1. Introduction
The Southern Ocean is one of the most dynamic environments in the global ocean. In sea level anomaly maps, the Antarctic Circumpolar Current (ACC) pathway is marked by exceptionally high mesoscale eddy activity (e.g., Stammer 1998; Hughes 2005). These mesoscale eddies play a significant role in the ACC momentum balance and Southern Ocean overturning circulation. Southern Ocean overturning is commonly cast as the residual circulation in which the Ekman flow driven by the predominantly zonal winds is largely cancelled by poleward eddy fluxes above submarine ridges and by a much smaller geostrophic flow below the ridges (e.g., Karsten and Marshall 2002). This leads to different dynamics dominating the surface (Ekman) and deep (below submarine ridges) layers and the intermediate depths in between. In particular, along-stream pressure gradients at intermediate depths are precluded by the absence of meridional boundaries. The steady and circumpolarly integrated momentum balance is thought to be governed by the vertical stress divergence, the eddy momentum flux divergence, and the Coriolis force (Johnson and Bryden 1989, hereafter JB89; Olbers 1998). Within this balance, mesoscale eddies are simultaneously implicated in the lateral transfer of heat across the ACC and the downward transmission of momentum (i.e., Bryden 1979; de Szoeke and Levine 1981; JB89; Hughes 2005).
Apart from its impact on ACC dynamics, the meridional eddy heat flux is of interest for its role in the global overturning circulation of the oceans. How, where, and how much heat is transferred by eddies in the Southern Ocean has repercussions for climate change. Model results (Wolfe and Cessi 2010) suggest that the middepth stratification of the World Ocean is determined primarily in the ACC, from the competition between mean and eddy overturning. Observational studies have recently documented a clear oceanic warming over the last half century (Gille 2002; Vaughan et al. 2003; Stroeve et al. 2007) that confirmed model predictions about the amplification of climate change in polar regions (Holland and Bitz 2003). Hence, information on the vertical distribution of the eddy heat fluxes, particularly in the rarely observed mixed layer and the transition layer below, is needed to improve our understanding of the Southern Ocean overturning circulation and future climate change scenarios.
Estimating eddy fluxes from observations requires densely sampled or long time series data to accurately distinguish transient fluctuations from the mean fields. Efforts to estimate Southern Ocean eddy heat fluxes have been hampered by the difficulty and expense of obtaining observations sufficiently resolved in time and space to attain statistically significant results. Simultaneous observations of both velocity and temperature and consequently statistically significant eddy heat flux estimates are rare and vary by region and depth (negative values correspond to poleward heat fluxes). Prior estimates summarized by Gille (2003b) include values of −6.7 kW m−2 (2700-m depth; Bryden 1979), −17 kW m−2 (1000–2500-m depth; Sciremammano et al. 1980), −3.7 kW m−2 (500–2700-m depth; Nowlin et al. 1985), and −12 kW m−2 (580–3560-m depth; JB89) derived from moorings in Drake Passage and −11.3 kW m−2 (400–3700-m depth and 2–90 day bandpassed; Phillips and Rintoul 2000) from moorings south of Tasmania. Neutrally buoyant floats provided global eddy heat flux estimates of −5 to −10 kW m−2 at 900 m across the core of the ACC (Gille 2003b). More recently, Walkden et al. (2008) reported moored current meter estimates of −12 ± 5.8 kW m−2 at 2750-m depth across the Antarctic Polar Front (PF) at Shag Rocks Passage, downstream of Drake Passage.
Eddy momentum flux divergences, estimated from velocity covariances, are generally thought to be of minor importance in ACC dynamics relative to the terms dependent on the eddy heat flux (JB89; Bryden and Heath 1985; Phillips and Rintoul 2000). The few existing observational estimates of velocity covariance show marked inhomogeneity along the ACC pathway. For instance, altimetric estimates range from 25 to 50 cm2 s−2 in energetic regions, whereas zonal averages are typically less than 10 cm2 s−2 (e.g., Morrow et al. 1994; Stammer and Theiss 2004). Current meter observations give estimates of 1.6 cm2 s−2 (2–90 day bandpassed) over the 420–3320-m depth range south of Tasmania (Phillips and Rintoul 2000) and 52.6 cm2 s−2 (all frequencies) at 1000-m depth range in the southwest Pacific (Bryden and Heath 1985). Variability in eddy momentum fluxes may impact the organization of the ACC frontal jets. The time-mean flow of the ACC comprises multiple jets (Orsi et al. 1995; Gille 2003a), with as many as nine observed south of Tasmania (e.g., Sokolov and Rintoul 2007) and typically three in the Drake Passage constriction (Lenn et al. 2008, hereafter L08). Better understanding of Southern Ocean eddy-mean flow interaction requires resolution of the eddy momentum flux terms for each flow regime.
A further complication in assessing Southern Ocean eddy dynamics is obtaining observations of adequate spatial and vertical resolution for evaluating lateral and vertical gradients of the eddy fluxes appearing in the momentum balance. Deep moored current meters provide point estimates of vertical eddy heat flux divergence (Bryden 1979; Bryden and Heath 1985; Phillips and Rintoul 2000). Moored arrays (Phillips and Rintoul 2000) and global studies employing neutrally buoyant floats (Gille 2003b) or altimetry (Morrow et al. 1994; Hughes and Ash 2001; Stammer and Theiss 2004) provide estimates of lateral gradients, although the results thus far have been of varying sign and remain inconclusive. Upper-ocean observations are particularly scarce because of the high probability of damage to moored instrumentation by strong currents, icebergs, waves, and wind. Consequently, numerical models have been used to explore these terms because they can provide fluxes on the required scales (e.g., Stevens and Ivchenko 1997; Drijfhout 2005; Griesel et al. 2009). However, confidence in the modeling results requires validation by observations.
In this regional study, we present new estimates of the eddy momentum and heat fluxes from repeated high-resolution upper-ocean observations in Drake Passage and interpret their role in local ACC dynamics. However, as the narrowest constriction of the ACC, these Drake Passage observations may not be representative of the full ACC because of anisotropy in the mean ACC flow, which varies considerably along its path. Although our observations do not allow for the full evaluation of the regional ACC momentum balance, the eddy terms resolved here represent rare observational estimates of these quantities and provide insight into the eddy impact on local ACC fronts and the transfer of heat. The use of a “natural coordinate” frame defined by dynamic height streamlines allows us to directly compare eddy forcing of the Drake Passage ACC fronts in both the observations and a 1/10° Parallel Ocean Program (POP) global general circulation model simulation, despite marked differences in the mean velocity and temperature fields. The POP model is used to assess the degree of temporal aliasing in the Drake Passage observational eddy flux estimates and to refine our understanding of the eddy dynamics. A circumpolar analysis of the momentum balance using POP results is not possible using existing archived output. Only in the Drake Passage region are all the needed quantities saved at sufficiently high temporal resolution for a consistent comparison with the observations. It is anticipated that the needed fields for a global analysis will be archived in future simulations.
The study is laid out as follows: Additional background on the theory motivating this study is provided in section 2. The observations and the POP model are described in section 3. Methods used in the estimation of the eddy fluxes, the choice of mean reference velocity and temperature fields, and potential aliasing in the observations are discussed in section 4. The eddy momentum flux estimates are presented and their role in the momentum balance is discussed in section 5, whereas section 6 focuses on the eddy heat fluxes. Note that the model results are compared with the observations throughout the study, and the model biases are discussed where appropriate. Final conclusions are summarized in section 7.
2. ACC momentum balance
When the ACC is discussed on global scales, the momentum balance in Eq. (2) is typically integrated circumpolarly and vertically, which reduces the balance to three terms: iii, iv, and vi. In one such scenario proposed by JB89, if the frictional stress (term iv) and eddy momentum flux forcing (term vi) are negligible below the Ekman layer, then interfacial form stress represented by term iii directly balances the surface wind stress (i.e., FT ~ τ0). This explicitly links a poleward eddy heat flux to downward eddy momentum transport (JB89). Although eddies are thought to dominate the balance, there is likely a small contribution from a mean poleward geostrophic flow at depths below the shallowest sills (e.g., Gnanadesikan 1999), which does not appear in the intermediate layer balance [Eq. (2)]. Evaluations of FT at intermediate depths (500–3500 m) from observations (JB89; Phillips and Rintoul 2000; Gille 2003b) and numerical models (Stevens and Ivchenko 1997) have been on the order of magnitude required to balance the surface wind stress at each depth and appear to verify the JB89 theory. On regional scales, the imbalance between eddy and mean advection may be important, especially because the time-mean ACC alternates along stream between stable jets and multiple front filaments, indicating inhomogeneity in the eddy forcing. In many locations, the structure of the ACC frontal jets are thought to be subject to both topographic control and the eddy potential vorticity flux that comprises terms v and vi in Eq. (2) (Hughes and Ash 2001). However, this has yet to be adequately quantified by observations. Evaluating these eddy momentum flux forcing terms in regions where the observed 
As the observations do not allow all terms in Eq. (2) to be resolved, we do not attempt to evaluate the full momentum balance. Instead, this study focuses on the dynamical impact of the cross-correlated eddy momentum flux term (vi) and the eddy heat fluxes appearing in the interfacial form stress divergence (iii), which are resolved by the observations using Eq. (3) with statistical significance. The POP output allows us to extend this analysis by evaluating, in Earth coordinates [Eq. (4)], the balance between the mean advection (I and II) and eddy momentum flux terms (V and VI).
3. The Drake Passage datasets
a. ADCP and XBT/XCTD observations
Underway upper-ocean velocity and temperature data were collected aboard the Antarctic Research and Supply Vessel (ARSV) Laurence M. Gould (LMG) during transects between South America and the Antarctic Peninsula. This analysis uses acoustic Doppler current profiler (ADCP) data from 156 Drake Passage crossings made approximately twice monthly in all seasons between September 1999 and October 2006 (Fig. 1), when the LMG was en route to scientific cruises around the Antarctic Peninsula or carrying supplies to Palmer Station. These ADCP observations constitute an irregular 7-yr time series of horizontal currents in the upper 300 m of Drake Passage that has been described in detail by Lenn et al. (2007).
Map of Drake Passage with grayscale bathymetry and the 200-m isobath contoured. LMG cruise tracks are overlaid (thin black lines) with the XBT survey lines highlighted (black and white dashed lines). Mean SAF, PF, and SACCF (dark gray dashed lines) as determined by L08 are shown. The thick black dashed line indicates the shortest distance between the north and south 500-m isobaths and is the y axis of the down-/cross-passage coordinate system. The three most commonly repeated lines, west, middle, and east, are shown in white and are labeled W, M, and E respectively. Also shown are TdF, the Shackleton Fracture Zone, and Bransfield Strait.
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Map of Drake Passage with grayscale bathymetry and the 200-m isobath contoured. LMG cruise tracks are overlaid (thin black lines) with the XBT survey lines highlighted (black and white dashed lines). Mean SAF, PF, and SACCF (dark gray dashed lines) as determined by L08 are shown. The thick black dashed line indicates the shortest distance between the north and south 500-m isobaths and is the y axis of the down-/cross-passage coordinate system. The three most commonly repeated lines, west, middle, and east, are shown in white and are labeled W, M, and E respectively. Also shown are TdF, the Shackleton Fracture Zone, and Bransfield Strait.
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Map of Drake Passage with grayscale bathymetry and the 200-m isobath contoured. LMG cruise tracks are overlaid (thin black lines) with the XBT survey lines highlighted (black and white dashed lines). Mean SAF, PF, and SACCF (dark gray dashed lines) as determined by L08 are shown. The thick black dashed line indicates the shortest distance between the north and south 500-m isobaths and is the y axis of the down-/cross-passage coordinate system. The three most commonly repeated lines, west, middle, and east, are shown in white and are labeled W, M, and E respectively. Also shown are TdF, the Shackleton Fracture Zone, and Bransfield Strait.
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
For this study, currents Ulmg were averaged in 10-m depth bins with the shallowest bin centered at 30-m depth, and the barotropic tide was removed using the TPXO6.2 model (Egbert et al. 1994). Measurement errors in absolute velocities computed from 15-min ensemble averages are negligible compared to the record-length standard deviation of currents in Drake Passage (~30–60 cm s−1). Calculations are limited to depth bins above 250-m depth as the degrees of freedom decrease at deeper levels because of missing or suspect data. Various coordinate frames are used as appropriate: geographic earth, passage, and streamwise. Passage coordinates xpc, ypc are rotated 23.6° anticlockwise from north (xpc = 0 axis is shown in Fig. 1) and are mostly used to display quantities in distance cross and along passage. Streamwise or natural coordinates use geostrophic streamlines as defined in section 4. Mean currents and eddy fluxes in this study are calculated from ADCP data taken between September 1999 and October 2006.
Since 1996, the LMG has also conducted repeat expendable bathythermograph (XBT) surveys of Drake Passage approximately six times per year. Sprintall (2003) provides a detailed description of the XBT observations. XBT probes were deployed every 6–10 km across the Subantarctic Front (SAF) and PF and every 10–15 km elsewhere between the 200-m isobaths at either side of Drake Passage (Fig. 1). The XBT probes consistently return water temperatures from the surface down to 800 m and were averaged within 10-m depth bins. The long-term mean temperatures used in this study are calculated from the full XBT time series, from September 1996 to October 2006. Of these, 50 XBT surveys of upper-ocean temperature from September 1999 to October 2006 coincided with roughly 30% of the ADCP sections and are used in the eddy heat flux calculation presented here.
b. POP model output
To complement the observations, this study also used output from a multidecadal 1/10°, 40-level global POP simulation (Maltrud and McClean 2005; McClean et al. 2006, 2008). POP is a three-dimensional, z-level, primitive equation general circulation ocean model with an implicit free surface (Smith et al. 1992; Dukowicz et al. 1993; Dukowicz and Smith 1994; see online at http://climate.lanl.gov). The simulation was configured on a displaced North Pole grid that is Mercator in the Southern Hemisphere. Its horizontal resolution is between 4 and 9 km in the Southern Ocean, such that the first baroclinic Rossby radius is resolved equatorward of 50°S. It includes the K-profile parameterization (KPP) mixed layer (Large et al. 1994) and has a model time step of 6.3 min. It was forced with daily fields (6-hourly fields averaged to one day) of wind stress, air temperature, air density, and specific humidity derived from a combination of National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis products for the period 1979–2003 (Kalnay et al. 1996). Monthly downward shortwave radiation and cloud fraction came from the International Satellite Cloud Climatology Project (ISCCP) and Rossow and Schiffer (1991), respectively. Monthly-mean precipitation data were taken from the Microwave Sounding Unit (MSU) and Xie–Arkin climatology (Xie and Arkin 1998). The model was spun up for two decades, and daily averages of both state variables and cross terms of the flux components were archived for the Drake Passage region for a 3-yr period, from 1 January 1999 to 31 December 2001. The POP Drake Passage domain ranged from 64°31.23′ to 53°32.18′S and from 67° to 53°W.
4. Methods
In this section, we discuss and compare the choice of the different mean reference fields used in the eddy flux calculations from the LMG observations and the POP model output. This is followed by a detailed description of how the eddy fluxes are calculated from the observations and POP model output and an evaluation of potential aliasing in the observational results.
a. Mean velocities and streamlines
In Drake Passage, the mean ACC flow is characterized by a steep slope in dynamic height corresponding to a sizeable transport carried primarily within the SAF, PF, and the Southern ACC Front (SACCF) (L08). The slope, transport, and resolution of these fronts provide useful metrics for evaluating the quality of the mean fields used in the eddy flux estimates. In this study, subsurface temperature criteria are used to define the three ACC fronts (summarized in Table 1): the SAF corresponds to the maximum subsurface temperature gradient between the 4° and 5°C isotherms at 400-m depth (Orsi et al. 1995; Sprintall 2003); the PF is defined by the northernmost extent of the 2°C isotherm at a depth of 200 m (Botnikov 1963; Joyce et al. 1978; Sprintall 2003); and the SACCF corresponds to the intersection of the 1.8°C isotherm with the depth of the maximum temperature gradient (Orsi et al. 1995).
Subsurface temperature definitions for the SAF, PF, and SACCF and the corresponding streamfunction values from the L08 and POP mean fields. The range of streamlines associated with each frontal region is given, and bold numbers indicate individual streamlines associated with the core of each front.
In an earlier study, L08 presented a new high-resolution estimate of the mean upper-ocean velocity field and associated dynamic height streamfunction on a 25 km × 25 km grid in Drake Passage using the LMG ADCP observations and satellite sea level anomalies. L08 subtracted geostrophic velocity anomalies, inferred from sea level anomalies, to reduce aliasing in the velocity observations before objectively mapping with a geostrophic constraint to determine mean near-surface ACC currents 
Objectively mapped mean streamlines (white contours) associated with the (a) ψL08 streamfunction (reproduced with permission from L08) and (b) ψpop mean POP model sea surface height; bathymetry is shaded in grayscale with streamlines plotted at dψ = 5 cm intervals, alternating between thick and thin lines. (c),(d) Locations of the mean SAF (gray crosses and solid line), PF (gray dots and dashed line) and SACCF (dark gray crosses and thick line) as defined by subsurface temperature criteria are overlaid on ψL08 and ψpop streamlines (black lines) plotted at 10-cm intervals. Note that in (c) the instantaneous XBT-inferred front positions are shown, whereas in (d) the mean front positions determined from the mean POP temperature field are shown. Passage coordinates are defined in section 3a and Fig. 1.
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Objectively mapped mean streamlines (white contours) associated with the (a) ψL08 streamfunction (reproduced with permission from L08) and (b) ψpop mean POP model sea surface height; bathymetry is shaded in grayscale with streamlines plotted at dψ = 5 cm intervals, alternating between thick and thin lines. (c),(d) Locations of the mean SAF (gray crosses and solid line), PF (gray dots and dashed line) and SACCF (dark gray crosses and thick line) as defined by subsurface temperature criteria are overlaid on ψL08 and ψpop streamlines (black lines) plotted at 10-cm intervals. Note that in (c) the instantaneous XBT-inferred front positions are shown, whereas in (d) the mean front positions determined from the mean POP temperature field are shown. Passage coordinates are defined in section 3a and Fig. 1.
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Objectively mapped mean streamlines (white contours) associated with the (a) ψL08 streamfunction (reproduced with permission from L08) and (b) ψpop mean POP model sea surface height; bathymetry is shaded in grayscale with streamlines plotted at dψ = 5 cm intervals, alternating between thick and thin lines. (c),(d) Locations of the mean SAF (gray crosses and solid line), PF (gray dots and dashed line) and SACCF (dark gray crosses and thick line) as defined by subsurface temperature criteria are overlaid on ψL08 and ψpop streamlines (black lines) plotted at 10-cm intervals. Note that in (c) the instantaneous XBT-inferred front positions are shown, whereas in (d) the mean front positions determined from the mean POP temperature field are shown. Passage coordinates are defined in section 3a and Fig. 1.
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Mean POP streamlines in Drake Passage are contours of the mean streamfunction ψpop (Fig. 2b) representing the average POP sea surface height fields over the full 3-yr (1999–2001) period. The mean POP velocities 
L08 demonstrated that the cores of the instantaneous ACC fronts, determined from the XBT temperature data, closely correspond to particular instantaneous streamlines determined from altimetric sea level anomalies when added to the ψL08 streamlines: −60 (SAF), −100 (PF), −160 cm (SACCF) (Fig. 2c; Table 1; see also Fig. 7 of L08). The cores of the mean POP fronts derived from the POP temperature fields are also aligned with particular ψpop streamlines: −50 (SAF) and −110 cm (PF/SACCF) (Fig. 2d; Table 1). Overlaying the instantaneous XBT-inferred front locations on ψL08 provides a sense of the transient meandering of each front relative to its mean streamline (Fig. 2c). This transient meandering clearly contributes to broadening each mean frontal jet over a range of streamlines about its core (Fig. 2c).
Notable differences exist between the ACC fronts resolved by the mean modeled and observed dynamic height fields. For instance, in ψpop there are more densely spaced streamlines of a faster, broader SAF (−90 cm < SAFpop < −20 cm; Fig. 2b) than inferred from observations (−65 cm < SAFL08 < −40 cm; Fig. 2a). In contrast, the PF streamlines are considerably more widely spaced in POP (−120 cm < PFpop < −105 cm; Fig. 2b) and trace a more convoluted path compared to ψL08 (−125 cm < PFL08 < −80 cm; Fig. 2a). In southern Drake Passage, the SACCFL08 is clearly defined as a separate front (−160 cm < ψL08 < −145 cm; Fig. 2a), whereas the mean SACCFpop is indistinguishable from PFpop (Fig. 2d).
These differences in the fronts are reflected by mean 30–250-m-layer cumulative transports through Drake Passage (Fig. 3), computed from model output along 65°W and from ADCP currents across three frequently repeated LMG transects (locations marked in Figs. 1, 5b). The ADCP transport calculation has been updated from Lenn et al. (2007); for this study, we excluded a 0–30-m slab layer and incorporated an additional 2 yr of data. The cumulative transports show the SAFL08 and PFL08 carry about 90% of the (30–250 m) ACC transport in roughly equal parts (Fig. 3), whereas the SAFpop carries most of the Drake Passage transport [~17 Sv (1 Sv ≡ 106 m3 s−1); Fig. 3], which is roughly ~10 Sv more than the PFpop (Fig. 3). However, the total Drake Passage transports from both the ψpop and ψL08 dynamic height fields agree to within 1 Sv of 27 Sv. This is because both the observed and POP mean dynamic height fields are approximately 140 cm higher at Tierra del Fuego (TdF) than at the Antarctic Peninsula, although their absolute values differ slightly (Figs. 2a,b). Thus, despite discrepancies in the ACC fronts, we note that the agreement between ψL08 and ψpop with respect to the total Drake Passage upper-ocean transport implies that the large-scale forcing and underlying dynamics of the Southern Ocean is successfully reproduced by the POP model.
Comparison of mean 30–250-m-layer cumulative ACC transports calculated from observations along the west repeat transect (gray dashed line), middle repeat transect (gray dashed–dotted line), east repeat transect (gray solid line), and POP model output along the 65°W longitude line in Drake Passage (black line). Note that the west transect coincides with longitude 65°W. Locations of repeat transects are shown in Figs. 1 and 5b.
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Comparison of mean 30–250-m-layer cumulative ACC transports calculated from observations along the west repeat transect (gray dashed line), middle repeat transect (gray dashed–dotted line), east repeat transect (gray solid line), and POP model output along the 65°W longitude line in Drake Passage (black line). Note that the west transect coincides with longitude 65°W. Locations of repeat transects are shown in Figs. 1 and 5b.
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Comparison of mean 30–250-m-layer cumulative ACC transports calculated from observations along the west repeat transect (gray dashed line), middle repeat transect (gray dashed–dotted line), east repeat transect (gray solid line), and POP model output along the 65°W longitude line in Drake Passage (black line). Note that the west transect coincides with longitude 65°W. Locations of repeat transects are shown in Figs. 1 and 5b.
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
One question to be addressed in this study is how eddies influence the mean flow. If the eddy forcing is important in determining the strength and location of the ACC fronts, then it is possible that differences between ψL08 and ψpop may stem from the resolution of mesoscale eddies in POP. For instance, in northern Drake Passage, where ADCP data and altimetry show mesoscale eddy features of up to 100-km scales that are comparable in width to the frontal jets (Lenn et al. 2007), the POP model explicitly resolves realistic mesoscale eddies. In southern Drake Passage, where the first Rossby internal deformation radius is ~9 km, the observed mesoscale eddies tend to be O(10–20 km). This renders the eddies as subgrid-scale processes in POP, such that the exchange of momentum between the eddies and mean flow is not explicitly resolved.
b. Mean reference temperatures
The mean three-dimensional temperature field 
Mean temperatures calculated from (a)–(c) the XBT observations and (d)–(f) the POP model output at three depths: (a),(d) 30 m; (b),(e) 100 m; and (c),(f) 250 m. Mean streamlines used in the eddy flux calculations are overlaid (black lines). The x axis in all panels is kilometers down passage. Passage coordinates are defined in section 3a and Fig. 1.
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Mean temperatures calculated from (a)–(c) the XBT observations and (d)–(f) the POP model output at three depths: (a),(d) 30 m; (b),(e) 100 m; and (c),(f) 250 m. Mean streamlines used in the eddy flux calculations are overlaid (black lines). The x axis in all panels is kilometers down passage. Passage coordinates are defined in section 3a and Fig. 1.
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Mean temperatures calculated from (a)–(c) the XBT observations and (d)–(f) the POP model output at three depths: (a),(d) 30 m; (b),(e) 100 m; and (c),(f) 250 m. Mean streamlines used in the eddy flux calculations are overlaid (black lines). The x axis in all panels is kilometers down passage. Passage coordinates are defined in section 3a and Fig. 1.
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
The mean XBT temperatures decrease poleward (Figs. 4a–c), reflecting the change in water mass properties across the ACC fronts. The biggest upper-ocean temperature change occurs across the PF, with Subantarctic Surface Water found to the north of the front and Antarctic Surface Water found to the south of the front (Sprintall 2003). In austral winter and spring, the very cold (T < 0°C) and fresh Antarctic Surface Water spreads equatorward from the Antarctic Peninsula in a layer more than 100 m thick (Sprintall 2003). In summer, surface heating caps this cold layer resulting in a mean subsurface temperature minimum of Winter Water located at ~100-m depth (Fig. 4b). Below the Antarctic Surface Water lies the warmer (T ~ 2°C) and saltier Upper Circumpolar Deep Water (Fig. 4c).
Mean POP temperatures 
Differences between the mean temperature fields imply that the POP model’s stratification south of the PF was suboptimal in this region. The Winter Water properties and the depth of the winter mixed layer depend on the surface atmospheric fluxes, lateral forcing (e.g., representation of dense overflows from Antarctic shelf seas), and the vertical mixing scheme of the model. It seems likely that deficiencies in the surface and more southerly lateral forcing may be the cause of this model bias. In the future, it is possible that the water mass structure in POP will be improved in fully coupled models that include active atmospheric and ice components. The eddy flux analysis that is the focus of this study is not intended to provide insight into the water mass formation in POP; the imperfect representation of the upper-ocean stratification will, however, influence the POP eddy heat flux estimates.
The JB89 parameterizations require calculations of the mean vertical temperature section by averaging the time-mean gridded temperature profiles along the appropriate mean ψL08 streamlines (not shown). The mean vertical temperature gradient 
c. Calculating observed eddy fluxes
Eddy velocity fluctuations 
In computing the ACC eddy fluxes from observations, statistical significance of the eddy flux estimates is enhanced by increasing the number of degrees of freedom (i.e., independent observations) and thereby reducing the errors. Averaging the eddy momentum and heat fluxes along the mean streamlines (Fig. 2a) allowed us to combine all the available Drake Passage transects to produce mean sections of cross- and along-stream flux estimates. It is then straightforward to compute cross-stream gradients of eddy momentum fluxes to interpret the dynamical impact of this eddy term. Without streamwise averaging, the standard errors of the gridded eddy fluxes are too high to allow for statistically significant differentiation along stream, such that terms i and v from Eq. (2) cannot be resolved from the observations. In any case, along-stream differentiation becomes less and less possible as horizontal extent (i.e., δx) of the observations decreases sharply as the LMG cruise tracks converge to the north (Fig. 1).
For the purposes of streamwise averaging (denoted by ψ superscript), the gridded velocity fluctuations are first projected into mean stream coordinates such that u′ is the along-stream component and υ′ is the cross-stream component. The gridded Reynolds stresses (u′u′, υ′υ′, u′υ′, υ′T′, and u′T′) are then averaged along ψ contours to compute along- and cross-stream velocity variances 
Standard errors for each eddy flux term were calculated as the standard deviation divided by the square root of the number of degrees of freedom. Bryden (1979) found that velocities observed at deep moored current meters in Drake Passage were decorrelated after 10–12 days on average. Typically, the ADCP transects are separated by more than 9 days but sometimes by as much as up to 4 months so that we assume each transect to provide one degree of freedom. Therefore, eddy momentum fluxes and EKE have 156 degrees of freedom and are presented as momentum fluxes per unit density in units of cm2 s−2, whereas eddy heat fluxes with fewer concurrent ADCP and XBT transects have 50 degrees of freedom and are presented as heat fluxes per unit density per specific heat capacity in units of °C cm s−1. A typical density for the Drake Passage upper ocean is 1027 kg m−3 (Levitus and Boyer 1994), and the specific heat capacity of seawater is 4000 J kg−1 °C−1.
d. Calculating POP eddy fluxes
The POP model output, unlike the observations, is a fully realized dataset without temporal or spatial gaps. Eddy fluxes computed from the full model output faithfully represent the model ocean state; hence, model standard deviations are not analogous to the observational standard errors that represent sampling-dependent confidence intervals for the true ocean state. Because this analysis uses the results from a single model simulation, confidence limits are not assigned to the POP eddy fluxes.
Previous studies by Jayne and Marotzke (2002) and Drijfhout (2005) have noted that it is important to distinguish between rotational and irrotational components of the eddy heat flux. This is because the rotational component of the eddy heat flux recirculates the heat, whereas the irrotational component provides the actual lateral heat flux. Griesel et al. (2009) have shown that the rotational component accounts for more than 95% of the Southern Ocean eddy heat fluxes in this study’s POP model simulation. Griesel et al. (2009) speculate that in the POP model, as in some idealized Southern Ocean models (Wilson and Williams 2004; Cerovečki et al. 2009), the balance between the rotational eddy heat flux and eddy advection so dominates the eddy variance equation that it is difficult to resolve the residual eddy heat flux. This residual eddy heat flux in turn balances the conversion of eddy potential energy to EKE. The observed fluxes can neither be directly decomposed into irrotational and rotational fluxes nor resolve the EKE conversion term that is dependent on vertical velocities. Hence, in the following, we do not separate the rotational from irrotational fluxes in the POP estimates, keeping in mind this characteristic of the POP eddy heat fluxes estimates.
e. Assessing aliasing in the LMG eddy flux estimates
The representation of eddy variability in the model is first assessed by a comparison of POP and observed EKE (Fig. 5). The POP simulation reproduces the northern enhancement of mesoscale eddy activity observed in Drake Passage (Fig. 5), although the maximum EKEpop (Fig. 5b) is smaller (~600 cm2 s−2) than observed (>700 cm2 s−2; Fig. 5a). This ability of POP to reproduce key features in the eddy variability and its lack of data gaps makes it useful for investigating potential aliasing in the observed eddy fluxes due to the irregular LMG sampling scheme. Potential aliasing is evaluated by subsampling the POP dataset in a manner consistent with the frequency and distribution of the LMG surveys and then compared to eddy fluxes calculated from the full POP archive. In the remainder of this section, the “pop” subscript refers to fluxes computed from the full 3-yr POP archive, and the “sub” subscript refers to fluxes computed from subsampled POP data at the same frequency as the LMG surveys.
Maps of depth-averaged EKE (30–300 m) computed from (a) the LMG ADCP observations and (b) the POP model output. The locations of three frequently repeated LMG Drake Passage transects (west, middle, and east from left to right) are overlaid as white lines in (b). Passage coordinates are defined in section 3a and Fig. 1.
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Maps of depth-averaged EKE (30–300 m) computed from (a) the LMG ADCP observations and (b) the POP model output. The locations of three frequently repeated LMG Drake Passage transects (west, middle, and east from left to right) are overlaid as white lines in (b). Passage coordinates are defined in section 3a and Fig. 1.
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Maps of depth-averaged EKE (30–300 m) computed from (a) the LMG ADCP observations and (b) the POP model output. The locations of three frequently repeated LMG Drake Passage transects (west, middle, and east from left to right) are overlaid as white lines in (b). Passage coordinates are defined in section 3a and Fig. 1.
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
The January 1999–December 2001 POP record overlaps with only 28 months of the LMG ADCP observations that began in September 1999. To utilize the full POP record, we transposed individual LMG cruise dates from the 36-month period, beginning January 2000 and ending December 2002, to one year earlier to provide a subsampling template that overlaps with the POP record. Similarly, for the eddy heat flux calculation, we sampled POP data on every day the LMG was in Drake Passage conducting an XBT survey, from January 2000 to December 2002, again transposing individual dates by one year. Note that the observed estimates of eddy fluxes over the 7-yr time period have more than twice the number of degrees of freedom as the subsampled POP eddy fluxes derived from the 3-yr POP archive.
An examination of the terms 
Momentum and eddy momentum fluxes computed from POP model output at 112-m depth: (a) 
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Momentum and eddy momentum fluxes computed from POP model output at 112-m depth: (a)
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Momentum and eddy momentum fluxes computed from POP model output at 112-m depth: (a)
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Eddy heat fluxes computed from the full 3-yr POP record 
Meridional POP eddy heat fluxes 
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Meridional POP eddy heat fluxes
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Meridional POP eddy heat fluxes
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Zonal POP eddy heat fluxes 
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Zonal POP eddy heat fluxes
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Zonal POP eddy heat fluxes
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
5. Eddy momentum fluxes
a. Results
The streamwise-averaged observed EKEψlmg reaches a maximum between the SAF and PF before decreasing in the poleward direction (Fig. 9c), with roughly equal contributions from both 
The observed streamwise-averaged eddy velocity variances (a) 
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
The observed streamwise-averaged eddy velocity variances (a)
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
The observed streamwise-averaged eddy velocity variances (a)
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
The eddy momentum flux 
(a) Streamwise- and depth-averaged near-surface eddy momentum fluxes 
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
(a) Streamwise- and depth-averaged near-surface eddy momentum fluxes
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
(a) Streamwise- and depth-averaged near-surface eddy momentum fluxes
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Where significant, our estimates of 
The streamwise-averaged POP eddy momentum flux 
b. Eddy momentum flux forcing of the ACC
In Drake Passage, 
One source of bias in the discrepancies between the observed and modeled eddy fluxes is the limitation in model horizontal resolution discussed in section 3a. Another source of bias in the POP simulation stems from the coarse resolution of the surface forcing. Scatterometer observations have shown that ocean wind stress curl and divergence are characterized by persistent small-scale features unresolved by numerical weather prediction models (e.g., Chelton et al. 2004), such as the NCEP/NCAR products used to force this POP simulation.
The Southern Ocean is richly populated by these small-scale wind features (O’Neill et al. 2003). Chelton et al. (2004) attributed the small-scale features to air–sea heat fluxes that modify the local marine atmospheric boundary layer, with additional drag from sea surface currents further modifying the wind field that feed back on the flow. This is consistent with the small-scale discrepancies between POP and the observations having little impact on the large-scale flow (e.g., similar total Drake Passage transport in Fig. 3).
Despite discrepancies in magnitude and regional influence, broad agreement in 
A statistically significant 
Statistically significant positive 
The POP model provides further insight on the role of the 
Maps of momentum flux divergence, averaged over the top 250 m, calculated in geographical coordinate frame from POP; units are given in m s−2. Mean advection terms (a) 
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Maps of momentum flux divergence, averaged over the top 250 m, calculated in geographical coordinate frame from POP; units are given in m s−2. Mean advection terms (a)
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Maps of momentum flux divergence, averaged over the top 250 m, calculated in geographical coordinate frame from POP; units are given in m s−2. Mean advection terms (a)
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
We showed earlier that the POP model mean momentum advection term 
6. Eddy heat fluxes
a. Results
As noted in section 4c, the observed eddy heat fluxes have about a third of the degrees of freedom as the eddy momentum fluxes, because we only have 50 cruises with concurrent temperature and velocity observations. This leads to bigger error estimates. To increase the signal-to-noise ratio, the eddy heat fluxes were filtered with a box-car filter of width dψ = 10 cm, which reduced the high-frequency noise. Even with smoothing, the calculation is impacted by the fewer degrees of freedom, and only with streamwise averaging are the eddy heat fluxes resolved with some statistical significance. Where significant, positive 
The along-stream eddy heat flux 
Streamwise-averaged eddy heat fluxes computed from (a),(b) the LMG observations and (c),(d) the POP model output are plotted against ψL08 (left y axis) and ψpop (right y axis). (a),(c) Cross-stream heat fluxes 
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Streamwise-averaged eddy heat fluxes computed from (a),(b) the LMG observations and (c),(d) the POP model output are plotted against ψL08 (left y axis) and ψpop (right y axis). (a),(c) Cross-stream heat fluxes
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Streamwise-averaged eddy heat fluxes computed from (a),(b) the LMG observations and (c),(d) the POP model output are plotted against ψL08 (left y axis) and ψpop (right y axis). (a),(c) Cross-stream heat fluxes
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Historical observed estimates of the zonal heat flux have primarily been well below the surface layer and hence are much smaller than those reported in this study. At 900 m, Gille (2003b) reports along-stream heat fluxes along the core of the ACC to be of similar size to the cross-stream heat fluxes of 0.12°–0.24°C cm s−1 and generally directed downstream, although this calculation is very sensitive to the mean field used. Bryden and Heath (1985) found that zonal heat fluxes estimated from current meters southeast of New Zealand decreased with depth, ranging from −0.69°C cm s−1 at 1000 m to −0.005°C cm s−1 at 5000 m. These moored estimates were directed westward, upstream along the ACC, except at 2000 m, and were of similar magnitude or smaller than the meridional heat fluxes.
Cross-stream eddy heat fluxes 
Cross-stream eddy heat fluxes (a) 
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Cross-stream eddy heat fluxes (a)
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Cross-stream eddy heat fluxes (a)
Citation: Journal of Physical Oceanography 41, 7; 10.1175/JPO-D-10-05017.1
Moored estimates of 
Cross-stream eddy heat fluxes 
An interesting feature of the POP eddy heat fluxes is that both horizontal components are largest and change sign across the axis of the SAF: on the northern flank of the SAF the eddy heat flux is poleward and downstream, whereas on the southern flank of the SAF the eddy heat flux is equatorward and upstream (Figs. 12c,d). This provides the sense of a cyclonic circulation of the heat in the SAF region. Toward the south, the horizontal eddy heat flux components remain anticorrelated, changing sign across the PF near ψpop = −110 cm (Figs. 12c,d). This pattern may be due to the high rotational component of the POP eddy heat flux noted by Griesel et al. (2009). In comparison, the lateral divergences in the observed cross- and along-stream eddy heat fluxes north of the PF (Figs. 12a,b) appear to correlate in the opposite sense to the POP eddy heat fluxes, suggesting the possibility of an anticyclonic rotational heat flux. However, the correlation in the observed eddy heat flux divergences does not continue across the PF and to the south, implying that the rotational component of the eddy heat flux may be less important in the observations than in POP.
b. Implications for the interfacial form stress
Disparities between the streamwise-averaged observed and POP eddy heat fluxes, together with model bias in the water mass stratification, lead us to confine our discussion of eddy heat flux dynamics to the observations. The meridional eddy heat fluxes appear in the parameterized interfacial form stress FT in the ACC momentum balance equation [Eqs. (2) and (3)]. In this study, calculations of FT are limited to where 
The JB89 parameterization FT is a good approximation to Fρ over much of the globe where the ocean is stably stratified in temperature, such as in the Drake Passage SAF, where 
Nonetheless, the FT parameterization is appropriate in the Drake Passage SAF below the surface Ekman layer (~100 m deep; Lenn and Chereskin 2009). Our observational estimate of FT ~ 0.2 N m−2 in the SAF (Fig. 13d) is of the magnitude required to directly balance the observed mean Southern Ocean wind stress (~0.2 N m−2; Gille 2005). Mooring estimates (Phillips and Rintoul 2000; JB89), neutrally buoyant floats (Gille 2003b), and numerical models (Stevens and Ivchenko 1997) have also produced estimates of FT in Drake Passage and elsewhere in the Southern Ocean that were large enough to balance the surface wind stress. However, the divergence of 
7. Conclusions
The main goal of this study was to evaluate the role of eddy momentum and heat fluxes in Drake Passage upper-thermocline dynamics, resolved by observations and 1/10° POP model simulation. POP eddy fluxes, subsampled according to the LMG observational scheme, show that the observed eddy flux estimates are not substantially aliased. However, statistical significance would be improved by increasing the number of degrees of freedom (i.e., increasing the number of concurrent XBT and ADCP observations), particularly in the case of the eddy heat flux calculations. The POP simulation successfully reproduced the upper-ocean transport observed in Drake Passage (section 4a) but inadequately resolved mesoscale eddies at higher southerly latitudes. This was attributed to the model’s horizontal resolution and the coarseness of the NCEP/NCAR surface forcing employed in POP that excludes submesoscale features in the wind stress curl and divergence, which feedback on the local ocean dynamics (Chelton et al. 2004). These model biases resulted in discrepancies with the observed distribution of the eddy momentum flux forcing and the observed location and strength of the ACC fronts.
Despite the model biases, the role of the eddy momentum flux forcing was consistent between the observations and POP. Broad agreement in 
The POP eddy heat fluxes are subject to model biases in water mass stratification and are also dominated by the rotational component of the heat flux (Griesel et al. 2009), considerably more than indicated by the observations. Consequently, our discussion of the dynamical implications of the eddy heat fluxes is based on the observations. Where statistically significant, observed cross-stream Drake Passage eddy heat fluxes 
In the SAF, where stably stratified temperatures permitted sensible estimates of the JB89 interfacial form stress, we found that FT varied little with depth between 100 (the estimated Ekman depth) and 250 m. We found that FT could balance the surface wind stress and transmit the wind-input momentum down below the Ekman layer (section 6b). The vertical divergence estimated over the depth range 100–250 m [term iii from Eq. (2)] was only an order of magnitude greater than the eddy momentum forcing [term vi from Eq. (2)] in the SAF. Thus, although we find the eddy momentum flux forcing to be of secondary importance in Drake Passage, it is nonetheless not negligible compared to the interfacial form stress divergence here.
This study demonstrated how a unique set of concurrent underway velocity and temperature observations in Drake Passage can provide valuable insight into the dynamics of the rarely observed upper-thermocline layer of the ACC. These observations have great potential for advancing our knowledge of upper-ocean dynamics and play a useful role in validating numerical models. However, these observations cannot provide the spatial and temporal resolution required for exhaustive studies on ocean dynamics. The continued development of eddy-resolving ocean models, in terms of both improving submesoscale parameterizations and/or increasing grid resolution, provides further opportunities to better understand Southern Ocean physics.
Acknowledgments
We acknowledge the National Science Foundation (NSF) Office of Polar Programs (OPP) and Division of Ocean Sciences (OCE) for sponsoring the ADCP and XBT observing programs on the LMG and this research through Grants OPP-9816226/-0338103, OCE-0327544, OPP-0003618, and OCE 0549225. Additional support was provided by the Office of Science, U.S Department of Energy through Research Grant DE-FG02–05ER64119. The global POP simulation was carried out by Julie McClean and Matthew Maltrud (LANL) as part of a Department of Defense High Performance Computing Modernization Program (HPCMP) grand challenge grant at the Maui High Performance Computing Center (MHPCC). We are also grateful to the captain and crew of the ARSV Laurence M. Gould and to Raytheon Polar Services Corporation for their excellent technical and logistical support on the cruises. Eric Firing, Jules Hummon, and Sharon Escher have made invaluable contributions to the ADCP data collection, processing, and editing. Conversations with Sarah Gille, Paola Cessi, Alexa Griesel, Jeff Polton, and Chris Wilson have provided helpful additional insight into the problem.
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