Residual-mean Theory Research Articles

Extending Residual-Mean Overturning Theory to the Topographically Localized Transport in the Southern Ocean

Abstract The Southern Ocean plays a major role in global air–sea carbon fluxes, with some estimates suggesting it contributes to up to 40% of the oceanic anthropogenic carbon dioxide uptake, despite only comprising about 20% of oceanic surface area. Thus, the Southern Ocean overturning, the circulation that transports tracers between the surface and deep ocean interior, is particularly important for climate. Recent studies show that vertical velocities and tracer transport are largest just downstream of bottom topography; these quantities are related to the overturning, but provide incomplete information about the net Lagrangian transport, usually described with the residual-mean theory in a zonally integrated sense. This study uses an idealized Southern Ocean–like channel model with particle tracking to visualize the thickness-weighted velocities that capture the net overturning transport of a parcel, connecting residual-mean overturning theory to the three-dimensional, localized nature of the overturning. From this, we split the flow into three main drivers of transport: a wind-driven Ekman pumping into or out of a density layer, and standing eddies and transient eddies, both of which are localized near the topography. In this framework, the three-dimensional overturning circulation is not a small residual between the eddy and Eulerian-mean transport. The existence of a ridge weakens the response of the overturning to changes in wind, especially in the lower cell. This local understanding of the overturning framework suggests that careful modeling and sampling of specific regions near topography in the Southern Ocean are vital to understand climate sensitivity, transport, carbon export, and connections with the oceans to the north.

Sensitivity of the Antarctic Circumpolar Current transport to surface buoyancy conditions in the North Atlantic

The sensitivity of the Antarctic Circumpolar Current (ACC) transport to surface buoyancy conditions in the North Atlantic is investigated using a sector configuration of an ocean general circulation model. We find that the sensitivity of the ACC transport is significantly weaker than previous studies. We attribute this difference to the different depth of the simulated Atlantic Meridional Overturning Circulation. Because a fast restoring buoyancy boundary condition is used that strongly constrains the surface buoyancy structure at the Southern Ocean surface, the ACC transport is determined by the isopycnal slope that is coupled to the overturning circulation in the Southern Ocean. By changing the surface buoyancy in the North Atlantic, the shared buoyancy contour between the North Atlantic and the Southern Ocean is varied, and consequently the strength of the overturning circulation is modified. For different depth of the simulated overturning circulation, the response of the ACC transport to changes in the strength of the overturning circulation varies substantially. This is illustrated in two conceptual models based on the residual-mean theory of overturning circulation. Our results imply that the sensitivity of the ACC transport to surface forcing in the North Atlantic could vary substantially in different models depending on the simulated vertical structure of the overturning circulation.

A Multibasin Residual-Mean Model for the Global Overturning Circulation

AbstractThe ocean’s overturning circulation is inherently three-dimensional, yet modern quantitative estimates of the overturning typically represent the subsurface circulation as a two-dimensional, two-cell streamfunction that varies with latitude and depth only. This approach suppresses information about zonal mass and tracer transport. In this article, the authors extend earlier, zonally averaged overturning theory to explore the dynamics of a “figure-eight” circulation that cycles through multiple basins. A three-dimensional residual-mean model of the overturning circulation is derived and then simplified to a multibasin isopycnal box model to explore how stratification and diabatic water mass transformations in each basin depend on the basin widths and on deep and bottom-water formation in both hemispheres. The idealization to multiple, two-dimensional basins permits zonal mass transport along isopycnals in a Southern Ocean–like channel, while retaining the dynamical framework of residual-mean theory. The model qualitatively reproduces the deeper isopycnal surfaces in the Pacific Basin relative to the Atlantic. This supports a transfer of Antarctic Bottom Water from the Atlantic sector to the Pacific sector via the Southern Ocean, which subsequently upwells in the northern Pacific Basin. A solution for the full isopycnal structure in the Southern Ocean reproduces observed stratification differences between Atlantic and Pacific Basins and provides a scaling for the diffusive boundary layer in which the zonal mass transport occurs. These results are consistent with observational indications that North Atlantic Deep Water is preferentially transformed into Antarctic Bottom Water, which undermines the importance of an adiabatic, upper overturning cell in the modern ocean.

Sensitivity of Southern Ocean overturning to wind stress changes: Role of surface restoring time scales

The influence of different surface restoring time scales on the response of the Southern Ocean overturning circulation to wind stress changes is investigated using an idealised channel model. Regardless of the restoring time scales chosen, the eddy-induced meridional overturning circulation (MOC) is found to compensate for changes of the direct wind-driven Eulerian-mean MOC, rendering the residual MOC less sensitive to wind stress changes. However, the extent of this compensation depends strongly on the restoring time scale: residual MOC sensitivity increases with decreasing restoring time scale. Strong surface restoring is shown to limit the ability of the eddy-induced MOC to change in response to wind stress changes and as such suppresses the eddy compensation effect. These model results are consistent with qualitative arguments derived from residual-mean theory and may have important implications for interpreting past and future observations.

Connecting Antarctic Cross-Slope Exchange with Southern Ocean Overturning

Abstract Previous idealized investigations of Southern Ocean overturning have omitted its connection with the Antarctic continental shelves, leaving the influence of shelf processes on Antarctic Bottom Water (AABW) export unconsidered. In particular, the contribution of mesoscale eddies to setting the stratification and overturning circulation in the Antarctic Circumpolar Current (ACC) is well established, yet their role in cross-shelf exchange of water masses remains unclear. This study proposes a residual-mean theory that elucidates the connection between Antarctic cross-shelf exchange and overturning in the ACC, and the contribution of mesoscale eddies to the export of AABW. The authors motivate and verify this theory using an eddy-resolving process model of a sector of the Southern Ocean. The strength and pattern of the simulated overturning circulation strongly resemble those of the real ocean and are closely captured by the residual-mean theory. Over the continental slope baroclinic instability is suppressed, and so transport by mesoscale eddies is reduced. This suppression of the eddy fluxes also gives rise to the steep “V”-shaped isopycnals that characterize the Antarctic Slope Front in AABW-forming regions of the continental shelf. Furthermore, to produce water on the continental shelf that is dense enough to sink to the deep ocean, the deep overturning cell must be at least comparable in strength to wind-driven mean overturning on the continental slope. This results in a strong sensitivity of the deep overturning strength to changes in the polar easterly winds.

Comparison of four mixed layer mesoscale parameterizations and the equation for an arbitrary tracer

In this paper we discuss two issues, the inter-comparison of four mixed layer mesoscale parameterizations and the search for the eddy induced velocity for an arbitrary tracer. It must be stressed that our analysis is limited to mixed layer mesoscales since we do not treat sub-mesoscales and small turbulent mixing. As for the first item, since three of the four parameterizations are expressed in terms of a stream function and a residual flux of the RMT formalism (residual mean theory), while the fourth is expressed in terms of vertical and horizontal fluxes, we needed a formalism to connect the two formulations. The standard RMT representation developed for the deep ocean cannot be extended to the mixed layer since its stream function does not vanish at the ocean’s surface. We develop a new RMT representation that satisfies the surface boundary condition. As for the general form of the eddy induced velocity for an arbitrary tracer, thus far, it has been assumed that there is only the one that originates from the curl of the stream function. This is because it was assumed that the tracer residual flux is purely diffusive. On the other hand, we show that in the case of an arbitrary tracer, the residual flux has also a skew component that gives rise to an additional bolus velocity. Therefore, instead of only one bolus velocity, there are now two, one coming from the curl of the stream function and other from the skew part of the residual flux. In the buoyancy case, only one bolus velocity contributes to the mean buoyancy equation since the residual flux is indeed only diffusive.

Control of Lower-Limb Overturning Circulation in the Southern Ocean by Diapycnal Mixing and Mesoscale Eddy Transfer

Abstract A simple model is developed of the lower limb of the meridional overturning circulation in the Southern Ocean based on residual-mean theory. It is hypothesized that the strength of the lower-limb overturning (Ψ) is strongly controlled by the magnitude of abyssal diapycnal mixing (κ) and that of mesoscale eddy transfer (K). In particular, it is argued that Ψ ∝ κK. The scaling and associated theory find support in a suite of sensitivity experiments with an idealized ocean general circulation model. This study shows that intense diapycnal mixing is required to close the buoyancy budget of the lower-limb overturning circulation, in contrast to the upper limb, where air–sea buoyancy fluxes can provide the required diabatic forcing.

Residual-Mean Solutions for the Antarctic Circumpolar Current and Its Associated Overturning Circulation

Residual-mean theory is applied to the streamwise-averaged Antarctic Circumpolar Current to arrive at a concise description of the processes that set up its stratification and meridional overturning circulation on an f plane. Simple solutions are found in which transfer by geostrophic eddies colludes with applied winds and buoyancy fluxes to determine the depth and stratification of the thermocline and the pattern of associated (residual) meridional overturning circulation.