Topographic Form Stress Research Articles

Maintenance of the Zonal Momentum Balance of the Antarctic Circumpolar Current by Barotropic Dynamics

Abstract The vertically integrated zonal momentum balance of the Antarctic Circumpolar Current (ACC) is dominated by wind stress at the surface and topographic form stress (TFS) at the bottom. It has been argued that wind stress is transferred from the surface to the bottom by transient baroclinic eddies, via interfacial form stress, to establish the balance between wind stress and TFS. However, ocean models indicate TFS responds rapidly to changes in wind stress, suggesting that barotropic processes play a role in this balance. We investigate the dynamics governing the wind–TFS balance of the ACC and its response to wind using an idealized, wind- and buoyancy-driven channel model. We show that the balance is established and maintained at equilibrium by the barotropic dynamics. The balance results from the continuity of the flow, in which the Ekman transport at the surface, balanced by wind stress, is compensated by a return flow at depth, balanced by TFS. This leads to a match between wind stress and TFS which is independent of momentum stresses in the interior. Transient baroclinic eddies oppose the wind-driven isopycnal steepening via eddy buoyancy fluxes, which act to flatten the isopycnals. The eddy-driven isopycnal flattening corresponds to a reduction in the zonal geostrophic shear and thus a redistribution of the zonal momentum in the interior via eddy momentum stresses. The maintenance of the vertically integrated ACC momentum balance by the barotropic dynamics explains the fast response of the wind–TFS balance to changes in wind forcing.

Formation of Eastern Boundary Undercurrents via Mesoscale Eddy Rectification

Abstract Eastern boundary upwelling systems (EBUSs) host equatorward wind-driven near-surface currents overlying poleward subsurface undercurrents. Various previous theories for these undercurrents have emphasized the role of poleward alongshore pressure gradient forces (APFs). Energetic mesoscale variability may also serve to accelerate undercurrents via mesoscale stirring of the potential vorticity gradient imposed by the continental slope. However, it remains unclear whether this eddy rectification mechanism contributes substantially to driving poleward undercurrents in EBUS. This study isolates the influence of eddy rectification on undercurrents via a suite of idealized simulations forced either by alongshore winds, with or without an APF, or by randomly generated mesoscale eddies. It is found that the simulations develop undercurrents with strengths comparable to those found in nature in both wind-forced and randomly forced experiments. Analysis of the momentum budget reveals that the along-isobath undercurrent flow is accelerated by isopycnal advective eddy momentum fluxes and the APF and retarded by frictional drag. The undercurrent acceleration may manifest as eddy momentum fluxes or as topographic form stress depending on the coordinate system used to compute the momentum budget, which reconciles these findings with previous work that linked eddy acceleration of the undercurrent to topographic form stress. The leading-order momentum balance motivates a scaling for the strength of the undercurrent that explains most of the variance across the simulations. These findings indicate that eddy rectification is of comparable importance to the APF in driving poleward undercurrents in EBUSs and motivate further work to diagnose this effect in high-resolution models and observations and to parameterize it in coarse-resolution ocean/climate models.

Inertial Effect and Its Dependency on the Topographic Geometries in Barotropic Channel Models under the Weakly Nonlinear Regime

Abstract Recent studies have shown that the sensitivity of the circumpolar transport of channels to the westerlies is controlled by wind-driven gyre circulations. Although the form stress associated with the gyres has been shown to be controlled by eddies, bottom friction, and topographic width, the role of inertial effects has not been fully understood. In this study, we conduct a series of sensitivity analyses using the barotropic model with and without the advection term (hereinafter, the model without the advection term is denoted as linear model). Experiments showed that the sensitivity of the circumpolar transport decreased under the westerly winds compared to the linear model, while it increased under the easterly winds. We show that the inertial effect of western boundary currents generates anomalous anticyclonic circulations over the topography, producing the westward topographic form stress anomalies regardless of the wind directions. In addition, we discuss the sensitivity of the inertial effect mechanism to topographic height, width, and geometries. The inertial effect mechanism is robust as long as the gyre circulations dominate while its relative importance changes. We also found that the dynamics of the barotropic channel strongly depend on the geometries of geostrophic contours f/h. Therefore, we conclude that the dynamics of barotropic channel models might be interpreted with caution to understand the dynamics of the Southern Ocean. Significance Statement Previous studies have studied baroclinic and barotropic channel models as a benchmark of the Southern Ocean, but the nonlinear dynamics of channels have not been fully understood. In this paper, we show that the inertial effect by the mean flow works to decrease the sensitivity to the westerly winds in the barotropic channel models using numerical experiments. We also show that the inertial effect is robust as long as gyre circulations exist, while its relative importance differs.

The sensitivity of the Eocene–Oligocene Southern Ocean to the strength and position of wind stress

Abstract. The early Cenozoic opening of the Tasmanian Gateway (TG) and Drake Passage (DP), alongside the synergistic action of the westerly winds, led to a Southern Ocean transition from large, subpolar gyres to the onset of the Antarctic Circumpolar Current (ACC). However, the impact of the changing latitudinal position and strength of the wind stress in altering the early Southern Ocean circulation has been poorly addressed. Here, we use an eddy-permitting ocean model (0.25∘) with realistic late Eocene paleo-bathymetry to investigate the sensitivity of the Southern Ocean to paleo-latitudinal migrations (relative to the gateways) and strengthening of the wind stress. We find that southward wind stress shifts of 5 or 10∘, with a shallow TG (300 m), lead to dominance of subtropical waters in the high latitudes and further warming of the Antarctic coast (increase by 2 ∘C). Southward migrations of wind stress with a deep TG (1500 m) cause the shrinking of the subpolar gyres and cooling of the surface waters in the Southern Ocean (decrease by 3–4 ∘C). With a 1500 m deep TG and maximum westerly winds aligning with both the TG and DP, we observe a proto-ACC with a transport of ∼47.9 Sv. This impedes the meridional transport of warm subtropical waters to the Antarctic coast, thus laying a foundation for thermal isolation of the Antarctic. Intriguingly, proto-ACC flow through the TG is much more sensitive to strengthened wind stress compared to the DP. We suggest that topographic form stress can balance surface wind stress at depth to support the proto-ACC while the sensitivity of the transport is likely associated with the momentum budget between wind stress and near-surface topographic form stress driven by the subtropical gyres. In summary, this study proposes that the cooling of Eocene Southern Ocean is a consequence of a combination of gateway deepening and the alignment of maximum wind stress with both gateways.

Momentum Governors of California Undercurrent Transport

AbstractThe California Undercurrent (CUC) transport, with significant variability ranging from weeks to decades, has consequences for both the climate and biogeochemistry of the California Current system. This study evaluates the governors of the CUC transport and its temporal variability from a momentum perspective, using a mesoscale-resolving regional model. From a 16-yr mean perspective, the along-isobath pressure gradient acts to accelerate the CUC, whereas eddy advection retards it. The topographic form stress, which is part of the volume integrated along-isobath pressure gradient, not only acts in the direction of the time-mean CUC, but also greatly modulates the temporal variability of the CUC transport. This temporal variability is also correlated with the eddy momentum advection. The eddy stress plays a role in transferring both the equatorward wind stress and poleward CUC momentum downward. A theory is formulated to show that, in addition to the conventional vertical redistribution of momentum, the eddy stress can also redistribute momentum horizontally in the area where the correlation between the pressure anomaly and isopycnal fluctuations has large spatial variability.

Does Topographic Form Stress Impede Prograde Ocean Currents?

AbstractTopographic form stress (TFS) plays a central role in constraining the transport of the Antarctic Circumpolar Current (ACC), and thus the rate of exchange between the major ocean basins. Topographic form stress generation in the ACC has been linked to the formation of standing Rossby waves, which occur because the current is retrograde (opposing the direction of Rossby wave propagation). However, it is unclear whether TFS similarly retards current systems that are prograde (in the direction of Rossby wave propagation), which cannot arrest Rossby waves. An isopycnal model is used to investigate the momentum balance of wind-driven prograde and retrograde flows in a zonal channel, with bathymetry consisting of either a single ridge or a continental shelf and slope with a meridional excursion. Consistent with previous studies, retrograde flows are almost entirely impeded by TFS, except in the limit of flat bathymetry, whereas prograde flows are typically impeded by a combination of TFS and bottom friction. A barotropic theory for standing waves shows that bottom friction serves to shift the phase of the standing wave’s pressure field from that of the bathymetry, which is necessary to produce TFS. The mechanism is the same in prograde and retrograde flows, but is most efficient when the mean flow arrests a Rossby wave with a wavelength comparable to that of the bathymetry. The asymmetry between prograde and retrograde momentum balances implies that prograde current systems may be more sensitive to changes in wind forcing, for example associated with climate shifts.

Small‐Scale Topographic Form Stress and Local Dynamics of the Southern Ocean

AbstractThe contribution of small‐scale abyssal hill topography to the topographic form stress and local dynamics of the Southern Ocean is investigated using a high‐resolution model of the sector of the Southern Ocean south of Tasmania and New Zealand. The results of two simulations, with and without small, O(1–100 km), scale topography, confirm that the effects of small‐scale topography are exerted through the generation of strong topographic form stress leading to transient eddy dissipation and changes in flow meanders. Small‐scale topographic form stress is comparable in magnitude to that generated by large‐scale topography, but with a pairwise distribution of positive and negative stress values upstream and downstream of the Macquarie Ridge, consistent with the meandering of the flow. In the experiment without small‐scale topography, the bottom mean flow speed increases, while the surface mean speed slightly decreases, making the mean flow more barotropic. Eddy kinetic energy also greatly enhances throughout the water column after removing small‐scale topography. Our results suggest that small‐scale topography has strong impact on transient eddies and plays an important role for setting the vertical structure of the flow and the equilibration and position of flow meanders.

Is the Coefficient of Eddy Potential Vorticity Diffusion Positive? Part I: Barotropic Zonal Channel

AbstractThe question of whether the coefficient of diffusivity of potential vorticity by mesoscale eddies is positive is studied for a zonally reentrant barotropic channel using the quasigeostrophic approach. The topography is limited to the first mode in the meridional direction but is unlimited in the zonal direction. We derive an analytic solution for the stationary (time independent) solution. New terms associated with parameterized eddy fluxes of potential vorticity appear both in the equations for the mean zonal momentum balance and in the kinetic energy balance. These terms are linked with the topographic form stress exerted by parameterized eddies. It is demonstrated that in regimes with zonal flow (analogous to the Antarctic Circumpolar Current), the coefficient of eddy potential vorticity diffusivity must be positive.

Interfacial Form Stress in the Southern Ocean State Estimate

AbstractThe wind stress that drives the Antarctic Circumpolar Current (ACC) exits the fluid via topographic form stress (TFS) at the sea floor; interfacial form stress (IFS) is thought to carry much of this momentum from source to sink. These form stresses combine to help set the strength and structure of the Southern Ocean meridional overturning circulation (MOC), a key nexus of heat and gas exchange between the deep ocean and the atmosphere. For the first time in a general circulation model, we calculate the time‐varying, three‐dimensional IFS field directly from zonal pressure gradients across vertical perturbations in isopycnal layer interfaces. We confirm previous findings that IFS compensates wind stress at the surface and topographic form stress at the seafloor in the Drake Passage latitudes. We find that zonal and time‐mean IFS is primarily responsible for this surface wind stress compensation, with some contribution from transient eddy IFS. Mean, standing eddy, and transient eddy IFS combine to compensate topographic form stress at depth. Both standing and transient eddy IFS concentrate at stationary meanders along the ACC, and transient eddy IFS dominates standing eddy IFS in regions of high eddy kinetic energy. Finally, total IFS changes sign from balancing eastward wind stress to balancing westward topographic form stress around 28.1 kg m−3, close to the upper limit of Antarctic Bottom Water, indicating the role of buoyancy forcing in setting the structure of the IFS field.

Reshaping the Antarctic Circumpolar Current via Antarctic Bottom Water Export

AbstractZonal momentum input into the Antarctic Circumpolar Current (ACC) by westerly winds is ultimately removed via topographic form stress induced by large bathymetric features that obstruct the path of the current. These bathymetric features also support the export of Antarctic Bottom Water (AABW) across the ACC via deep, geostrophically balanced, northward flows. These deep geostrophic currents modify the topographic form stress, implying that changes in AABW export will alter the ocean bottom pressure and require a rearrangement of the ACC in order to preserve its zonal momentum balance. A conceptual model of the ACC momentum balance is used to derive a relationship between the volume export of AABW and the shape of the sea surface across the ACC’s standing meanders. This prediction is tested using an idealized eddy-resolving ACC/Antarctic shelf channel model that includes both the upper and lower cells of the Southern Ocean meridional overturning circulation, using two different topographic configurations to obstruct the flow of the ACC. Eliminating AABW production leads to a shallowing of the sea surface elevation within the standing meander. To quantify this response, the authors introduce the “surface-induced topographic form stress,” the topographic form stress that would result from the shape of the sea surface if the ocean were barotropic. Eliminating AABW production also reduces the magnitude of the eddy kinetic energy generated downstream of the meander and the surface speed of the ACC within the meander. These findings raise the possibility that ongoing changes in AABW export may be detectable via satellite altimetry.

Beta-plane turbulence above monoscale topography

Using a one-layer quasi-geostrophic model, we study the effect of random monoscale topography on forced beta-plane turbulence. The forcing is a uniform steady wind stress that produces both a uniform large-scale zonal flow $U(t)$ and smaller-scale macroturbulence characterized by standing and transient eddies. The large-scale flow $U$ is retarded by a combination of Ekman drag and the domain-averaged topographic form stress produced by the eddies. The topographic form stress typically balances most of the applied wind stress, while the Ekman drag provides all of the energy dissipation required to balance the wind work. A collection of statistically equilibrated numerical solutions delineate the main flow regimes and the dependence of the time average of $U$ on parameters such as the planetary potential vorticity (PV) gradient $\unicode[STIX]{x1D6FD}$ and the statistical properties of the topography. We obtain asymptotic scaling laws for the strength of the large-scale flow $U$ in the limiting cases of weak and strong forcing. If $\unicode[STIX]{x1D6FD}$ is significantly smaller than the topographic PV gradient, the flow consists of stagnant pools attached to pockets of closed geostrophic contours. The stagnant dead zones are bordered by jets and the flow through the domain is concentrated into a narrow channel of open geostrophic contours. In most of the domain, the flow is weak and thus the large-scale flow $U$ is an unoccupied mean. If $\unicode[STIX]{x1D6FD}$ is comparable to, or larger than, the topographic PV gradient, then all geostrophic contours are open and the flow is uniformly distributed throughout the domain. In this open-contour case, there is an ‘eddy saturation’ regime in which $U$ is insensitive to large changes in the wind stress. We show that eddy saturation requires strong transient eddies that act effectively as PV diffusion. This PV diffusion does not alter the kinetic energy of the standing eddies, but it does increase the topographic form stress by enhancing the correlation between the topographic slope and the standing-eddy pressure field. Using bounds based on the energy and enstrophy power integrals, we show that as the strength of the wind stress increases, the flow transitions from a regime in which the form stress balances most of the wind stress to a regime in which the form stress is very small and large transport ensues.

Topographic form stress in the Southern Ocean State Estimate

AbstractWe diagnose the Southern Ocean momentum balance in a 6 year, eddy‐permitting state estimate of the Southern Ocean. We find that 95% of the zonal momentum input via wind stress at the surface is balanced by topographic form stress across ocean ridges, while the remaining 5% is balanced via bottom friction and momentum flux divergences at the northern and southern boundaries of the analysis domain. While the time‐mean zonal wind stress field exhibits a relatively uniform spatial distribution, time‐mean topographic form stress concentrates at shallow ridges and across the continents that lie within the Antarctic Circumpolar Current (ACC) latitudes; nearly 40% of topographic form stress occurs across South America, while the remaining 60% occurs across the major submerged ridges that underlie the ACC. Topographic form stress can be divided into shallow and deep regimes: the shallow regime contributes most of the westward form stress that serves as a momentum sink for the ACC system, while the deep regime consists of strong eastward and westward form stresses that largely cancel in the zonal integral. The time‐varying form stress signal, integrated longitudinally and over the ACC latitudes, tracks closely with the wind stress signal integrated over the same domain; at zero lag, 88% of the variance in the 6 year form stress time series can be explained by the wind stress signal, suggesting that changes in the integrated wind stress signal are communicated via rapid barotropic response down to the level of bottom topography.

Submesoscale Instability and Generation of Mesoscale Anticyclones near a Separation of the California Undercurrent

AbstractThe California Undercurrent (CUC) flows poleward mostly along the continental slope. It develops a narrow strip of large negative vertical vorticity through the turbulent boundary layer and bottom stress. In several downstream locations, the current separates, aided by topographic curvature and flow inertia, in particular near Point Sur Ridge, south of Monterey Bay. When this happens the high-vorticity strip undergoes rapid instability that appears to be mesoscale in “eddy-resolving” simulations but is substantially submesoscale with a finer computational grid. The negative relative vorticity in the CUC is larger than the background rotation f, and Ertel potential vorticity is negative. This instigates ageostrophic centrifugal instability. The submesoscale turbulence is partly unbalanced, has elevated local dissipation and mixing, and leads to dilution of the extreme vorticity values. Farther downstream, the submesoscale activity abates, and the remaining eddy motions exhibit an upscale organization into the mesoscale, resulting in long-lived coherent anticyclones in the depth range of 100–500 m (previously called Cuddies) that move into the gyre interior in a generally southwestward direction. In addition to the energy and mixing effects of the postseparation instability, there is are significant local topographic form stress and bottom torque that retard the CUC and steer the mean current pathway.

The Injection of Zonal Momentum by Buoyancy Forcing in a Southern Ocean Model

AbstractAn overturning circulation, driven by prescribed buoyancy forcing, is used to set a zonal volume transport in a reentrant channel ocean model with three isopycnal layers. The channel is designed to represent the Southern Ocean such that the forced overturning resembles the lower limb of the meridional overturning circulation (MOC). The relative contributions of wind and buoyancy forcing to the zonal circulation are examined. It is found that the zonal volume transport is strongly dependent on the buoyancy forcing and that the eddy kinetic energy is primarily set by wind stress forcing. The zonal momentum budget integrated over each layer is considered in the buoyancy-forced, wind-forced, and combined forcing case. At equilibrium, sources and sinks of momentum are balanced, but the transient spinup reveals the source of momentum for the current. In the buoyancy-forced case, the forcing creates a baroclinic shear with westward flow in the lower layer, allowing topographic form stress and bottom friction to act as the initial sources of eastward momentum, with bottom friction acting over a longer time frame. In the wind-forced and combined forcing cases, the surface wind stress dominates the initial momentum budget, and the time to reach equilibration is shorter in the combined forcing simulation. These results imply that future changes in the rate of formation of Antarctic Bottom Water may alter the volume transport of the Antarctic Circumpolar Current.

Establishment of momentum balance by form stress in a wind-driven channel

We examine the establishment of form stress in the spinup of a rotating isopycnal wind-driven channel model, with reference to the Antarctic Circumpolar Current. Initially, the force balance resembles Ekman layer transport, where zonal surface winds are balanced by the Coriolis forces in the upper layers, while the bottom layers consist of an opposing meridional flow balanced by topographic form stress. As the meridional transport increases, the isopycnal slopes and zonal transport also increase and the flow becomes baroclinically unstable, leading to the development of interfacial form stresses due to small-scale baroclinic eddies. This form stress alters the force balance of the layers, causing the system to geostrophically readjust to new states with progressively lower meridional transports. This trend continues until the meridional transport stops and the current is balanced solely by winds and form stress. The final state is a turbulent flow consisting of a several meandering jets that are maintained by the mesoscale eddy field. Our results resemble recent observations of the Antarctic Circumpolar Current and illustrate the contribution of mesoscale eddies to the force balance of the Southern Ocean.

Wave-induced topographic formstress in baroclinic channel flow

Large-scale zonal flow driven across submarine topography establishes standing Rossby waves. In the presence of stratification, the wave pattern can be represented by barotropic and baroclinic Rossby waves of mixed planetary topographic nature, which are locked to the topography. In the balance of momentum, the wave pattern manifests itself as topographic formstress. This wave-induced formstress has the net effect of braking the flow and reducing the zonal transport. Locally, it may lead to acceleration, and the parts induced by the barotropic and baroclinic waves may have opposing effects. This flow regime occurs in the circumpolar flow around Antarctica. The different roles that the wave-induced formstress plays in homogeneous and stratified flows through a zonal channel are analyzed with the BARBI (BARotropic-Baroclinic-Interaction ocean model, Olbers and Eden, J Phys Oceanogr 33:2719–2737, 2003) model. It is used in complete form and in a low-order version to clarify the different regimes. It is shown that the barotropic formstress arises by topographic locking due to viscous friction and the baroclinic one due to eddy-induced density advection. For the sinusoidal topography used in this study, the transport obeys a law in which friction and wave-induced formstress act as additive resistances, and windstress, the effect of Ekman pumping on the density stratification, and the buoyancy forcing (diapycnal mixing of the stratified water column) of the potential energy stored in the stratification act as additive forcing functions. The dependence of the resistance on the system parameters (lateral viscosity ε, lateral diffusivity κ of eddy density advection, Rossby radius λ, and topography height δ) as well as the dependence of transport on the forcing functions are determined. While the current intensity in a channel with homogeneous density decreases from the viscous flat bottom case in an inverse quadratic law ~δ –2 with increasing topography height and always depends on ε, a stratified system runs into a saturated state in which the transport becomes independent of δ and ε and is determined by the density diffusivity κ rather than the viscosity: κ/λ 2 acts as a vertical eddy viscosity, and the transport is λ 2/κ times the applied forcing. Critical values for the topographic heights in these regimes are identified.

Adjustment of the Southern Ocean to Wind Forcing on Synoptic Time Scales

Abstract This study addresses the response of the Southern Ocean to high-frequency wind forcing, focusing on the impact of several barotropic modes on the circumpolar transport. A suite of experiments is performed with an unstratified model of the Southern Ocean, forced with a stochastic wind stress that contains a large range of frequencies with synoptic time scales. The Southern Ocean adjustment displays a different character for frequencies below and above 0.2 cpd. The low-frequency range is dominated by an “almost-free-mode” response in the region where contours of f /H are obstructed by only a few bathymetric features; the truly free mode only plays a minor role. Topographic form stress, rather than friction, is the dominant decay mechanism of the Southern Mode. It leads to a spindown time scale on the order of 3 days. For the high-frequency range, the circumpolar transport is dominated by the resonant excitation of oscillatory modes. The “active” response of the ocean leads to strong changes and even discontinuities in the phase relation between transport and wind stress.

Atmosphere–Ocean Momentum Exchange in General Circulation Models

A series of two-layer quasigeostrophic solutions for the ocean circulation driven by a steady wind in a channel with topography and in a flat bottom rectangular basin are presented in which the atmosphere and ocean are inertially coupled through the surface stress relation. The only other frictional processes are biharmonic lateral friction (under free-slip boundary conditions) and topographic form stress; there is no bottom friction involved. The results indicate that realistic momentum balances can be obtained on this physical basis. Two types of solutions are obtained, which are called (i) the I series in which the inertial coupling relation is applied directly in the earth reference frame with no current averaging and almost steady stream fields occur and (ii) the S series in which the inertial coupling relation is applied for long current averaging periods, of the order 100 days, rather than instantaneously. The solutions for the longer current averaging periods produce vigorous eddy fields, but their time-mean is very similar to the corresponding solution with no current averaging. Surface Stokes drift streamfields are also generated by the inertial coupling mechanism. Some implications of the results for general circulation modeling are discussed.

The Southern Ocean Momentum Balance: Evidence for Topographic Effects from Numerical Model Output and Altimeter Data

Abstract The momentum balance of the Antarctic Circumpolar Current is investigated using both output from a high-resolution primitive equation model and sea surface height measurements from the Geosat altimeter. In the Semtner–Chervin general circulation model, run with approximately one-quarter degree resolution and time-varying ECMWF winds, topographic form stress is the dominant process balancing the surface wind forcing. Detailed examination of form stress in the model indicates that it is due to three large topographic obstructions located at Kerguelen Island, Campbell Plateau, and Drake Passage. The difference between wind stress and form stress represents the lateral transfer of momentum into and out of the ACC. It is examined both in zonal coordinates to conform to the model architecture and along mean streamlines in order to reduce the effects of standing eddies. In this particular model, in stream coordinates, biharmonic friction dominates the lateral transfer of momentum. Since biharmonic frict...

The zonal momentum balance in an eddy-resolving general-circulation model of the Southern Ocean

The momentum balance in the zonally unbounded region of the Southern Ocean is examined using an eddy-resolving ocean general-circulation model (namely FRAM). Momentum, which is input at the surface and accelerates the Antarctic Circumpolar Current, is transferred down the water column and removed by topographic form stress. Bottom friction and lateral eddy viscosity are found to be negligible. the poleward flux of eastward momentum has a small effect in redistributing momentum. In spite of this, below the wind-driven surface layer and above the level of topography, the poleward momentum-flux divergence provides the main balance along with the ageostrophic flux of planetary vorticity (although the magnitude of these terms is an order of magnitude smaller than the wind stress). Below the Ekman layer, standing eddies produce a drag on the flow whilst transient eddies accelerate the flow. However, the impact of transient eddies is smaller. the downward transfer of momentum is achieved by interfacial form stress. This can be understood in terms of a poleward density (heat) flux. the main contribution comes from standing eddies, with a smaller contribution from transient eddies. Both contributions assist the transfer. the flux of density (heat) from the neighbouring oceans (to the north and south of the Drake Passage latitudes) influences the depth penetration of zonal momentum, particularly in the upper 1000 m. the Johnson-Bryden theory is generalized to give an additional term which is proportional to the stream function for the residual circulation associated with Eliassen-Palm cross-sections.