1. Introduction
The Antarctic Circumpolar Current (ACC) plays a key role in the ventilation of dense water masses and the closure of the global overturning circulation (e.g., Marshall and Speer 2012). Recent work has highlighted the impact of the ACC’s local dynamics on interbasin transport (Jones and Cessi 2016; Thompson et al. 2016) as well as meridional heat and tracer transport (Dufour et al. 2015). Although eddy kinetic energy (EKE) and isopycnal slopes vary along the path of the ACC, zonally averaged isopycnal slopes have, in general, been found to be insensitive to changes in the wind stress in models and observations (Böning et al. 2008; Abernathey et al. 2011). This effect and the relative insensitivity of the ACC’s zonal baroclinic transport to an observed increase in wind stress over the ACC between 1958 and 2000 (Marshall 2003), commonly referred to as “eddy saturation” (Hogg et al. 2008, 2015), has highlighted the need to mechanistically understand both the global and local response of the ACC to a modified surface wind stress (see also Downes and Hogg 2013; Bishop et al. 2016). There is evidence that zonally symmetric increases in wind stress are principally balanced by localized changes in bottom form drag, communicated via interfacial form stress (Ward and Hogg 2011; Thompson and Naveira Garabato 2014; Masich et al. 2015).
Intensification of the surface wind stress over the ACC has been linked to an increase in the baroclinicity of the flow and a subsequent release of energy through baroclinic instability, diagnosed from increased EKE calculated from satellite altimetry-derived velocities (Meredith and Hogg 2006; Hogg et al. 2015). Locally, the increase in EKE is dominated by regions immediately downstream of major topographic features; in regions removed from topography, changes are more moderate. These regions may even experience a suppression of EKE (Bischoff and Thompson 2014; Abernathey and Cessi 2014; Bishop et al. 2016). The magnitude of tracer transport is also heterogeneously distributed in the ACC, with modulations set by interactions between the flow and topographic features (Lu and Speer 2010; Ferrari and Nikurashin 2010; Naveira Garabato et al. 2011; Thompson and Sallée 2012; Abernathey and Cessi 2014; Dufour et al. 2015). Most studies have sought to understand this spatial variability in terms of modifications to the flow’s baroclinicity (Chapman et al. 2015; Bischoff and Thompson 2014), although interactions with topography also produce significant changes to the flow’s barotropic shear. Here we focus on along-stream transitions in the dynamical regimes of an idealized ACC meander, accounting for both eddy buoyancy and momentum fluxes and thus both baroclinic and barotropic instability, respectively.
Our analysis will primarily consider the dynamical properties of the major standing meanders of the ACC. These regions, located downstream of topographic features, share many similarities with atmospheric storm tracks—regions of elevated EKE (Hoskins and Valdes 1990; Hoskins and Hodges 2002; Chang et al. 2002). The shape and life cycle of atmospheric storm tracks have been, in part, linked to the standing components (i.e., standing meanders) and their ability to modify the local baroclinicity of the flow (Kaspi and Schneider 2011, 2013). While baroclinic instability plays a key role in these interactions, in the atmosphere barotropic instabilities also influence standing meanders (Williams et al. 2007; Chang et al. 2002). A defining characteristic of atmospheric storm tracks is a displacement of regions of peak baroclinicity and peak EKE, which also occurs in fully nonlinear ACC-like scenarios (Chapman et al. 2015) and is related to classical studies of linear instability in domains with along-stream variations in the background stratification (Pierrehumbert 1984; Pedlosky 1989). A key difference is that oceanic standing meanders, or storm tracks, have a separation of characteristic length scales between the standing meander and transient eddies (Williams et al. 2007; Chapman et al. 2015), which influence energy transfer properties of the flow.
An example of the interplay between barotropic and baroclinic instabilities is the barotropic governor. This mechanism was first introduced by James and Gray (1986) to explain why atmospheric simulations with the same baroclinicity but larger barotropic shears have smaller eddy kinetic energy. James (1987) presented both linear and nonlinear characteristics associated with the barotropic governor and found that barotropic shear may suppress the growth of a baroclinically unstable fluid due to the destructive effect of the shear on the exponentially growing normal modes. James (1987) also recognized that the decay of baroclinic eddies may also be responsible for generating or sustaining the barotropic shear. Building on the nonlinear aspect of the barotropic governor, Nakamura (1993) specifically showed that normal-mode baroclinic waves are sensitive to vertically integrated eddy momentum fluxes generated by barotropic shear. The resulting upgradient momentum fluxes limit the conversion of available potential energy into eddy kinetic energy. In other ocean-focused studies, Rivière et al. (2004) found that the baroclinicity often overwhelms the barotropic governor mechanism, but Solodoch et al. (2016) presented Southern Ocean and idealized (respectively) flow regimes with characteristics consistent with the barotropic governor. In this study, by diagnosing both momentum and buoyancy fluxes within and far from the meander, we examine the relevance of this mechanism in the ACC.
Here we adopt the geometric stability method, described in Marshall et al. (2012), Waterman and Hoskins (2013), and Waterman and Lilly (2015), to examine the stability properties and energy conversion rates of an ACC meander with a higher degree of granularity than in earlier studies that have focused primarily on differences between meander and quasi-zonal regions of the ACC. Waterman and Hoskins (2013) showed how the statistics of eddy geometry, calculated for an idealized barotropic jet, agree with simple predictions of eddy–mean energy exchange. More recently, Waterman and Lilly (2015) used the same model to consider the geometric decomposition of eddy feedbacks and showed that both the angle and the anisotropy of transient eddies are important for the evolution of the mean flow. Recently, Tamarin et al. (2016) extended this horizontal analysis to show the consistency of ray-tracing theory with the geometric method. This method is useful for its physical interpretation and connection to linear stability theory. A motivation for this approach is that the horizontal eddy shape can be observed remotely, leading to an assessment of eddy momentum fluxes without the need to compute correlations (Marshall et al. 2012). A global analysis in this framework was carried out by Stewart et al. (2015) using a global general circulation model. These previous studies [with the exception of Marshall et al. (2012)] only consider barotropic flow regimes, and therefore the statistical description of the eddy geometry is limited to the horizontal plane. The ACC, however, has a significant baroclinic component, which motivates our adoption of the generalized three-dimensional eddy geometry developed by Marshall et al. (2012).
Using an idealized MITgcm channel model with a meridional ridge, we examine the three-dimensional shape of transient eddies to determine their evolution and interaction with ACC meanders; these diagnostics are compared with energy conversion terms. Diagnosing both kinetic and potential energy conversions allows us to assess the relative importance of both barotropic and baroclinic instabilities in the life cycle of an ACC meander. The model and methods are described in section 2. In section 3, we discuss the spatial distribution of energy conversion terms and analyze the localization of this exchange. Following Marshall et al. (2012), we examine the geometric stability of the domain in section 4. In section 5, these results are interpreted in terms of the interaction between barotropic and baroclinic instabilities and are compared to previous studies of storm tracks and jet regions; we conclude with a summary in section 6.
2. Methods
a. Energy conversion
We consider the following five terms in this study following Chen et al. (2014):
- the rate of change of MAPE from horizontal eddy density (buoyancy) fluxes (
where uH is the horizontal velocity vector and ∇H is the horizontal gradient operator; - the rate of change of eddy energy (EKE and EAPE) due to horizontal eddy density (buoyancy) fluxes (
- the rate of change in EKE from EAPE (
where w is the vertical velocity and g is the gravitational acceleration constant; - the rate of change in MKE due to eddy momentum fluxes (
- and the rate of change of EKE due to eddy momentum fluxes (
The baroclinic instability pathway is described by the D terms 
We note that 
b. Eddy geometry
In addition to the energy conversion terms described above, we also employ an eddy shape analysis to examine eddy–mean flow interactions within the meander. While the geometric diagnostics essentially use the same information as the conversion terms—eddy fluxes of momentum and buoyancy—the geometric framework has proven insightful in mapping the spatial distribution of eddy–mean flow interaction (Waterman and Lilly 2015). The derivation of the eddy geometry terms is provided in Marshall et al. (2012).
Schematic relating eddy orientation and stability [both (top) barotropic and (middle) baroclinic] and (bottom) relating anisotropy and energy transfer. The black arrows to the left show the shear related to the mean flow u, and the dashed lines are the eddy streamfunction contours ψ′. Purely barotropic eddies tilt in the horizontal (top) and ψ′ is a function of u′ and υ′; purely baroclinic eddies tilt in the vertical (middle) and ψ′ is a function of υ′ and b′. When the eddy major axis tilts with the shear, the eddies are stable and decay, giving energy to the mean flow, which increases the shear. When the eddy major axis tilts against the shear, the eddies are unstable and grow, taking energy from the mean flow, which reduces the shear.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0160.1
Larger anisotropy—given by γm in the horizontal and γt in the vertical—of the eddy fluxes is associated with stronger eddy–mean flow interactions. The angle of the eddy (ϕm, ϕt), with respect to the mean flow determines the stability of the flow, is represented schematically in Fig. 1. When the eddy, represented by an eddy streamfunction, tilts against the mean flow shear, the perturbation is growing and extracting energy from the mean flow. When the eddy is tilted with the mean flow shear, the perturbation is decaying and exchanging energy back into the mean flow (Pedlosky 2013). For energy to transfer between the mean and eddy components, the eddy flux anisotropy and eddy streamfunction tilt must both be nonzero, with larger anisotropy, γ → 1, providing more effective energy transfer. This conceptual picture has been effective in describing barotropic flows (Waterman and Lilly 2015) and can be extended to describe the physical shape of a barotropic eddy. The physical interpretation is more challenging when extended to the vertical because the eddy geometry now depends on eddy buoyancy fluxes instead of just eddy momentum fluxes, that is, depends on u′, υ′, and b′. Nevertheless, below we show that the eddy orientation provides a consistent picture when compared to the more traditional energy conversion terms.
c. Model
Eddy kinetic energy at 177-m depth for experiments with wind stress forcing (a) τ0 = 0.1 N m−2 and (b) τ = 0.2 N m−2. Thick white contours indicate the region containing EKE that is at least 80% of the peak EKE. Thin lines show potential temperature contours and are separated by 1°C. Thick lines show where the Gaussian ridge, centered at 800 km, rises above 3800-m depth.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0160.1
3. Energy conversion
We first present the energy conversion terms to diagnose the spatial patterns of the eddy–mean flow interactions. The diagnosed depth-averaged eddy energy conversion terms are defined in section 2a. The largest amplitudes of 
Depth-integrated energy conversion terms (W m−2) for the experiment with τ0 = 0.1 N m−2. Contour lines show temperature every degree Celsius at 177-m depth. Term 
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0160.1
As in Fig. 3, but depth-integrated energy conversion terms (W m−2) with τ0 = 0.2 N m−2.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0160.1
In contrast, the patterns of 
The conversion of MKE from the eddy momentum fluxes, 
Comparing the two imposed wind stress amplitudes, all conversion terms have larger magnitudes for the τ0 = 0.2 N m−2 experiment (Figs. 3, 4). This is consistent with a mechanically induced increase in the EAPE reservoir; the stronger wind stress generates a larger-amplitude, near-surface Ekman convergence and divergence. However, qualitatively there is no appreciable change in the physical extent of the conversion region with a change in winds, which differs from the results of Bischoff and Thompson (2014). In this previous study, which used a Gaussian bump instead of a ridge, the physical extent of the storm track was strongly sensitive to the magnitude of the wind stress.
The relative insensitivity of the zonal baroclinic mean flow to the wind stress is a common feature of these ACC-like channel models, a property known as eddy saturation, but the sensitivity of the energy budget and the exchange between different reservoirs has been explored to a lesser extent. We consider the regionally averaged energy characteristics using a Lorenz diagram similar to those used in Chen et al. (2014) (Fig. 5). Within the meander, defined by boxes on the left-hand side of Figs. 3 and 4, eddy fluxes consistent with barotropic instability are a primary component of energy transfer. This is represented by the conversion of MKE into EKE, which occurs in a barotropically unstable system. In contrast, downstream of the meander, defined by the right-hand boxes in Figs. 3 and 4, EKE is converted back to MKE, consistent with upgradient eddy momentum fluxes. In the downstream domain, there is an excess of energy being introduced from upstream, consistent with advection out of the upstream domain shown in the Lorenz diagram.
Lorenz diagram from two different regions, indicated by the boxes in Figs. 3 and 4. The meander region is located just downstream of the ridge and the downstream domain refers to a region with quasi-zonal jets. The values provided in the diagram are depth-integrated, domain-averaged quantities (W m−2). The diagrams follow those shown in Chen et al. (2014).
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0160.1
For the potential energy transfer components of the Lorenz diagram, in both regions, MAPE is converted into EAPE, which is then converted into EKE: the traditional baroclinic instability energy pathway. However, 
With a change in wind stress, the magnitude of the energy transfers in the Lorenz diagram tends to increase. Within the meander, the conversion of MAPE to EAPE is doubled when the wind stress is doubled, but the conversion of EAPE to EKE is only increased by 60%. The conversion of MKE to EKE, on the other hand, increases by over 3.5 times. We see that as the wind stress increases, the total contribution to EKE changes from mostly from EAPE to almost the exact same magnitude between EAPE and MKE. In the downstream region, the conversion of EKE to MKE is doubled when the wind stress is doubled, but the conversion between MAPE to EKE is basically unchanged.
To summarize, in the meander regions, the fluxes of EAPE to EKE and of MKE to EKE are both downgradient and roughly the same magnitude, consistent with mixed instability. In the downstream region, the buoyancy fluxes are downgradient, consistent with baroclinic instability, but the momentum fluxes are upgradient. However, in this region the energy leaving EKE due to eddy momentum fluxes (
4. Geometric analysis
Analyzing the same simulations using the geometric framework described in section 2b produces a similar interpretation of the instability and energy conversion properties of the flow. However, this geometric method can provide a more physical interpretation of the energy exchange terms. The angles of the eddies with respect to the mean flow have a direct analogy to linear stability theory (Marshall et al. 2012; Pedlosky 2013). When the eddies are tilted with the shear, they are giving energy to the mean flow, corresponding to stability, and when the eddies are tilted against the shear, they are growing and taking energy from the mean flow, corresponding to instability (Fig. 1).
For our geometric analysis we first analyze the flow in the horizontal, 2D plane, similar to Waterman and Lilly (2015). Using depth-averaged (i.e., vertical average weighted by the layer thickness) anisotropy, we find that topography locally modifies eddy anisotropy (Figs. 6, 7). In the case where τ0 = 0.2 N m−2, elevated anisotropy occurs on the flanks of the jet as the meander deflects southward. This highlights a key role for the topography: in order to conserve potential vorticity and mass, streamlines tighten upon crossing the ridge, which increases the horizontal shear and the potential for barotropic instability. We also speculate that rapid changes in the orientation of the streamlines can produce regions where coherent eddies are transiently tilted against the mean shear before adjusting to the new shear orientation—a form of eddy memory related to the finite adjustment time of a coherent eddy in a spatially variable mean flow. Analysis of the horizontal eddy tilt is complicated because of the changing orientation of the streamlines (as opposed to perfectly horizontal streamlines; Waterman and Lilly 2015). Within the meander itself, though, the momentum fluxes tend to be downgradient, or the eddies are tilted against the mean flow shear. Immediately downstream of the meander at about x = 1500 km, where the analysis is easier, all eddies tilt with the shear corresponding to upgradient momentum fluxes. The sign of the momentum fluxes agrees with the distribution of 
(a) Depth-averaged eddy anisotropy in color and (b) the tilt for τ0 = 0.1 N m−2; both diagnostics are dimensionless. The color shows the magnitude of the velocity at 177-m depth. The temperature is contoured every degree at 177-m depth, and the bold line is a streamline computed from the velocities and is used in Fig. 8.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0160.1
(a) Depth-averaged eddy anisotropy in color and (b) the tilt for τ0 = 0.2 N m−2; both diagnostics are dimensionless. The color shows the magnitude of the velocity at 177-m depth. The temperature is contoured every degree at 177-m depth and the bold line is a streamline computed from the velocities and is used in Fig. 9.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0160.1
Next we consider the vertical eddy geometry (3D flow), which provides information about the interactions between baroclinic eddies and the mean flow. The vertical anisotropy is high in several locations, particularly over the ridge and downstream of the ridge. There are sporadic instances of high vertical anisotropy in the remainder of the domain as well (Figs. 8, 9). In the downstream, quasi-zonal jet region, the rapid changes of the eddy anisotropy are partly related to an imperfect agreement between the jet cores and the streamline used for the along-stream analysis. The flow generally has downgradient buoyancy fluxes over and around the ridge. The one exception is that for the τ0 = 0.2 N m−2 case, just downstream of the ridge, the flow has both low anisotropy and upgradient buoyancy fluxes in a small region.
(a) Vertical eddy anisotropy and (b) the tilt into the vertical with respect to the mean flow [(16)] for τ0 = 0.1 N m−2. The calculations are complete along the streamline shown in Fig. 6. The solid black lines show the location of the black dots in (c) and the dashed line shows the location of the asterisk in (c). A positive tilt (red) represents downgradient buoyancy fluxes, and a negative (blue) tilt represents upgradient buoyancy fluxes. (c) A measure of the horizontal shear 
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0160.1
As in Fig. 8, but for τ0 = 0.2 N m−2 along the streamline shown in Fig. 7.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0160.1
A comparison of the spatial characteristics of the vertical eddy geometry in Figs. 8 and 9 are also largely consistent with the 
5. Discussion
a. Mixed instability in the ACC
The large-scale tilt of density surfaces across the ACC highlights the importance of baroclinic instability in setting the current’s equilibrated structure. A close analysis of eddy energy transfers in the most energetic regions of the ACC, the major standing meanders, suggests that baroclinic conversion alone is insufficient to describe both the stratification and distribution of EKE. The magnitude of energy transfer into EKE via 
The notion that barotropic instability may play a leading-order role in the equilibration of standing meanders and therefore impact larger-scale properties of the ACC has received little attention. Indeed, Vallis (2006, chapter 16.6) uses a scaling analysis to suggest that the lateral momentum fluxes can be neglected in comparison to the eddy buoyancy fluxes. However, this is based on bulk properties of the ACC, which are modified significantly within the standing meanders, as described above. The elevation of the eddy momentum fluxes and the importance of barotropic instability in the meander have important implications. The momentum balance is typically described as a balance between input from surface winds and the vertical transfer, via interfacial form stress, to the solid earth. It is baroclinic instability and eddy buoyancy fluxes that carry out this vertical transfer. As eddy momentum fluxes become more important, a larger proportion of this momentum can be diverged laterally or, as shown here, exchanged back to the mean flow and carried away from the regions with significant topographic features. Finally, interfacial form stress is intricately linked to the overturning circulation through the meridional transfer of mass and heat related to the coupled nature of eddy buoyancy, heat, and thickness fluxes (Marshall and Speer 2012). A change in the partitioning of barotropic or baroclinic instability properties in response to a change in surface wind stress will then also impact the overturning circulation.
As discussed in the introduction, the incomplete conversion of EAPE to EKE has, in the atmospheric literature, been associated with the barotropic governor mechanism. It occurs because during the growth process of baroclinic eddies, some of the EAPE may be converted into MKE through upgradient momentum fluxes when there is a barotropic shear. Thompson and Richards (2011) have used model output to suggest that upgradient momentum fluxes might be relevant in the ACC. However, baroclinic growth is not the only mechanism responsible for generating upgradient momentum fluxes. Advection of energy between different regions of the domain or the barotropic decay of eddies could also result in the upgradient momentum flux as well. The energy analysis here indicates that upgradient fluxes of momentum are collocated with downgradient fluxes of buoyancy. This arrangement is consistent with the description of the barotropic governor provided by Nakamura (1993), where upgradient momentum fluxes occur in a baroclinically unstable flow. The flow has both a barotropic and baroclinic shear, which can interact, leading to mixed instability and feedbacks.
b. Meander life cycle
The focus on energy transfer diagnostics across a single meander provides insight into the life cycle of fluid parcels passing through this localized region, offering a more nuanced view of eddy–mean flow interactions in the complex ACC. Upstream of the meander there are upgradient momentum fluxes that remove energy from the eddies and accelerate the mean flow, predominantly in narrow jets with a lateral scale comparable to the deformation radius. The jets are steered by topography upon encountering the meridional ridge. Over the ridge, conservation of potential vorticity results in strengthening of the horizontal shear and baroclinicity of the jet(s). At the crest of the ridge, both the eddy momentum and the eddy buoyancy fluxes are transiently upgradient. We hypothesize that the upgradient buoyancy fluxes, in particular, are a result of an abrupt transition in the orientation of the mean flow.
Immediately downstream of the ridge, the enhancement of barotropic shear becomes a source of EKE, but may also act to suppress linear baroclinic instability through the distortion of normal modes. The displacement of the locations of maximum baroclinicity and maximum EKE has been linked to convective instability (Pierrehumbert 1984; Abernathey and Cessi 2014), which certainly contributes to the equilibrated distribution of EKE. However, the strongest release of EKE through baroclinic instability, diagnosed by 
Based on surface velocities retrieved from altimetric observations, restricting the analysis to barotropic eddy–mean flow interactions and to relatively coarse scales (~100 km), Williams et al. (2007) find that upstream of the maximum jet velocity the eddy vorticity fluxes are upgradient, while downstream of this region they are downgradient. This agrees well with the eddy momentum flux distributions seen in the barotropic component of our flow. The addition of a ridge also generates an along-stream evolution of the eddy–mean flow interactions that has a number of similarities to the idealized western boundary current jet studied by Waterman and Jayne (2011), for example, high horizontal eddy anisotropy on the flanks of the jet (Fig. 7). Abernathey and Cessi (2014) find that eddies generated in the meander are often advected downstream, where they continue to extract energy from the mean flow, which agrees with our understanding of the energy budget in our domain showing that some processes are nonlocal (Fig. 5). In agreement with our analysis of standing meanders, Bischoff and Thompson (2014) find that in the lee of topography isopycnal tilt increases due to the standing component of lateral buoyancy fluxes, but is relaxed due to the transient eddy buoyancy fluxes. Complementing these earlier studies, this analysis combines both baroclinic and barotropic instabilities and their impact on the mean flow, as summarized in Fig. 10.
Schematic summarizing the various regimes in the ACC-like channel; critically, there are multiple regimes within the meander region itself. Colors indicate the direction of the eddy buoyancy and momentum fluxes. Upstream of the meander as the flow encounters the topography, the convergence of streamlines both in the horizontal and vertical leads to an increase in eddy anisotropy. Immediately downstream of the ridge crest, the strong rotation of flow direction leads to upgradient buoyancy fluxes and upgradient and downgradient momentum fluxes. The flow becomes barotropically and baroclinically unstable, resulting in rapid generation of EKE. Downstream, zonal jets develop and baroclinic instability dominates with upgradient momentum fluxes.
Citation: Journal of Physical Oceanography 47, 6; 10.1175/JPO-D-16-0160.1
6. Conclusions
This study provides one of the first applications of the geometric stability method, derived by Marshall et al. (2012), to consider both barotropic and baroclinic components of the flow. The eddy–mean flow interactions implied from this analysis are consistent with energy conversion and regional Lorenz energy diagrams diagnosed in the simulations. The consideration of both barotropic and baroclinic instability characteristics reveals the importance of barotropic instability in the ACC.
The stability analysis of the ACC meander shows the detailed evolution of the flow’s stability properties through the meander, which is summarized by Fig. 10. The region upstream of the meander is characterized by upgradient momentum fluxes and downgradient buoyancy fluxes, consistent with baroclinic instability and the barotropic governor. In the meander itself, we have both downgradient buoyancy and momentum fluxes consistent with both barotropic and baroclinic instability or mixed instability. Downstream of the meander, we have upgradient momentum fluxes and downgradient buoyancy fluxes, indicating continued baroclinic growth and barotropic decay.
Simulations run with two different wind stress magnitudes resulted in qualitatively similar patterns of eddy fluxes. However, as the forcing changed, the relative interactions between the baroclinic and barotropic flows were modified. This could modify tracer transport and impact the meridional overturning circulation. Accurately representing these fluxes is likely to be critical for simulating how energy is dissipated in numerical models of the Southern Ocean.
Acknowledgments
We are grateful for useful discussions with Andreas Klocker, David Marshall, Andrew Stewart, and Joe Pedlosky. The authors all acknowledge support from NSF OCE-1235488. MKY also acknowledges support from the AMS Graduate Student Fellowship.
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