drake Passage drives a poleward transport, which Stommel argued passes through Drake Passage and returns equatorward in a western boundary current—the Malvinas Current. The observed ACC transport (134 ± 13 Sv; Nowlin and Klinck 1986) (Sv ≡ 106 m3 s−1) is not inconsistent with that predicted by the Sverdrup theory (190 ± 60 Sv; Baker 1982). In contrast, Johnson and Bryden (1989), Straub (1993), and others have suggested that the ACC transport is controlled by an integral angular momentum budget, which can involve a complex interplay between surface wind forcing, buoyancy forcing, eddy fluxes, and friction. Note that Sverdrup balance may still apply locally, but in this interpretation it does not constrain the strength of the ACC [see Hughes (1997), Olbers (1998), and Rintoul et al. (2000) for useful discussions].
The essential difference between the Southern Ocean and other ocean basins is the absence of continental barriers at the latitudes of Drake Passage, and hence the presence of uninterrupted circumpolar potential vorticity contours. As we will argue in section 2 and demonstrate through a series of numerical experiments in sections 3 and 4, this means that a substantial circumpolar transport can exist even in the presence of weak forcing. Thus the ACC may be somewhat analogous to the inertial recirculation subgyres found in the Sargasso Sea and other subtropical basins, which are maintained through an integral balance between forcing and dissipation (Niiler 1966; Marshall 1986).
Several modeling studies have been performed to examine ACC dynamics. These have generally consisted either of simple eddy-permitting models (often quasigeostrophic) with idealized topography and forcing, or realistic-domain GCMs, with parameterized or partially resolved eddies. McWilliams et al. (1978) showed that the resolved eddies can provide interior fluxes of momentum and potential vorticity that allow a balanced mean flow. Wolff et al. (1991) examined the relative role of standing and transient eddies using the same model with different topographic ridges. More recently, Gnanadesikan and Hallberg (2000) and Gent et al. (2001) have shown that water mass transformation can also alter ACC transport and thus they conclude that ACC transport is neither determined by Sverdrup balance nor the mean wind stress. While eddy-permitting general circulation models such as the Parallel Ocean Climate Model, the Parallel Ocean Program model, the Fine Resolution Antarctic Model (FRAM) and the Ocean Circulation and Climate Advanced Model (e.g., Gille 1997; Hughes et al. 1999; Saunders et al. 1999) provide the most realistic representation of the Southern Ocean, such models cannot be run to thermohaline equilibrium and are too expensive to allow a detailed exploration of parameter space.
In this paper we return to a simpler, eddy-permitting model. We consider a purely wind-driven circumpolar current with no buoyancy forcing, although our dynamical framework can be easily extended to include buoyancy forcing if desired. We perform a large number of experiments with different wind forcing and idealized domain geometries to determine the conditions under which the simple theories of ACC transport put forward by previous authors hold, how the different ideas fit together, and where the theories break down. The paper is organized as follows: in section 2 we review the theoretical background; in section 3 we describe the numerical model and the experimental setup; in section 4 we present and analyze the numerical model results; and finally, section 5 contains a brief concluding discussion.
2. Theoretical background
The dynamics of the Southern Ocean is often regarded as distinct from that of wind-driven gyres in closed ocean basins. However the governing equations are the same. The aim of this section is to briefly review the vorticity dynamics of wind-driven gyres and circumpolar currents within a unified framework and to highlight the dynamical similarities and differences. A more extensive review is given by Rintoul et al. (2000).
a. Barotropic theory
In a closed barotropic basin the background absolute vorticity (q) contours follow latitude circles and are blocked by the lateral boundaries. Free, unforced flow is impossible, but the source of vorticity from the surface winds drives flow across latitude circles and the gyre is closed by a frictional western boundary current. For weak winds (Fig. 1a) the gyre transport is determined by the integrated wind stress curl along latitude circles or “Sverdrup balance” (Sverdrup 1947). However, with realistic levels of wind forcing (Fig. 1b), fluid parcels advect low values of absolute vorticity northward within the western boundary current. If the q contours close, then there is the possibility of free recirculating flow, enhancing the overall gyre transport. At leading order vorticity is conserved by fluid parcels, but the strength of the recirculation along closed q contours is determined by an integral balance between sources and sinks of vorticity (Niiler 1966; Marshall 1986).
b. Baroclinic theory
- a barotropic transport:
- a baroclinic transport:
If we consider an ocean at rest and then switch on an eastward wind stress, the resulting equatorward Ekman transport will gradually increase the tilt of the isopycnals until eddy or diapycnal transports can balance the Ekman transport. There are several closely related approaches to the problem. Here we choose to focus on the mass budget of the upper layer, although similar results are obtained by focusing on the angular momentum or potential vorticity budgets. In the following we neglect diapycnal transfers between the isopycnal layers, which have been studied in some detail by Gnanadesikan and Hallberg (2000), and introduce an additional term into the balances below.
1) Weak wind stress (Straub 1993)
2) Stronger wind stress (Johnson and Bryden 1989)
3. Numerical model
To test the competing theories reviewed in section 3, we now present a series of experiments with varying wind strengths using a balanced “geostrophic vorticity” model. The geostrophic vorticity equations are described by Schär and Davies (1988) and Allen et al. (1990); a detailed model description is given in Tansley and Marshall (2000).
Our experiments use two constant density layers within a zonally reentrant channel. The upper-layer thickness is initially 1200 m, and the total ocean depth is 4 km (except above topographic features).
4. Results
We perform our experiments in idealized domains, both for pedagogical purposes and to simplify the diagnostics. We start with the simplest case of a flat-bottom channel (Fig. 4a). We then introduce, in turn, ridge a 2 km high (Fig. 4b), partial land barriers to represent Drake Passage (Fig. 4c), and additional topographic features downstream of the model Drake Passage (Fig. 4d).
a. Flat-bottom channel
1) Standard parameters
Figure 6 shows the mean barotropic and baroclinic transport values after spinup for a range of wind stress values. Even for very low values of wind stress, there is a considerable baroclinic transport as predicted by Straub (1993). The current only becomes unstable when there is a finite vertical shear, and only then can eddies act to keep the system near an equilibrium state. However, due to the weak Ekman transport, the increase in transport is slow—for τ0 = 0.01 N m−2, it takes 110 years for the transport to reach quasi equilibrium. Straub's formula for the baroclinic transport (8) predicts 146 Sv for our model parameters. This compares favorably with the baroclinic transport of 151 Sv we find for this case.
As the wind stress increases, so does the transport. Figure 7 is a log–log plot of wind stress against baroclinic transport. For weak wind stress, the dependence on wind stress is small, as predicted by Straub. However, for wind stress values greater than τ0 = 0.075 N m−2 the baroclinic transport is roughly proportional to the square root of the wind stress, as predicted by Johnson and Bryden (1989).
As expected from the results of Panetta (1993) and Sinha and Richards (1999), the flow is organized into zonal jets. Figure 8 shows the time-mean eastward velocity in the upper layer for two different values of wind stress. For a weak wind stress of τ = 0.01 N m−2 there are several jets across the channel. As the wind stress increases, the number of jets is reduced. For a wind stress given by τ = 0.15 N m−2 we only find one clear jet. As discussed by Sinha and Richards (1999), the jet spacing is consistent with associated changes in the Rhines scale (Rhines 1975).
The mass budget across streamlines (21) for this simple case is shown in Fig. 9, with a weak wind stress of τ0 = 0.01 N m−2 and a stronger wind stress of τ0 = 0.15 N m−2. The horizontal axis shows the mean or “equivalent” latitude of the streamline along which we are integrating. Wind forcing drives a northward Ekman transport, while the eddy bolus transport is southward in both cases. For the case with weak wind forcing, the Reynolds transport is northward in the jets and is of a similar magnitude to the Ekman and bolus transports; the frictional transport is significant and generally acts in the opposite sense. For the stronger wind forcing, the Ekman transport and bolus transport are dominant, and almost cancel, apart from in the center of the jet where there is a significant northward Reynolds transport. Thus, this case with stronger forcing is more in accord with the ideas of Johnson and Bryden, with a dominant balance between the Ekman transport and eddy bolus transport.
2) Influence of model dissipation
If we increase the bottom friction by a factor of 5, we find a decrease in the depth-integrated circumpolar transport by almost a factor of 5. This is consistent with (20) since the depth-integrated transport is dominated by Tbarotropic. Note that, if the transport of the model circumpolar current were simply determined by Sverdrup balance, then in our experiments we would find only a weak dependence between circumpolar transport and dissipation. However, the flat-bottom case is a special limit due to the absence of zonal pressure gradients at all depths.
The baroclinic transport is also sensitive to the dissipation. In general, we might expect an increase in model dissipation to damp eddy activity and thus reduce the efficiency of the eddies in limiting the north–south interface slope. Similar results are obtained in eddy-resolving simulations of inertial recirculation gyres (e.g., see Barnier et al. 1991). For a wind stress of τ0 = 0.15 N m−2, an increase in the biharmonic diffusion coefficient by a factor of 4 indeed results in an increase in the baroclinic transport by about 16%. However, if we instead increase the bottom friction by a factor of 5, we find a decrease in the baroclinic transport by about a third. The latter can be explained by the reduced barotropic transport in the presence of increased bottom friction. Lateral shear in the barotropic flow is known to inhibit baroclinic instability (James 1987). Increased bottom friction therefore increases the instability of the current, thus decreasing the circumpolar transport.
b. 2-km ridge
1) Standard parameters
As found by Wolff et al. (1991) and Krupitsky and Cane (1997), inclusion of a 2-km ridge in the channel (as shown in Fig. 4b) blocks the potential vorticity contours in the lower layer. This effectively eliminates the barotropic component of the circumpolar transport, and we are left with a circumpolar current of a far more realistic strength.
Figure 10 shows the transport for different wind stresses with the 2-km ridge. Even for τ0 = 0.2 N m−2, the barotropic component of the circumpolar transport is less than 5 Sv, but there are nevertheless barotropic recirculation gyres of considerable magnitude. For the weakest wind stress, τ0 = 0.01 N m−2, the baroclinic circumpolar transport of 138 Sv is again close to the prediction of 146 Sv given by Straub's formula (8). The slight reduction in baroclinic transport from the flat-bottom case is probably due to the reduced lateral shear in the barotropic flow, which, as mentioned above, is likely to increase the instability of the current (James 1987). For stronger wind stresses, the dependence of transport on wind stress is weaker than that predicted by the standard baroclinic adjustment theories. Figure 11 shows a log–log plot of wind stress against baroclinic transport. Discounting the weakest wind stress experiment, the remaining data fall onto a reasonably straight line of approximate gradient 1/13, compared with the values of 1/2 predicted by Johnson and Bryden (1989) and 1/3 predicted by Rintoul et al. (2000).
The time-averaged Bernoulli potential for τ0 = 0.01 N m−2 (Fig. 12) shows that the flow in the upper layer is still mainly zonal, although there is a slight deflection over the ridge, and downstream of the ridge the current is focused into three tighter jets. As the wind stress increases, the current is deflected further by the ridge until all the flow is deflected toward the northern boundary, and there is one large standing wave downstream of the ridge (Fig. 13). In both cases, the potential vorticity contours closely follow the Bernoulli streamlines (not shown), supporting the interpretation of the ACC as a “free mode.”
To understand the reduced sensitivity of the circumpolar transport to the surface wind forcing in the presence of a topographic barrier, we now consider the integral mass budget across mean Bernoulli streamlines, as detailed in (21). With weak wind stress forcing, the mass budget is similar to that obtained in the flat-bottom case (Fig. 14a). The Reynolds transport is large, and is generally of opposite sign to the eddy bolus transport, while the frictional is transport is also significant. However, with stronger wind forcing, the balance is rather different from the flat-bottom case (Fig. 14b). Here the Reynolds transport is consistently southward, and the eddy bolus transport is therefore slightly reduced compared to the flat-bottom case. While we have eliminated the direct effect of the standing eddies by integrating along a streamline, standing eddies established downstream of the ridge still contribute implicitly to the overall mass budget. Downstream of the ridge the streamlines are focused into a sharp meandering jet, within which the bolus and Reynolds transports are locally enhanced (not shown) as described by MacCready and Rhines (2001). The stronger the wind forcing, the greater the amplitude of the standing eddies, leading to increased local enhancement of the bolus and Reynolds transports. Equilibrium can thus be achieved with a smaller increase in circumpolar transport than in the flat-bottom case, resulting in reduced sensitivity of the circumpolar transport to surface wind forcing. The standing eddies also locally enhance the frictional transport, although the frictional transport remains relatively small in the overall mass budget.
2) Influence of model dissipation
As in section 4a, we take a wind stress of τ0 = 0.15 N m−2 and examine the influence of changing the dissipation coefficients on the baroclinic transport.
As for the flat-bottom case, when we increase the biharmonic diffusion coefficient by a factor of 4, we find an increase in the baroclinic transport, but this time only by 7%. However, in contrast to the flat-bottom case, if we increase the bottom friction by a factor of 5, we find an increase (by about 15%) in baroclinic transport. This last result is the opposite to that found in the simple buoyancy-forced model of Gnanadesikan and Hallberg (2000). Gent et al. (2001) also find a reduction in baroclinic transport with an increase in dissipation coefficient since increasing the dissipation coefficient in their eddy bolus transport parameterization leads to an increased slumping of the isopycnals. In our experiments with a 2-km ridge, increasing the dissipation also damps the standing waves so that the current becomes more zonal. The mass budget across mean Bernoulli streamlines shows a change in the Reynolds transport so that for high bottom friction it is northward over most of the channel. Thus, the dependence on model dissipation is complex. This sensitivity to model parameters highlights the delicate balance between the surface forcing, topography, eddies, and frictional processes, each of which affects the model ACC transport.
c. 2-km ridge with land barriers
Including idealized land barriers to represent Drake Passage leads to a decrease in the baroclinic transport (Fig. 15). However, even with a very small wind stress, a reasonable circumpolar current is generated (e.g., Fig. 16 shows the 42 Sv current for a wind stress of τ0 = 0.01 N m−2). Note that if we scale the predicted transport for a baroclinically adjusted current from (8) by a factor of 0.22, to represent the reduced extent of the meridionally connected part of the domain, we get a transport of 32 Sv. Note also that Sverdrup balance, as advocated by Warren et al. (1996), predicts a transport of only 6 Sv. The circumpolar current is confined to the open latitude circles. As the wind stress increases, the interior Sverdrup flow increases. Figure 17 shows the time-mean streamlines for a wind stress given by τ0 = 0.15 N m−2. Part of the flow through “Drake Passage” is deflected north along the model coastline, as seen in data and the FRAM model (Best et al. 1999). A standing wave develops near the line of zero wind stress curl, which can be identified as a “Moore wave” (Moore 1963). For large wind stress values, the transport through Drake Passage only increases slightly with increasing wind stress, as for the case above without the land barriers. Figure 18 shows the mass budget for experiments with weak and stronger wind forcing for this model configuration. The mass budgets are shown only across circumpolar streamlines. With weak wind forcing the balance is very similar to that found across the inertial jets in the flat-bottom case: the Reynolds transport is almost as large as the Ekman transport and is northward (Fig. 18a). With stronger wind forcing, the bolus transport is greatly reduced compared to the flat-bottom and ridge cases (Fig. 18b). Where the streamlines follow the land boundary as the current turns north to the east of Drake Passage, the Reynolds transport and frictional transport make significant contributions and further decrease the sensitivity of the circumpolar transport to surface wind forcing.
d. Downstream topography
The path of the model circumpolar current is strongly modified by topography downstream from Drake Passage. To investigate the importance of downstream topography in influencing the circumpolar transport, we now introduce an idealized topographic seamount (representing the Kerguelen Plateau) and a downstream ridge (representing the Pacific–Antarctic Ridge) into the model (as shown in Fig. 4d). Figure 19 shows the time-average streamlines with a wind stress given by τ0 = 0.15 N m−2. The downstream topography focuses the flow into tighter jets. The bump has a clear upstream effect, with jets appearing north and south of the bump, as described by Webb (1993). The flow is also deflected over the second 1-km ridge. However, despite the changes in the background state, the baroclinic transport in this experiment remains very similar to the experiment without downstream topography (shown in Fig. 17).
We have performed a large number of experiments with different downstream topographies, by extending the topographic seamount southward across Drake Passage and varying the height of the downstream ridge. The downstream topography has a clear impact on the time-mean circulation in all cases. In many of these experiments we find a small change in the baroclinic transport, typically of order 5%. In some cases we find a decrease in transport and in others we find an increase, dependent on the influence of the topographic obstacles on the structure, and hence stability, of the the time-mean circulation. However, the precise nature of the change is difficult to predict.
5. Conclusions
The relation between the transport of the ACC and surface wind forcing has been frequently discussed in the oceanographic literature. In this paper we have sought to examine whether there is a straightforward relation in the context of an idealized, two-layer representation of the Southern Ocean. Our main results are as follows.
For weak wind stress, as predicted by Straub (1993), the baroclinic (i.e., thermal wind) component of the eastward transport can be approximately predicted from the critical vertical shear required for baroclinic instability.
For stronger wind stresses and in the special case of a flat-bottomed channel, the eastward baroclinic transport is roughly proportional to the square root of the wind stress, as predicted by Johnson and Bryden (1989).
The circumpolar transport is not proportional to the wind stress curl, as predicted by Sverdrup balance theories. This has been demonstrated by Samelson (1999), Gnanadesikan and Hallberg (2000), and Gent et al. (2001) in models with thermodynamic forcing. Here we have shown this is the case even for a purely wind-driven current.
In general, in the presence of topographic and land barriers, the circumpolar transport is dependent on a complicated interaction between wind forcing, eddy fluxes, topographic effects, and friction. There appears to be no simple relation between the circumpolar transport and the wind forcing, although the sensitivity is greatly reduced compared with that predicted by Johnson and Bryden (1989).
The theory and results discussed in this paper suggest that it may be helpful to think of the ACC as a “free mode,” which is then modified by Sverdrup balance (as proposed by Hughes 1997). In a free mode, the transport is determined by a delicate integral balance between weak forcing and dissipation. Consequently, the ACC transport is likely to be extremely sensitive to a wide range of parameters in numerical models. A similar sensitivity is seen in the inertial recirculation of the Gulf Stream (e.g., Pedlosky 1996 and references therein). It is interesting to note that there is relatively little attention focused on predicting the transport of the Gulf Stream recirculation, while we are still seeking a definitive answer to the question of what controls the ACC transport. If free-mode ideas are pertinent to the ACC, then this issue may not be well posed until the geostrophic eddy field is far better resolved by general circulation models.
The ACC transport will also be influenced by diapycnal processes, as argued by Gnanadesikan and Hallberg (2000). This is because changes in the meridional density gradients associated with surface thermodynamic forcing directly affect the zonal velocity of the ACC through thermal wind balance. The theoretical framework presented here can be easily extended to include thermodynamic forcing. Indeed, diapycnal fluxes simply appear as an additional term on the right-hand side of (7) and, in principle, can simply be added to the surface wind forcing. However, due to the nonlinear relation between surface wind forcing and circumpolar transport, we suggest that the addition of buoyancy forcing is unlikely to significantly modify the overall circumpolar transport.
In summary, it seems unlikely that there is a simple relationship between ACC transport and wind stress. However our numerical experiments suggest that the circumpolar transport is significantly less sensitive to surface wind forcing than predicted by the baroclinic adjustment theory of Johnson and Bryden (1989). The reduced sensitivity arises due to changes in the structure of the mean circulation with stronger wind forcing, which acts to increase the effective dissipation of the current.
Acknowledgments
We thank Chris Hughes, David Webb, Roger Samelson, and two anonymous reviewers for helpful comments on preliminary drafts. We are also grateful to Alistair Adcroft for providing us with the three-dimensional multigrid solver. This study was supported by the U.K. Natural Environment Research Council, Grant GR3/10157.
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APPENDIX
Derivation of the Upper Layer Mass Budget
Subtropical ocean gyres in a closed basin for a homogeneous, flat-bottom ocean. (a) In a closed basin, with weak wind forcing, absolute vorticity (q) contours follow latitude circles and intersect the boundaries. There can be no free, unforced flow along q contours. Wind forcing drives fluid parcels across q contours and the streamfunction (ψ) is given by Sverdrup balance. (b) If the wind forcing is strong, absolute vorticity contours are advected northward in the boundary current, and an inertial recirculation may be formed in the northwest corner of the gyre. The recirculating flow enhances the gyre transport
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Subtropical ocean gyres in a closed basin for a homogeneous, flat-bottom ocean. (a) In a closed basin, with weak wind forcing, absolute vorticity (q) contours follow latitude circles and intersect the boundaries. There can be no free, unforced flow along q contours. Wind forcing drives fluid parcels across q contours and the streamfunction (ψ) is given by Sverdrup balance. (b) If the wind forcing is strong, absolute vorticity contours are advected northward in the boundary current, and an inertial recirculation may be formed in the northwest corner of the gyre. The recirculating flow enhances the gyre transport
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Subtropical ocean gyres in a closed basin for a homogeneous, flat-bottom ocean. (a) In a closed basin, with weak wind forcing, absolute vorticity (q) contours follow latitude circles and intersect the boundaries. There can be no free, unforced flow along q contours. Wind forcing drives fluid parcels across q contours and the streamfunction (ψ) is given by Sverdrup balance. (b) If the wind forcing is strong, absolute vorticity contours are advected northward in the boundary current, and an inertial recirculation may be formed in the northwest corner of the gyre. The recirculating flow enhances the gyre transport
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Ocean dynamics in an open channel. (a) The open latitudes of Drake Passage allow free flow along unblocked, circumpolar q contours. Hence, even with weak wind forcing we may have a significant flow, with a slight deflection due to Sverdrup balance. (b) If the wind forcing is stronger, the current is deflected northward after passing through Drake Passage, and the path will be distorted further by nonlinear effects
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Ocean dynamics in an open channel. (a) The open latitudes of Drake Passage allow free flow along unblocked, circumpolar q contours. Hence, even with weak wind forcing we may have a significant flow, with a slight deflection due to Sverdrup balance. (b) If the wind forcing is stronger, the current is deflected northward after passing through Drake Passage, and the path will be distorted further by nonlinear effects
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Ocean dynamics in an open channel. (a) The open latitudes of Drake Passage allow free flow along unblocked, circumpolar q contours. Hence, even with weak wind forcing we may have a significant flow, with a slight deflection due to Sverdrup balance. (b) If the wind forcing is stronger, the current is deflected northward after passing through Drake Passage, and the path will be distorted further by nonlinear effects
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Components of transport across a Bernoulli streamline for an idealized two-layer ocean. Northward Ekman transport, TEkman, leads to a tilt in the interface between the layers until it is balanced by the sum of the eddy bolus transport, Tbolus, the Reynolds transport, TReynolds, and frictionally driven transport, Tfriction. Note that only the sum of these last three terms must be southward—the individual terms could be of either sign
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Components of transport across a Bernoulli streamline for an idealized two-layer ocean. Northward Ekman transport, TEkman, leads to a tilt in the interface between the layers until it is balanced by the sum of the eddy bolus transport, Tbolus, the Reynolds transport, TReynolds, and frictionally driven transport, Tfriction. Note that only the sum of these last three terms must be southward—the individual terms could be of either sign
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Components of transport across a Bernoulli streamline for an idealized two-layer ocean. Northward Ekman transport, TEkman, leads to a tilt in the interface between the layers until it is balanced by the sum of the eddy bolus transport, Tbolus, the Reynolds transport, TReynolds, and frictionally driven transport, Tfriction. Note that only the sum of these last three terms must be southward—the individual terms could be of either sign
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Idealized model topography for the four different sets of experiments: (a) flat bottom, (b) 2-km ridge, (c) 2-km ridge with land barriers to represent Drake Passage, and (d) additional downstream topography. Contour interval is 250 m
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Idealized model topography for the four different sets of experiments: (a) flat bottom, (b) 2-km ridge, (c) 2-km ridge with land barriers to represent Drake Passage, and (d) additional downstream topography. Contour interval is 250 m
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Idealized model topography for the four different sets of experiments: (a) flat bottom, (b) 2-km ridge, (c) 2-km ridge with land barriers to represent Drake Passage, and (d) additional downstream topography. Contour interval is 250 m
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
(a) Time series of the circumpolar transport for a flat-bottom experiment, driven by a wind stress of τ0 = 0.1 N m−2. (b) Time series of the kinetic energy for the same experiment
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
(a) Time series of the circumpolar transport for a flat-bottom experiment, driven by a wind stress of τ0 = 0.1 N m−2. (b) Time series of the kinetic energy for the same experiment
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
(a) Time series of the circumpolar transport for a flat-bottom experiment, driven by a wind stress of τ0 = 0.1 N m−2. (b) Time series of the kinetic energy for the same experiment
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Time average barotropic transport, baroclinic transport, and total eastward transport for a series of flat-bottom experiments driven by different strengths of wind forcing
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Time average barotropic transport, baroclinic transport, and total eastward transport for a series of flat-bottom experiments driven by different strengths of wind forcing
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Time average barotropic transport, baroclinic transport, and total eastward transport for a series of flat-bottom experiments driven by different strengths of wind forcing
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Log–log plot of wind stress against baroclinic transport for the flat-bottom experiments. Also shown are lines with gradients of 1/2 and 1/3
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Log–log plot of wind stress against baroclinic transport for the flat-bottom experiments. Also shown are lines with gradients of 1/2 and 1/3
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Log–log plot of wind stress against baroclinic transport for the flat-bottom experiments. Also shown are lines with gradients of 1/2 and 1/3
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Time-average zonal velocity in the upper layer for flat-bottom channel with two different values of wind stress
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Time-average zonal velocity in the upper layer for flat-bottom channel with two different values of wind stress
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Time-average zonal velocity in the upper layer for flat-bottom channel with two different values of wind stress
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Mass transport diagnostics across a streamline [Eq. (30)] for flat-bottom experiments with (a) τ0 = 0.01 N m−2 and (b) τ0 = 0.15 N m−2: transport due to Reynolds stresses (TReynolds), transport due to eddy mass fluxes (Tbolus), Ekman transport due to wind forcing (TEkman), and transport due to friction (Tfriction). The horizontal axis shows the equivalent latitude for the streamline along which we are integrating—this is the latitude that a zonal streamline that encompasses an equivalent area to the south would have. Note that the vertical scale is 6 times larger in the lower plot
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Mass transport diagnostics across a streamline [Eq. (30)] for flat-bottom experiments with (a) τ0 = 0.01 N m−2 and (b) τ0 = 0.15 N m−2: transport due to Reynolds stresses (TReynolds), transport due to eddy mass fluxes (Tbolus), Ekman transport due to wind forcing (TEkman), and transport due to friction (Tfriction). The horizontal axis shows the equivalent latitude for the streamline along which we are integrating—this is the latitude that a zonal streamline that encompasses an equivalent area to the south would have. Note that the vertical scale is 6 times larger in the lower plot
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Mass transport diagnostics across a streamline [Eq. (30)] for flat-bottom experiments with (a) τ0 = 0.01 N m−2 and (b) τ0 = 0.15 N m−2: transport due to Reynolds stresses (TReynolds), transport due to eddy mass fluxes (Tbolus), Ekman transport due to wind forcing (TEkman), and transport due to friction (Tfriction). The horizontal axis shows the equivalent latitude for the streamline along which we are integrating—this is the latitude that a zonal streamline that encompasses an equivalent area to the south would have. Note that the vertical scale is 6 times larger in the lower plot
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Time-average barotropic transport, baroclinic transport, and total transport for a series of experiments with a 2-km ridge, driven by different strengths of wind forcing
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Time-average barotropic transport, baroclinic transport, and total transport for a series of experiments with a 2-km ridge, driven by different strengths of wind forcing
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Time-average barotropic transport, baroclinic transport, and total transport for a series of experiments with a 2-km ridge, driven by different strengths of wind forcing
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Log–log plot of wind stress against baroclinic transport for the experiments with a 2-km ridge. Also shown are lines with gradients of 1/2 and 1/3
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Log–log plot of wind stress against baroclinic transport for the experiments with a 2-km ridge. Also shown are lines with gradients of 1/2 and 1/3
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Log–log plot of wind stress against baroclinic transport for the experiments with a 2-km ridge. Also shown are lines with gradients of 1/2 and 1/3
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Time-average Bernoulli potential in (a) the upper layer and (b) the lower layer for an experiment with a 2-km ridge (as shown in Fig. 4b) and wind stress given by τ0 = 0.01 N m−2. Contour intervals are 1.0 m2 s2 for the upper layer and 0.5 m2 s2 for the lower layer
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Time-average Bernoulli potential in (a) the upper layer and (b) the lower layer for an experiment with a 2-km ridge (as shown in Fig. 4b) and wind stress given by τ0 = 0.01 N m−2. Contour intervals are 1.0 m2 s2 for the upper layer and 0.5 m2 s2 for the lower layer
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Time-average Bernoulli potential in (a) the upper layer and (b) the lower layer for an experiment with a 2-km ridge (as shown in Fig. 4b) and wind stress given by τ0 = 0.01 N m−2. Contour intervals are 1.0 m2 s2 for the upper layer and 0.5 m2 s2 for the lower layer
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
As for Fig. 12 but with a wind stress given by τ0 = 0.15 N m−2
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
As for Fig. 12 but with a wind stress given by τ0 = 0.15 N m−2
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
As for Fig. 12 but with a wind stress given by τ0 = 0.15 N m−2
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
As Fig. 9 but for experiments with a 2-km ridge and wind stress given by (a) τ0 = 0.01 N m−2 and (b) τ0 = 0.15 N m−2
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
As Fig. 9 but for experiments with a 2-km ridge and wind stress given by (a) τ0 = 0.01 N m−2 and (b) τ0 = 0.15 N m−2
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
As Fig. 9 but for experiments with a 2-km ridge and wind stress given by (a) τ0 = 0.01 N m−2 and (b) τ0 = 0.15 N m−2
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Baroclinic transport as a function of wind stress for experiments with a flat bottom, a 2-km ridge, and a 2-km ridge with land barriers to represent Drake Passage
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Baroclinic transport as a function of wind stress for experiments with a flat bottom, a 2-km ridge, and a 2-km ridge with land barriers to represent Drake Passage
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Baroclinic transport as a function of wind stress for experiments with a flat bottom, a 2-km ridge, and a 2-km ridge with land barriers to represent Drake Passage
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Time-average Bernoulli potential in (a) the upper layer and (b) the lower layer for an experiment with a 2-km ridge and land barriers (shown in Fig. 4c), with a wind stress given by τ0 = 0.01 N m−2. Contour intervals are 1.0 m2 s2 for the upper layer and 0.5 m2 s2 for the lower layer
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Time-average Bernoulli potential in (a) the upper layer and (b) the lower layer for an experiment with a 2-km ridge and land barriers (shown in Fig. 4c), with a wind stress given by τ0 = 0.01 N m−2. Contour intervals are 1.0 m2 s2 for the upper layer and 0.5 m2 s2 for the lower layer
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Time-average Bernoulli potential in (a) the upper layer and (b) the lower layer for an experiment with a 2-km ridge and land barriers (shown in Fig. 4c), with a wind stress given by τ0 = 0.01 N m−2. Contour intervals are 1.0 m2 s2 for the upper layer and 0.5 m2 s2 for the lower layer
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
As for Fig. 16 but with τ0 = 0.15 N m−2
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
As for Fig. 16 but with τ0 = 0.15 N m−2
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
As for Fig. 16 but with τ0 = 0.15 N m−2
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
As Fig. 9 but for experiment with a 2-km ridge and land barriers, with (a) τ0 = 0.01 N m−2 and (b) τ0 = 0.15 N m−2. Diagnostics are only shown for circumpolar streamlines
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
As Fig. 9 but for experiment with a 2-km ridge and land barriers, with (a) τ0 = 0.01 N m−2 and (b) τ0 = 0.15 N m−2. Diagnostics are only shown for circumpolar streamlines
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
As Fig. 9 but for experiment with a 2-km ridge and land barriers, with (a) τ0 = 0.01 N m−2 and (b) τ0 = 0.15 N m−2. Diagnostics are only shown for circumpolar streamlines
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Time-average Bernoulli potential in (a) the upper layer and (b) the lower layer for an experiment with additional downstream topography (Fig. 4d) and wind stress given by τ0 = 0.15 N m−2. Contour intervals are 1.0 m2 s2 for the upper layer and 0.5 m2 s2 for the lower layer
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Time-average Bernoulli potential in (a) the upper layer and (b) the lower layer for an experiment with additional downstream topography (Fig. 4d) and wind stress given by τ0 = 0.15 N m−2. Contour intervals are 1.0 m2 s2 for the upper layer and 0.5 m2 s2 for the lower layer
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Time-average Bernoulli potential in (a) the upper layer and (b) the lower layer for an experiment with additional downstream topography (Fig. 4d) and wind stress given by τ0 = 0.15 N m−2. Contour intervals are 1.0 m2 s2 for the upper layer and 0.5 m2 s2 for the lower layer
Citation: Journal of Physical Oceanography 31, 11; 10.1175/1520-0485(2001)031<3258:OTDOWD>2.0.CO;2
Model parameters
There are several different definitions of “barotropic” and “baroclinic” components in use in oceanography. Here we define the barotropic component as the bottom velocity component multiplied by the ocean depth, and the baroclinic component as the total depth-integrated transport less the barotropic component.