Southern Ocean Eddy Heat Flux and Eddy-Mean Flow Interactions in Drake Passage

The Antarctic Circumpolar Current (ACC) is a complex current system composed of multiple jets that is both unique to the world’s oceans and relatively under observed compared with other current systems. Observations taken by currentand pressure-recording inverted echo sounders (CPIES) over four years, from November 2007 to November 2011, quantify the mean structure of one of the main jets of the ACC the Polar Front in a composite-mean sense. While the array of CPIES deployed in Drake Passage included a 3 x 7 local dynamics array, analysis of the Polar Front makes use of the line of CPIES that spanned the width of Drake Passage (C-Line). The Polar Front tends to prefer one of two locations, separated along the C-Line by 1◦ of latitude, with the core of the jet centered on corresponding geopotential height contours (with a 17 cm difference between the northern and southern jets). Potential vorticity fields suggest that the Polar Front is susceptible to baroclinic instability, regardless of whether it is found upstream (farther south along the C-Line) or downstream (farther north along the C-Line) of the Shackleton Fracture Zone (SFZ), yet the core of the jet remains a barrier to smaller-scale mixing, as inferred from estimated mixing lengths. Within the local dynamics array of CPIES, the observed offset between eddy heat flux (EHF) and eddy kinetic energy (EKE) and the alignment of EHF with sea surface height (SSH) standard deviation motivates a proxy for depth-integrated EHF that can be estimated from available satellite SSH data. An eddy-resolving numerical model develops the statistics of a logarithmic fit between SSH standard deviation and cross-frontal EHF that is applied to the ACC in a circumglobal sense. We find 1.06 PW enters the ACC from the north and 0.02 PW exits towards Antarctica. The magnitude of the estimated EHF, along with contemporaneous estimates of the mean heat flux, suggests that the air-sea heat flux south of the PF is an overestimate. Long-term trends in EHF are calculated from January 1992 to December 2014 and reveal varying trends at the eight ACC EHF hot spots, with only three having statistically significant temporal trends of strengthening cross-frontal EHF. The dynamics of an oceanic storm track are investigated using CPIES observations in the local dynamics array to better understand the processes responsible for the spatial offset between EHF and EKE. Wave activity flux (W ), calculated from the total geostrophic stream-function, is used to diagnose eddy-mean flow interactions in the eddy-rich region immediately downstream of the SFZ. In the full four-year mean and in a composite of eddy events, elevated values of eddy potential energy (EPE) are aligned with the vertical component of W . This is indicative of a conversion of mean available potential energy to EPE through EHF associated with baroclinic instability. Emanating from this region, horizontal W vectors point towards the adjacent region of elevated EKE. A case study of an eddy event, lasting from 15 to 23 July 2010, is presented and highlights the capability of W to illustrate the evolution of the storm track in a snap-shot sense. The alignment of elevated values of EKE with the convergence of the horizontal W vectors indicates the importance of barotropic processes in transporting EKE away from the ACC’s interaction with the SFZ.

A million thanks to Brandon, whose patience knows no bounds.
To my Jamestown family who provided me with good food and a good laugh when I needed it most. And to the rest of my family and friends, it's been a long road, and I couldn't have done it without all your support.
To Patrick, who didn't mind when I lost my mind and who never underestimated the healing power of adorable dogs. Your kindness keeps me going and I thank you for it.
To Karen, thank you for the immeasurable amount of guidance you provided to me. I don't know where I'd be without your help.
To Jaime, thank you for making my last semester here as a TA so much fun and so worth it. Thank you for your genuine interest in my work. And to Jason and Stephen, thank you for being on my committee.
To Randy, thank you for always double-checking my units, for believing in my work, and for getting me back out of the tennis court.
And finally, to Kathy, I have been blessed to work for you. As a scientist and as a person, you inspire me. Thank you for everything, but especially thank you for trusting me with Nykki when you are away.
iv DEDICATION For the giants upon whose shoulders I stand, and for those who wish to stand upon mine.

Introduction
The Antarctic Circumpolar Current (ACC) is a unique feature of the world's oceans, unrestricted by continental boundaries in the latitude band of Drake Passage. To first order, the ACC is a wind-driven, generally eastward flowing current, strongly steered by large bathymetric features found throughout the Southern Ocean. In terms of global circulation and climate, the ACC's secondary circulation plays a key role. Vertical and meridional flow along isoneutral (constant buoyancy) surfaces in the ACC forms the southern limb of the global meridional overturning circulation. The buoyancy structure of the ACC, therefore, plays a crucial role in global circulation and stratification.
Global schematics and idealized theories often represent the ACC as one swift current, yet it has a complex structure with multiple fronts/jets. As these jets navigate the bathymetry of the Southern Ocean, each follows its own preferred path(s) over steep ridges, around shallow plateaus, or through narrow gaps, as a few examples. Enhanced eddy kinetic energy and increased particle crossings are noted in the lee of abrupt bathymetry and are thought to be indicative of enhanced cross-frontal eddy fluxes (Thompson and Sallée, 2012).
The number of ACC fronts varies with space and time. Historical hydrography pointed to 3 fronts in Drake Passage: Subantarctic Front (SAF), Polar Front (PF), and Southern ACC Front (SACCF) . Around the Southern Ocean, the hydrographic markers used to tag these fronts are commonly associated with a strong current, leading to the "classic" circumpolar view of the ACC . Given the nearly equivalent-barotropic and surface-intensified nature of the ACC's mean velocity, SSH contours well represent flow streamlines and satellite altimetry is a particularly useful tool to track fronts. Recently, Sokolov and Rintoul (2009a) showed in a circumpolar analysis that multiple distinct SSH contours are often associated with the "classic" fronts. For example, they find the PF aligns, circumpolarly, with 3 SSH values, and that about 20 cm of height separates the northernmost and southernmost fronts.
Satellite altimetry and numerical models reveal a highly complex frontal structure, especially in snapshots. That is, a particular frontal contour (of SSH, for example) does not maintain a consistently strong gradient along its circumpolar path. Moreover, these frontal contours converge together in some locations and separate in other locations or at other times. Thompson and Sallée (2012)  It is crucial to know the mean velocity and potential vorticity structure of the jet for an interpretation in the framework of linear instability theory. Studying departures from the basic state requires a priori knowledge of the basic state.
Many studies average geographically (e.g., Firing et al. (2011)), so the strength of a meandering jet appears weakened. Transformation of data into a streamcoordinate system centered on the front is ideal for investigating the jet's dynamics and stability properties. Within a mixing-length framework, Naveira-Garabato et al. (2011) show the PF is a barrier to mixing at all but one of the repeat WOCE transects in the Southern Ocean. Their study included transects SR1 and SR1b that are located just upstream and downstream of our study area (Figure 1.1).
We combine 4 years of moored current and pressure-recording inverted echo sounder (CPIES) data collected during the cDrake project with satellite altimetry to study the cross-frontal structure of the PF (Section 2). A stream coordinate system is developed and we find the jet takes two preferred locations about the SFZ (Section 3). The velocity and vorticity fields of the northern and southern PF are presented in Section 4. Section 5 discusses our choice of PF definition, and puts this work in the context of transport, mixing, and residual circulation; we conclude in Section 6. For more details on data processing see the cDrake CPIES data report .
The travel-time records have been processed further such that their variability reflects fluctuations in the baroclinic structure. That is, the time series are adjusted for changes in path length, inverted barometer effect by atmospheric pressure, changes in gravity due to latitude, and a seasonal cycle (following Baker-Yeboah et al. (2009) and ). The measurements are mapped -optimally interpolated to 10-km horizontal spacing -within the entire array of CPIES.
We chose to convert acoustic travel time to surface geopotential anomaly referenced to 3500 dbar, Φ 0−3500 (subscript neglected hereafter). A gravest empirical mode (GEM) technique relates travel-time values measured by the CPIES to temperature and salinity at chosen depth levels using historical hydrographic casts in the region . The data are then interpolated to a 10-dbar vertical grid to give T (τ, p) and S(τ, p). These T-GEM and S-GEM fields are vertically filtered along the pressure coordinate with a smoothing length ranging from the equivalent of 35 dbar in the thermocline to 500 dbar at depth. The intention is to preserve the thermocline structure while smoothing over noise at depth (due to sparsity of deep-reaching profiles). Φ at the surface can be calculated from T and S, effectively creating 2-dimensional GEM fields of T (Φ, p) and S(Φ, p).
When analyzing a jet's structure, a buoyancy GEM (b-GEM) is a natural next step from the T-and S-GEM. First, T and S are used to calculate neutral density, γ n , following . Then, buoyancy is b = g ρ 0 (γ n − γ 0 ), where g = 9.8 m s −2 is local gravitational acceleration, ρ 0 = 1035 kg m −3 is a standard ocean density, and γ 0 = 28.5 kg m −3 is a deep neutral density. Finally, the b-GEM is vertically smoothed consistently with the T-and S-GEMs. The scatter in the b-GEM, the standard deviation of buoyancy calculated from the CTD casts about the GEM value, is on the order of 2 -6×10 −4 m s −2 . Below 100 dbar, the spline fits of the b-GEM explain 95% or more of the variance in the CTD casts (not shown).

Altimetry
Our analysis uses satellite altimetry, which provides a 2-dimensional view of the sea surface. Addition of a weekly-mean sea level anomaly product to mean dynamic topography creates maps of SSH. Sea level anomaly is provided by AVISO with support from CNES (Archiving, Validation and Interpretation of Satellite Oceanographic data; Centre National d'Etudes Spatiales; 1/4 • resolution) and is combined with the mean dynamic topography product of CNES-CLS09 (CNES-Collecte Localisation Satellites 2009; 1/3 • resolution). The resulting SSH maps have 1/3 • horizontal resolution.
The SSH maps expand our perspective of the region and provide a first approximation for location of the PF. The angle from perpendicular, θ, at which the ACC crossed the C-Line is crucial for projection into our stream-coordinate system ( Figure 1.2). It is the angle clockwise-positive from the C-Line to the cross-frontal axis, Y P F = tan −1 (η x /η y ), where η is the weekly SSH data and the [x, y] subscripts are standard horizontal derivatives. Finally, θ is interpolated to the twice-daily resolution of the CPIES data.

Stream-coordinate system
Stream coordinates are especially useful for investigating features that shift laterally in time -in this case the meandering PF. A simple geographic average will smear the properties of a meandering front, widening its structure. With a line of measurements, the jet will appear weakened if it does not cross the line directly perpendicularly, as the cross-frontal gradient will be artificially reduced.
These issues are avoided by converting the data into stream coordinates that move and rotate with, in this case, the PF. A schematic of our stream-coordinate system is shown in Figure 1.2.
We use the SSH data to find its maximum 2-D gradient magnitude, |∇SSH|, over the 4 years of cDrake, along the C-Line, away from the northern and southern boundaries. The highest mean geostrophic velocity, maximum |∇SSH|, is associated with the -46.6 cm SSH contour, shown by the thick grey line in Figure 1.1.
On average, it occurs at 58.25 • S. Tracking the path of this contour, we only consider times when the altimeter shows it to be quasi-perpendicular to the C-line, i.e. |θ| < 20 • , for at least 2 consecutive weeks. This angle threshold ensures the along-line gradient of a measured value requires only minimal correction, because it is at least 94% of the actual 2-D gradient magnitude. Additionally, it can be noted that the choice to demand the PF to be slowly varying does not significantly impact the distribution of maximum ∇Φ. Figure 1.3, top left panel, shows the latitudinal distribution of the maximum ∇Φ for all quasi-perpendicular times in white and the subset of times that are also slowly-varying in red and blue, for comparison.
We use the CPIES twice-daily travel-time records (converted to geopotential anomaly, Φ) to refine the location of the PF's core by finding the maximum ∇Φ within the ±1/2 • interval of latitude around the -46.6 cm SSH contour. Figure 1.3 shows a bimodal distribution of maximum ∇Φ in latitude (and in Φ, compared in Section 5.1). The strongest gradient is preferentially located either north or south of 58.5 -58.6 • S, with a clear minimum atop the SFZ. Only 48 of the 1853 quasi-perpendicular half-days fall in the 58.5 -58.6 • S latitude range (Figure 1.3, top left panel). We see this as an opportunity to study the structure of the PF and investigate the influence of local bathymetry. We, therefore, choose to examine two composite-mean jets: a northern and a southern PF, flowing upstream and downstream of the SFZ, respectively. Figure 1.2 shows our stream-coordinate system with the angle, θ, from altimetry and location of the maximum ∇Φ from CPIES as the PF core. Geopotential anomaly values at the core, Φ P F , are allowed to change in time, always associated with the strongest along-line gradient. Earlier, we experimented with defining the core location by two fixed values of Φ, one for the PF-N and one for the PF-S, and found the structure of the jet doesn't significantly change in terms of width and strength, but its velocity peak was offset laterally by up to 20 km from the chosen Φ (not shown).
We exclude instances with rings and/or S-shapes (i.e. when Φ P F appears along the C-Line more than once) and when the altimeter shows the local angle at the core of the PF is oblique (i.e. |θ| > 20 • ). As a result, 1100 half-days of mapped fields are used for subsequent analyses, with a nearly 60-40 split between times considered PF-N and PF-S. Grey bars in the top right panel of Figure 1.3 show the ∇Φ distribution of the half-days that contribute to the final composite means.
1.5 Polar Front structure 1.5.1 Geopotential anomaly and buoyancy On average, the core of the northern PF is Φ N = 17.5 ± 0.4 m 2 s −2 , while that of the southern PF is Φ S = 15.9 ± 0.2 m 2 s −2 . The difference between these two cores is significant and equivalent to 17 cm of geopotential height. The cited errors represent standard errors of the mean. Degrees of freedom for the PF-N and PF-S are 23 and 17, respectively, based on the 15-day integral time scale of the travel-time records . In a time-mean sense, the core of PF-N crosses the line at 58 • S, but it shifts as far north as 56.8 • S (Figure 1.3, left column). The core of PF-S, on average, crosses at 59 • S, and only shifts as far south as 59.3 • S. Following the PF as defined above, we project the mapped Φ data onto the frontal axis such that Y P F = Y C = 0 km at the PF's core and (Figure 1.2). We then convert from Φ(Y P F , t) to b(Y P F , p, t) with the GEM technique described in Section 2.1. i.e. with decreasing Y P F . The northern PF is warmer and more buoyant, with mean core temperatures about 0.3 • C higher and isopycnals shifted about 200 dbar deeper, than its southern counterpart. The stratification, N 2 = b z , of the front is strongest on the poleward side (Y P F < 0) around 80 dbar, in the tongue of winter water coming up from the south.

Baroclinic velocity
Cross-stream buoyancy gradient is related to the vertical shear of along-stream baroclinic velocity, as expressed by the thermal wind relationship: The width of the jet is defined as the distance between surface baroclinic speed's first minimum or zero-crossing on either side of the core. Both extend 90 km north of the core (to Y = 90 km) where there is a zero-crossing for PF-N and local minimum for PF-S (Figure 1.5). On the poleward side, the PF-N has a local minimum at Y = -70 km and the PF-S has a zero-crossing at Y = -80 km.
Hence, we choose to define the southern extent of the PF as the average of these two distances, Y = −75 km. So, the width of the PF is 165 km, independent of latitude. This leads to a baroclinic transport relative to 3500 dbar of 49 Sv for both jets; more details on transport are found in Section 4.4.

Reference velocity
Neglecting any shear below 3500 dbar, we take the measured bottom velocity at each CPIES site to be the velocity at 3500 dbar, except at C10 where the nominal bottom pressure is 2540 dbar. At this shallow site, we adjust the measured velocity down to 3500 dbar using the mean shear profile at C10's distance from the PF's core, such that the reference velocity at C10 is the offset between the measured velocity and the baroclinic velocity at 2540 dbar. That is, where the overbar denotes a composite-mean value.
All reference velocities are converted into our stream-coordinate system with the standard vector rotation: Here, (u b , v b ) are the measured eastward and northward reference velocities, and α is the angle clockwise-positive from north to Y P F (Figure 1.2). Reference velocity measurements are then organized by distance from the jet's core and averaged in 20-km bins (Figure 1.6). The spacing of CPIES is such that a measurement does not fall in each bin every half-day and there are fewer data in each 20-km bin than in the mapped fields ( (Figure 1.6). This represents an advection of warm water poleward across the core of both jets. The maximum cross-stream speed is 0.08 m s −1 , found north of the jet's core (at Y = 50 km for the PF-N and on the very northern edge of the PF-S). Speeds decrease poleward across the core of the PF, by about a factor of 2 for the PF-N and to values not significantly different from zero for the PF-S.

Transport
The PF's total transport is the addition of the baroclinic transport and the reference transport. The baroclinic transport, T bcb , of the PF-N is 49.2 ± 4.8 Sv and that of the PF-S is 49.1±3.8 Sv. This was calculated using the mean potential energy anomaly (PEA) relative to 3500 dbar, i.e. Fofonoff Potential denoted by χ, along the frontal axis (Fofonoff , 1962). Fofonoff Potential is equivalent to a baroclinic mass transport function. This is appropriate because the composite-means are defined to be on either side of the SFZ, such that neither jet is interrupted at depth by topography. The volume transport and its standard error are given by Again, f is the local Coriolis parameter and ρ o = 1035 kg m −3 is a standard ocean density. The subscripts of χ represent location along the frontal axis, such that . For a more complete description of calculating baroclinic transport from PEA, we refer the reader to Section 2 in Rodrigues et al. (2010). to 80 km in reference transport and error calculations.
The total (along-stream) transport of the PF-N is 68.4 ± 5.5 Sv and that of the PF-S is 69.4 ± 5.7 Sv. These values do not differ statistically. The total error is made up of error due to the baroclinic field, error due to the reference field, and error due to the choice of the jet's width. Errors from the baroclinic and reference fields are explained and cited above. For the baroclinic field, the error due to 5 km of uncertainty in defining the width of the jet (Section 4.2) is less than 1 Sv. The error due to width of the reference field is negligible.

Relative vorticity
The baroclinic relative vorticity, ζ bcb , is shown as a fraction of f in Figure 1.5. It should be noted now that curvature in our analysis is negligible with averages on the order of 10 −6 and 10 −7 m −1 for the PF-N and PF-S (κ = [(η 2 x η yy + η 2 y η xx − η x η y (η xy + η yx ))/(η 2 x + η 2 y ) 3/2 ], where η is SSH and [x, y] subscripts represent horizontal derivatives, as before). Their respective standard deviations are an order of magnitude larger. The average curvature vorticity, κU bcb , of the PF-N and PF-S is 1% and 0.2% of f (and standard deviation is 5% and 2% of f , respectively). Therefore, baroclinic relative vorticity is well approximated by the cross-stream velocity shear, ζ bcb = −dU bcb /dY . nearly as large as 2% of f . Note that these values are on the same order as the baroclinic curvature, κU bcb , and small compared to their baroclinic counterparts.

Potential vorticity
Potential vorticity, Q, is calculated directly from velocity and buoyancy fields, expressed as Here, we use the full velocity field, U =Ū bcb +Ū ref , the addition of the reference velocity to the mean baroclinic velocity. Potential vorticity is smoothed horizontally with a cut-off distance of 100 km, consistent with reference velocity calculations.
The terms on the right-hand-side of equation 1.6, from left to right, represent thickness-, relative-, and twisting-Q. The bottom panel of Figure 1.7 shows the thickness-Q and relative-Q in the upper 200 dbar, where relative-Q is greatest due to increased horizontal velocity shear and stratification. Relative-Q is an order of magnitude less than thickness-Q, but intensifies the cross-stream ∇Q at the core. The magnitude of relative-Q decreases with depth to 5% of thickness-Q by 700 dbar. At the core of the PF-N and PF-S, the cross-stream ∇Q changes sign horizontally with distance and vertically with pressure. Recall that these are necessary, but not sufficient, conditions for barotropic and baroclinic instability, respectively.
The horizontal change in sign is noticeable in the upper 200 dbar (Figure 1.7, bottom panel). The vertical change in sign occurs between 400 and 600 dbar, below the pycnocline and deeper than the subsurface temperature inversion (not shown). where that deep sloped layer encounters a less sloped seafloor.
1.6 Discussion 1.6.1 Comments on PF definition We find, for times when the PF crosses the C-Line nearly perpendicularly, a northern and southern PF; it is rarely found directly over the SFZ (Figure 1.3).
Interestingly, the baroclinic velocity structure and transport of the PF-N and PF-S are statistically indistinguishable, yet the fronts are separated geographically by the SFZ and hydrographically by 17 cm of geopotential height. The PF-N centers on a Φ associated with a warmer and more buoyant profile than the PF-S. In the classic view of the ACC, the PF is found at the northern extent of the 2 • C isotherm along the temperature minimum at depths deeper than 200 m .
In our T-GEM, the Φ associated with this circumpolar definition coincides with Φ N .
We look for the PF by searching for the maximum ∇Φ at any time, while Thompson and Sallée (2012) used probability density functions (PDFs) to find fronts. Those authors take advantage of the low probability of finding a frontal contour where the horizontal gradients are large, and therefore fronts appear as local minima in PDFs. The areas of relative quiescence between the ACC's fronts makes this method so effective, as these inter-frontal zones manifest as local maxima in PDFs. In a histogram of Φ data along the C-Line, we find a broad minimum about the value of the southern PF, Φ S = 15.9 m 2 s −2 , spanning Φ values from 15 − 17 m 2 s −2 (not shown).
Note that this does not mean the northern PF doesn't exist (nor that it is an artifact of our method), but rather implies that the PF-N is not bracketed by two zones of relative quiescence, as the southern PF often is. The enhanced SSH variance ( Figure 1.1, right panel) in the region north of the PF, south of the SAF, could mask the manifestation of Φ N as a local minimum. If a jet is embedded within a region of high variability, the PDF method has trouble identifying it from the background variability. In fact,  shows that the PDF method breaks down in regions of low "signal-to-noise" ratio (e.g. mean ∇SSH relative to SSH variance). Since the PF-N is located in a more energetic and variable place than the PF-S (Figure 1.1), the maximum ∇Φ is a more appropriate search criterion than the minimum probability of Φ. There has been quite a bit of discussion in recent literature about the number of fronts in the ACC (e.g. Rintoul , 2007, 2009a,b). Though it is not our intention to address this question directly, we can offer a few remarks. The horizontal and vertical constriction of Drake Passage make it an unique sector of the Southern Ocean, and analyses done outside this region may not be applicable within it. Sokolov and Rintoul (2009b) tag the PF globally with three frontal contours, and the difference between the northernmost and southernmost is either 18 or 25 cm of SSH, depending on reference level (their Table 1). In this sense, our result of a 17-cm difference between the PF-N and PF-S aligns quite well with their circumpolar height range for the PF. However, we do not find a preferred Φ for a central PF in Drake Passage, as the local minimum at 19 m 2 s −2 is not as pronounced as that at 17.25 m 2 s −2 or 58.5 • S (Figure 1.3).
The width of the PF (165 km) is comparable to other studies of baroclinic jets in stream coordinates.  use data from south of New Zealand to study the SAF, and estimate its width as 220 km. Sokolov and Rintoul (2007) estimate the width of the PF from satellite data as 40 -90 km (converted here from degrees latitude, their Figure 3), less than the width we find by a factor of 2 -4.
Perhaps the definition of jet width plays a subtle role in determining the number of fronts needed to accurately characterize the ∇SSH field of the ACC. Additionally, confluence in Drake Passage may force the branches of the PF to merge into fewer, and perhaps broader, jets than other locations around the Southern Ocean.

Inferences from transport
The mean baroclinic transport of the PF-N and PF-S (49 Sv) constitutes a significant fraction of the total baroclinic transport of the ACC.  to PEA, so converting to stream coordinates is not necessary. Also note that since PEA is equivalent to baroclinic mass transport, it is directly convertible to volume transport (Sv, see Section 4.4).
Subsets of times included in our composite averages are shown in Figure 1.10.
Each example shows that the change in PEA made by either the PF-N or PF-S individually accounts for most, if not all, of the change in PEA spanning the PF region. That is, either the northern or southern jet carries the region's baroclinic transport rather than sharing it. This is further evidence that the PF-N and PF-S do not coexist in Drake Passage. Moreover, cumulative transport along repeat transect SR1b also shows the PF has a bimodal distribution in latitude (Meredith et al., 2011). Their Figure 10 shows that of the 15 hydrography cruises along the transect, 5 were classified as 'southern' years, 9 as 'northern' years, and only 1 as Clearly, a transition between these two states occurs, where water transfers from one core Φ P F to the other. The PF-N and PF-S, in this case, would act as end members in a larger PF system. The transition between these two core states of the PF is a topic of interest, and one where a process model may prove particularly useful. To remove the deep geographic mean circulation from the reference fields, we subtract CPIES site-mean bottom velocities prior to rotating and averaging. This residual (anomaly) is arguably the signature of the meandering PF.

Implications for residual circulation
The cross-stream component of both PF-N and PF-S is in the poleward direc- . This is indicative of warm water advection across the jet, associated with upwelling along isopycnals and veering of the PF (Lindstrom et al., 1997;Holton, 2004). The buoyancy fields presented in Figure 1.4 also imply upwelling and poleward residual circulation at the PF. That is, the buoyancy layers thin from north to south across the PF (see also Figure 1.9), indicative of a poleward residual transport in those layers (Karsten and Marshall , 2002).
We do not see any return of residual circulation here, i.e. we do not see any buoyancy layers thickening poleward across the PF except in the deepest layer that intersects with the ocean bottom (Figure 1.4). This could be because the downwelling and equatorward flow (a) doesn't occur within Drake Passage, or (b) doesn't occur at the PF (but could at the Southern ACC Front or the SAF, for example), or (c) doesn't occur at these particular times when the PF flows nearly straight through Drake Passage, or (d) occurs in the ageostrophic surface Ekman flow.

Implications for mixing and stability
The strong ∇Q present at the core is indicative of a barrier to isopycnal mix- Mixing lengths, L mix , are strongly suppressed at the core of the front in both cases, further indicating the jets are barriers to mixing. Specifically, we find that L mix < 50 km at the core of the PF, and slightly more so on the southern flank of the jets (Figure 1.11, bottom row). These results are the same whether temperature or salinity is used to calculate L mix . Naveira-Garabato et al. (2011) find the PF to be a barrier to mixing at most repeat hydrography lines around the Southern Ocean, including SR1 and SR1b that bracket our C-Line (black lines in Figure 1.1).
We find the PF is a barrier to mixing in Drake Passage as well.
While the PF acts as a barrier to isopycnal mixing, it still satisfies the necessary condition for baroclinic instability. Specifically, when averaged within buoy-ancy layers, there is a change in sign of cross-frontal ∇Q between the shallow and deep layers (Figure 1.9). It should be noted that the change in sign doesn't occur until the densest layer. Bathymetry, therefore, plays a key role in setting the stability properties of the jet.
Additionally, the sign of ∇Q changes with distance from the core of the jet, is particularly noticeable at the PF-S. A less-pronounced reversal in sign of ∇Q occurs on the northern flank of the PF-N. The relative-Q, though much smaller in magnitude, is enough to change the sign of ∇Q with distance from the PF's core.

Conclusions
Along the C-Line in Drake Passage, the PF alternates between 2 distinct cores -separated hydrographically by 17 cm of geopotential height and geographically by the SFZ. While the northern expression of the jet is slightly warmer and more buoyant, the baroclinic velocity structure of the PF-N and PF-S are comparable: maximumŪ bcb near 0.6 m s −1 , width of 165 km, and strong vertical shear.
Total transports (about 70 Sv) of the northern and southern PF are statistically indistinguishable, with just over 70% carried by their baroclinic fields. Baroclinic relative vorticity is greatest in magnitude along the southern flank of the PF (at Y = -30 km), but |ζ bcb | remains less than 10% of local f across the front.
The potential vorticity fields and mixing length estimates imply both jets act as a barrier to mixing by smaller scale processes, thus tending to preserve the frontal structure. Yet, the Q fields satisfy the necessary conditions for baroclinic and barotropic instability, so meander or mesoscale eddy processes can drive cross-frontal exchange at the PF-N and PF-S.
Differences between the PF-N and PF-S are found in the structure of the deep reference velocities that are locally influenced. It appears the the PF-N is more affected by deep cyclogenesis, while the PF-S is in a location of less variability so the mean deep circulation sets the shape of the deep flow. In both cases, the crossstream velocity advects warm water poleward across the core the jet, associated with the upwelling and veering at the PF. Buoyancy fields also imply an upwelling and poleward residual circulation.    Figure 1.2. Schematic of projection of CPIES data onto the PF-axis. Triangles represent CPIES sites and grey lines represent the mapped Φ field along the C-Line. The along-stream and cross-stream axes (X P F , Y P F ) are shown in red. Measured bottom velocities, u b = (u b , v b ), are presented as blue arrows. The bottom velocities, u b , are rotated into the stream-coordinate axis for each instantaneous orientation of the PF with angle α. The cross-front coordinate is Y P F = Y C−Line · cos θ. Both angles are defined to be clockwise-positive. The top row has been partitioned as a function of latitude, the bottom row as a function of Φ. Left column is the latitude associated with the maximum ∇Φ, center column is the Φ at maximum ∇Φ, and right column the corresponding ∇Φ. White bars with black outlines in the top left show the superset of times where the criterion of a slowly-varying angle has been relaxed (such that they represent anytime the SSH contour is quasi-perpendicular to the C-Line). Grey bars in the top right panel represent the subset of the times (excluding rings, S-shapes, and local obliquity) used in the composite means of the PF. Location of CPIES sites are shown in the left column; the SFZ crosses the C-Line at C10 (58.5 • S).
, averaged within buoyancy layers for the PF-N and PF-S (red and blue, respectively). Note the different limits on the y-axes. Also note that Q reverses its horizontal tendency in the densest layer, due to the deep buoyancy surfaces sloping into the ocean bottom in Figure 1

Introduction
Oceanic and atmospheric circulations transport heat poleward to balance the excess radiative heat experienced at the equator. In the southern hemisphere, the nearly zonal geostrophic flow of the Antarctic Circumpolar Current (ACC) acts as a barrier to direct poleward heat transport by the mean flow towards Antarctica and the southern seas. de Szoeke and Levine (1981)    and with localized regions of eddy activity (Thompson and Sallée, 2012), makes quantifying the total circumpolar integral of EHF through observations also a daunting task. Direct measurements of EHF in the ACC are limited to a handful of studies Ferrari et al., 2014;Sekma et al., 2013;, and the non-uniformity of the ACC eddy field complicates extrapolation from point measurements. Until the ACC and its eddy field are properly resolved with observations and the air-sea flux of heat is better constrained, closing the Southern Ocean heat budget will remain a matter of proxy measurements and bulk formula estimates. In this study, we use a high resolution numerical model and existing satellite altimetry to quantify EHF throughout the ACC.

Watts et al. (2016) demonstrate with direct observations in Drake Passage
that baroclinic instability is the driving mechanism for large EHF events. These events release mean available potential energy (APE) from the system, reduce the slope of isopycnal surfaces by transporting heat down the mean temperature gradient, and produce eddy potential energy (EPE) . The simplest theory of baroclinic instability has meanders growing into eddies over time, yet spatial growth of eddies is also possible. In the ACC, meanders are forced by the local bathymetric configuration and mean flow, supporting the link between large bathymetric features and localized hot spots of eddy activity, that are sometimes referred to as oceanic storm tracks.
Sea surface height (SSH) data are readily available throughout the ACC from satellite altimetry, and we use the temporal standard deviation of SSH, H * , as a proxy for time-mean EHF. Holloway (1986) uses SSH height variability, scaled by gravity and a local Coriolis parameter, as a proxy for eddy diffusivity and estimates EHF via the mean temperature gradient.  apply that method analogously to two pressure levels in the atmosphere to reproduce maps of the divergent component of the EHF with some success. Furthermore, as the dynamics in the zonally unbounded ACC are similar to those in the atmosphere, albeit with different scales, those authors suggest a straightforward extension to oceanic storm tracks. This method of estimating eddy diffusivity has been applied to SSH variability in the Southern Ocean (e.g. Karsten and Marshall , 2002).  and  use other techniques for estimating eddy diffusivity from altimetric data, but again rely on a diffusive closure scheme to draw conclusions about eddy mixing. In this study, instead of seeking an eddy diffusivity or mixing coefficient to predict a downgradient flux, we use H * directly as a proxy for the depth-integrated, divergent EHF in the ACC.
The eddy field of the ACC is likely to respond to the observed increase in circumpolar wind stress over the Southern Ocean  is not the best metric for EHF.
The following section presents motivating observations from the cDrake project  in Drake Passage: elevated EHF and H * are concentrated immediately downstream of the major bathymetric ridge, while the peak in mean surface EKE is offset further downstream (Section 2.1). This local relationship is confirmed throughout the circumpolar band of the ACC and a statistical relationship between EHF and H * is developed using data from an eddy-permitting numerical model (Section 2.2). A power-law fit is applied to about 23.5 years of satellite data (Section 2.3). Circumpolar path-integrated values of EHF, its spatial pattern throughout the ACC, and long-term temporal trends in EHF at several "hot spots" are presented in Section 3. Section 4 provides a discussion of H * as a proxy for EHF in the context of oceanic storm tracks, a comparison with the few other observations of EHF in the ACC, plus a discussion of the alongand cross-ACC structure of EHF and long-term trends. Section 5 summarizes the study.  Here, the vertical integration is from the surface to a common depth of 3500 m.  CPIES measurements also allow for calculation of total SSH, SSH cDrake , as the sum of a reference SSH from directly-measured bottom pressure and bottomreferenced baroclinic SSH, as described by . Figure 2.1c shows the standard deviation of the twice-daily SSH cDrake , H * cDrake calculated with the CPIES data as: where the subscript i represents the time index, and the overbar again denotes the time-mean value. We find that H * cDrake has a similar spatial pattern to [EHF ] cDrake : elevated values occur along the western edge of the local dynamics array immediately downstream of the SFZ (Figure 2.1b,c). While the spatial pattern of [EHF ] cDrake has some interannual variability, depending on time period of averaging, the maximum [EHF ] cDrake for any multiyear subset of the data is consistently on the western side of the CPIES array (see Figure 6 in Watts et al. (2016)). Moreover, the general agreement with the pattern of H * cDrake is also consistent for any multiyear subset of four-year record (not shown).
Figure 2.1d shows the mean surface EKE calculated from the cDrake CPIES data, EKE cDrake , as: where (u, v) = (u tot , v tot ) are the zonal and meridional geostrophic velocities at the sea surface. There are two peaks in EKE cDrake , with the highest value in the central longitudes of the local dynamics array, farther east than the peaks in [EHF ] cDrake and H * cDrake (Figure 2.1b,c,d). Again, interannual variability in the spatial pattern of EKE cDrake exists, but does not change its misalignment with [EHF ] cDrake averaged over the same multiyear subset (not shown).
In Drake Passage, [EHF ] cDrake and H * cDrake are concentrated in a relatively broad region immediately downstream of the SFZ, whereas EKE cDrake exhibits smaller spatial scales. The peaks are separated by 1-2 • of longitude. These observed spatial patterns from the cDrake project motivate our use of H * as a proxy for [EHF ] throughout the entire ACC. In linear instability theory , baroclinic instability acts to transport heat down the mean temperature gradient ( In log-log space, B is the slope of the line and |A| = 10 α , where α is the y-intercept.

Application to satellite data
The power-law fit given by Equation 2

Low-frequency [EHF sat ] time series
There is much interest in how the ACC eddy field responds to changes in zonal wind stress associated with the increasing wind stress noted by .
To investigate long-term trends in [EHF ]     Idealized model studies find that baroclinic conversion, and thus EHF , occurs in the region of highest baroclinicity, and that there is a spatial offset between this region and the region of highest eddy activity and EKE (e.g. . Baroclinic instability converts mean APE to EPE through a flux of heat across the mean temperature (or SSH) gradient . SSH cDrake variance, i.e. H * 2 cDrake , is dominated by the bottom-referenced baroclinic (or buoyancy) term rather than the bottom pressure term (comparison of Figure 3d     In a balanced world, the amount of heat crossing a streamline's verticalcircumpolar surface is equal to the total air-sea heat flux out of the sea surface encompassed south that closed streamline. In this case, the circumpolar and vertical integral of total heat flux across streamlines of SSH sat must balance the air-sea flux of heat out of the ocean to its south (neglecting a nominal mean geothermal heating from the seafloor of less than 50 mW m −2 ). Estimates of air-sea flux come with uncertainties of up to 70% ), yet the general consensus between models (e.g. Volkov et al., 2010; and bulk formulae estimates  found, for relatively stable time periods, a depth-mean temperature difference of 0.3 • C between a composite-mean PF upstream and downstream of the SFZ, some of which may be due to a convergence of EHF in the downstream jet. The above posited increases in temperature at each of the [EHF ] sat hot spots are analogous to the deep changes in buoyancy found in the OFES model by Thompson and Naveira-Garabato (2014). This increased temperature (or buoyancy) associated with lateral [EHF ] sat convergence is not able to interact with the atmosphere directly through air-sea flux, as it occurs throughout the water column. It must, therefore, be incorporated into the mean circulation of the ACC and leave the ACC laterally through mean heat flux associated with the overturning circulation (sometimes referred to as the Deacon cell). This is a topic of immediate interest, to both confirm the estimate of along-stream ∆T done here and to gain understanding of the relative importance of each hot spot of [EHF ] sat .

Along-stream structure of [EHF ] sat
In a broad sense, the locations of elevated [EHF ] sat correspond with where the SSH sat contours pinch together (Figure 2.7a). This is especially apparent at the PAR where the latitudinal width between the SAF and the southern edge of the ACC reduces to less than half its upstream width before expanding again downstream, i.e. from more than 10

Temporal trends of [EHF ] sat
There has been discussion in recent literature about the ACC eddy field's response to increasing and poleward-shifting winds in the Southern Ocean (e.g. Hogg et al., 2014;. In this study, the long-term trend in low-frequency [EHF ] sat in each hot spot is diagnosed in a running-mean sense using 4-year subsets of H * sat overlapped by 2 years (Figure 2.8).

Introduction
The Southern Ocean and its dynamics are unique to the world's oceans, dominated by the zonally unbounded Antarctic Circumpolar Current (ACC) system.
The deep-reaching stratification of the wind-driven ACC is thought to set the deep (≥500 m) isopycnal structure of the world's oceans (e.g. . Quantifying the strongly inhomogenous flow of the ACC, with along-and across-stream variability on many scales, is an observational challenge and numerical models require parameterization of processes crucial for setting the stratification of the ACC, i.e. eddy transports (of buoyancy, heat, momentum, carbon) and eddy-mean flow interactions. Predicting and preparing for future climates rely on properly parameterizing these processes in climate models that require validation with direct observations.
The large-scale dynamics of the ACC are analogous to those of the midlatitude atmosphere, with storm tracks of increased eddy activity downstream of localized forcing (e.g. . In the ACC, the forcing is orographic, due to the mean flow's encounter with large bathymetric features. The existence of these oceanic storm tracks makes it especially challenging to extrapolate local observations to the rest of the ACC and to interpret the results of studies framed in a zonal-mean sense at any particular location in the ACC. Work on the dynamics of atmospheric storm tracks (e.g. , that have been studied for much longer than oceanic storm tracks, guides our study of the dynamics of an oceanic storm track in Drake Passage. The dynamics of a localized storm track, be it atmospheric or oceanic, are rooted in the interaction between the eddying and the mean flow. That is, the storm track is defined as a region of relatively high eddy activity (often diagnosed through eddy kinetic energy, EKE) where the eddies are growing by gaining energy from the mean flow. In the ACC, episodic baroclinic instability events are the main mechanism for eddy heat flux . Each baroclinic instability event is associated with a conversion from mean available potential energy (APE) to eddy potential energy (EPE) through a flux of heat/buoyancy across the mean upper baroclinic front by the eddying flow . This step is followed by a conversion of EPE to EKE through vertical eddy buoyancy flux. EKE can also be produced directly from the mean kinetic energy pool through barotropic instability. A recent idealized model study, with dynamics representative of a standing meander in the ACC associated with a submarine ridge, illustrates the importance of mixed baroclinic-barotropic instability .
Elevated EKE values observed in the atmosphere downstream of the local forcing and region of highest baroclinicity have been explained, through use of numerical model simulations, by the idea of 'downstream baroclinic development' . Downstream baroclinic development has been observed in the atmosphere to be associated with large storms, e.g. a major winter blizzard . In this process, an individual eddy depends on its neighboring upstream eddy for its energy through geopotential flux convergence . Eddy energy budgets, based on time-mean eddy energy equations, are typ-ically used to study eddy-mean flow interactions in the ocean and can provide useful information when interpreted appropriately (e.g. . However, without knowledge of the physical process responsible for the different conversion terms, the interpretation of these eddy energy budgets is ambiguous . These ambiguities can be avoided by diagnosing a 'wave activity flux.  first formulated a wave activity flux for a zonally and temporally averaged mean flow, with eddies defined as any deviation from that mean. The EP flux, as it has come to be known, provides useful insight into the relative importance of eddy heat and momentum fluxes, i.e. of baroclinic and barotropic instabilities. While the EP flux, and the transformed Eulerian mean framework that often accompanies it, is a powerful tool for diagnosing eddy-mean flow interactions, the requisite zonally and temporally averaged background state makes it a difficult diagnostic to observe and makes interpretation a challenge in the ACC.  generalized the wave activity flux to three dimensions for a simple time-mean flow, eliminating the need for a zonally averaged background state.  further generalize wave activity flux to include the temporal dimension, i.e. the propagating component of the eddy is also included whereas the flux of  is for a stationary eddy. Therefore, the study of the interaction between propagating waves in three dimensions and the background mean flow is possible under the assumptions of their formulation (explicitly stated in Section 2). An export of wave activity, i.e. a divergence of its flux, is analogous to the mean flow losing energy to the eddying flow. Additionally, the vertical wave activity flux vector can be thought to be associated with baroclinic interactions and the horizontal flux vectors with barotropic interactions .
In this study, eddy-mean flow interactions in Drake Passage are diagnosed through wave activity flux along with eddy energy. Specifically, these diagnostics are used to shed light on the physical processes responsible for the spatial offset observed between eddy heat flux and EKE in Drake Passage (Foppert et al., in rev).
In the next section, an oceanic wave activity flux based on that of  is presented. Section 3 describes the Drake Passage dataset and the complementary satellite altimetry data used in this study. Section 4 presents our major results: four-year time-mean fields of wave activity flux and its components, and a case study highlighting the temporal evolution of an eddy event that went into making composite-mean fields. Section 5 discusses the results and Section 6 summarizes the study.

A primer on wave activity and its flux
For small amplitude, quasi-geostrophic disturbances on a background mean geostrophic flow, a linear combination of the eddy energy (EPE and EKE) and eddy enstrophy can be formulated such that where M is the wave activity density, W is the wave activity flux, and D is diabatic or frictional forcing . The wave activity M = ρ(A + E)/2, where A = (1/2)q q /|∇q| is the psuedomomentum with q being the quasi-geostrophic potential vorticity and an over-bar denoting the time-mean quantity and E = e/(|ū|−c p ) is a normalized eddy energy density with c p being the phase speed of the eddies that must be known a priori. Quasi-geostrophic potential vorticity anomaly, q = ∇ 2 ψ + (f 2 0 ψ z /N 2 ) z , has units of s −1 and the eddy energy, e = ψ xx + ψ yy + (f 0 ψ z /N ) 2 , has units of m 2 s −2 . Here, ψ is the total geostrophic stream-function with its associated geostrophic velocity, u = (u, v) = (−ψ y , ψ x ), and buoyancy, b = f 0 ψ z , f 0 in the local Coriolis parameter, N 2 =b z is the squared buoyancy frequency, and subscripts represent partial derivatives.
Written this way, the wave activity and its flux have no phase dependence, i.e.
do not depend on their location along the linear wave. The derivation of this wave activity and its flux by  assumes that (1) where ρ is a nominal ocean density. Note that the vertical flux is scaled by f 2 0 /N 2 . (2001) (2001) show that these second terms can be approximately interpreted as a flux of geopotential anomaly by the ageostrophic (sub-or super-geostrophic) flow.

Takaya and Nakamura
For a linear plane wave, Takaya and Nakamura (2001)  A gravest empirical mode analysis based on regional hydrography provides a profile of temperature and salinity, and thus geopotential height (φ), for every value of τ . Buoyancy is then calculated from each temperature and salinity profile. That is, b = g ρ 0 (γ − γ 0 ), where g = 9.8 m s −2 is a local gravitational acceleration, ρ 0 = 1035 kg m −3 is a standard ocean density, γ 0 = 28.5 kg m −3 is a deep neutral density, and γ is calculated with the neutral density package of .  demonstrate that the LDA allows for optimal-interpolation mapping of the total geostrophic stream-function, ψ, its horizontal derivatives (i.e. total geostrophic velocity), and horizontal velocity shear. A detailed error analysis is also detailed in Firing et al. Eddy energy, EPE and EKE, are calculated directly from the CPIES measurements. EPE is calculated from the buoyancy field as where N 2 =b z is the low-passed mean buoyancy frequency squared. EKE is calculated from the total geostrophic velocity as Again, as with W , the prime denotes any deviation from the slowly varying, 90-day low-passed 'mean' quantity.

Satellite altimetry
The analysis is complemented with satellite altimetry to give a broader picture of the regional sea surface height, SSH, that is the addition of the CNES-  (Figure 3.2).
The rotational W H in the eastern LDA appear collocated with a closed contour in the mean SSH field.
The four-year mean EKE and EP E are plotted in Figure 3.3. The EKE field has two peaks, both located adjacent to W z peaks. The EP E field shows elevated values in the northwest corner of the LDA, north of the main W z peak.
The maximum value of EP E (0.047 m 2 s −2 ) is slightly larger than that of EKE

Composite-mean fields
As the LDA is located in a region between the SAF and PF, the left column of Figure 3.5 presents composites of the same information as in Figures 3.2 and 3.3 for time periods of elevated W z (≥ 0.5 J m −3 ) in the western LDA. Additionally, the divergence of the horizontal wave activity flux, ∇·W H is plotted in Figure 3.5j.
About 20% of the four years of data, 297 days, were used in creating the composites shown here. This removes some of the 'noise' in the full four-year mean fields, and more clearly illustrates the wave activity flux pattern in Drake Passage.
The pattern of W z is similar to before, with a large peak in the western LDA, but the smaller local maximum more centrally located is eliminated (Figure 3.5a).  (Figure 3.5d,j), but this result is not statistically significant.
These composite-mean fields can be further decomposed into times when a (PF) trough and times when a (SAF) crest intruded in western LDA (Figure 3.5, middle and right column, respectively). While the overall patterns of W and EPE are quite similar for SAF and PF events -elevated values of W z and EPE in the western LDA and W H vectors pointing north-northeast -there are some slight differences. In particular, the maximum EPE and EKE for PF trough events (ψ > 0) is stronger by 0.02 m 2 s −2 and 0.01 m 2 s −2 , respectively, than that for SAF crest events (ψ < 0). Additionally, the location of the EPE peak is farther north for PF events than it is for SAF events (Figure 3.5b,c,e,f).
The EKE and horizontal divergence (∇ · W H ) fields show more spatial variability between the two subsets within the composites (Figure 3.5h,i,k,l). The peak in EKE is larger for PF trough events than SAF crest events and offset slightly south of the strongest W H vectors. In the composite of SAF crest events, the W H vectors point more directly from the peak in EPE, or W z , towards the peak of EKE (Figure 3.5i). The horizontal divergence of W H is weaker and located farther north for PF trough events than SAF crest events.
3.5.3 Case study: 15-23 July 2010 shown here from 15 to 23 July 2010, a positive ψ anomaly is present in the western part of the LDA, with an adjacent negative ψ anomaly more centrally located, and a smaller positive ψ anomaly in the east (Figure 3.6). This train of ψ anomalies is associated with a large meander that is also seen in the SSH field (recall that the SSH has not been low-pass filtered and an exact correspondence between SSH and ψ is not expected). July and a subsequent decrease in W z from 21 to 23 July, with its maximum value realized on 20 July. The vertical W z is offset slightly east from the western EPE peak (Figure 3.6, second row). In this case, the vertical W z peaks tends to fall between the western EPE peak and the EKE peak (Figure 3.6, third row).
Strong W H vectors are collocated with the W z peak and point northnortheast across the ψ contours from the western anomaly to the central anomaly ( Figure 3.6). Comparison of the ψ fields on 15 and 23 July shows that the large positive ψ anomaly has translated in the same direction. On 17 and 19 July, there is a convergence of W H that aligns well with the EKE peak. On 21 July, the vectors turn more eastward and converge into the center of the central ψ anomaly.
3.6 Discussion 3.6.1 4-year and composite-mean fields Wave activity flux, W , is a powerful diagnostic for examining the evolution of wave activity (a combination of total eddy energy and eddy enstrophy). In this framework, in the absence of adiabatic forcing or friction, a convergence of W is directly linked to an increase in wave activity (Equation 3.1) and the growth of an eddy. Here, the stationary component of W is calculated with observations of the total geostrophic stream-function in the eddy-rich Polar Frontal Zone in Drake Passage. The array of CPIES was deployed immediately downstream of the Shackleton Fracture Zone, a major submarine ridge (Figure 3.1).
In order to conserve potential vorticity, the jets of the ACC shift equatorward as they flow over the Shackleton Fracture Zone and poleward as they flow down the leeward side, mechanically forcing a stationary meander in the lee of the ridge.
Episodic events of SAF crests and PF troughs intruding into the western LDA are observed to be associated with strong eddy heat flux and baroclinic instability events . The four-year mean W field, averaged between 200 and 700 m depth, shows elevated values of the vertical W z and EP E in the western part of the LDA (Figure 3.2 and 3.3a). This is indicative of the conversion from mean APE to EPE associated with baroclinic instability.
Horizontal W H vectors emanate from this region, indicating that wave activity is being transported from the region of strongest W z (and eddy heat flux) northeast and out of the LDA. This is considered the main storm track in this region, such that the track trends northeast, almost perpendicular to the mean SAF crest seen in Figure 3.1. In an along-track sense, i.e. averaging over the region of elevated W z in sequential bins in the direction of the W H vectors, the largest values of EKE are found downstream of the largest W z and EP E (Figure 3.4). This is also where there is an along-track convergence of W H .
There is also a secondary region of elevated W z located in the central LDA between the mean SAF crest and mean ring (closed mean SSH contour; Figure 3.2).
Occasional intrusions of a PF trough and ring formation events have been observed in this region ). The horizontal W H vectors show cyclonic (clockwise) rotation that may be associated with this mean ring or with the deep recirculation in the Yaghan Basin, a deep basin in northern Drake Passage centered near 56 • S and 61 • W. There is also a secondary peak in EKE, again connected to the secondary W z peak by W H vectors (Figure 3.2 and 3.3). Here, the focus is on the dynamics of the western storm track, but it can be noted that a larger array in the future could help illuminate the complicated dynamics in this region.
In particular, it would help parse out whether the storm tracks continue farther downstream (outside of the array) or if they are disrupted by bathymetry and dissipate locally.
To highlight the dynamics of the western storm track, a composite-mean look at the W and eddy energy fields for a subset of eddy events is presented (Figure 3.5). An eddy event is defined as time when the regional-mean W z (west of 64 • W) is greater than 0.5 J m −3 . While the pattern in the western LDA doesn't change significantly, the secondary peak in W z is greatly reduced in magnitude relative to the primary peak immediately downstream of the Shackleton Fracture Zone. Again, the horizontal W H vectors point from the region of elevated EPE and W z towards the region of highest EKE. This is especially apparent for events involving a SAF crest (ψ < 0; Figure 3.5, right column). In a broad sense, where the strongest values of EKE are found, there is also a convergence of W H (Figure 3.5, bottom row). The association between the location of EKE peaks and the horizontal component of the wave activity flux (and/or its convergence) illustrates the importance of barotropic processes in the transport of wave activity and the production of EKE downstream from regions of highest baroclinicity.
3.6.2 Case study: 15-23 July 2010 The temporal evolution of a 'typical' meander event is shown in Figure 3.6.
During this time period, a PF trough (ψ > 0) is intruding into the western side of the LDA, strengthens, and begins to decay. Throughout the eight-day event, strong horizontal W H vectors emanate from the W z peak and generally point north-northeast from the western to the central ψ anomaly. Watts et al. (2016) show strong eddy heat flux in the western and central LDA during the first several days, with increasing flux from 16 to 19 July followed by decreasing flux from 22 to 25 July. Here, the largest W z values are found on 20 July. The strong W z and eddy heat flux, cited in Watts et al. (2016), are indicative of baroclinic growth and instability through a conversion from mean APE to EPE.
The offset between W z and EKE and the alignment of W z and EPE are not as pronounced in this event as they are in the four-year mean or composite-mean fields ( Figure 3.4 and 3.5). In fact, the W z peaks appear located between the EKE and EPE peaks, with the strongest EKE consistently found on the leading edge of the western ψ anomaly and EPE peaks found in the center of the western and central anomalies (Figure 3.6). It can be noted again here that the wave activity, M , is a combination of eddy energy and enstrophy and that the eddy enstrophy broadly mirrors the EPE field as potential vorticity is dominated by the thickness term (not shown).
In simple baroclinic instability, mean APE is converted to EPE through a horizontal eddy heat flux and EPE is converted to EKE through vertical eddy heat flux. Here, it is seen that the largest value of EPE is found on 23 July in the western ψ anomaly, while the largest value of EKE is found on 17 July. The enhanced EKE on 17 July, prior to the strongest W z and horizontal eddy heat flux (from Watts et al. (2016), Figure 7), implies that the EKE is being produced by a process other than baroclinic instability, i.e. barotropic instability, or that there is eddy heat flux and baroclinic growth occurring outside the LDA and the energy is being transported into the LDA. In fact, Figure 3.6 (third row) shows strong horizontal W H vectors in the southwest corner of the LDA on 15 and 17 July that show a flux of wave activity into the LDA.
Later in the event, as W z is at its strongest between 19 and 21 July, W H vectors point from the W z peak to the EKE peak. On 19 July, there is horizontal convergence of W H at the EKE peak, but on 21 July the convergence is farther downstream (in the center of the negative ψ anomaly). There is also some divergence of W H out of the western ψ anomaly on 23 July, which suggests the mean flow taking wave activity back from the eddies (or localized diabatic forcing).
Overall, the energetics of the storm track are strongly tied to both the horizontal and vertical components of W , highlighting the importance of barotropic and baroclinic processes, respectively, transferring wave activity through an oceanic storm track. Additionally, by diagnosing the dynamics of the storm track using W , the evolution of the eddy-mean flow interactions can be studied in a snap-shot sense.

Implications of this work
Orlanski and Sheldon (1995) describe three stages of downstream baroclinic development. At first, energy from a pre-existing mature eddy is carried downstream (by geopotential fluxes by the ageostrophic flow) to feed an adjacent eddy.
As the initial eddy decays and this downstream eddy matures, energy from it is carried farther downstream to feed a third eddy. As the second begins to decay, the third eddy matures, and so on until the energy eventually dissipates. In the situation described by , the wave is purely baroclinic, i.e. there is no barotropic mode, and dissipation occurs far downstream. In the ACC, both barotropic and baroclinic modes exist together. Additionally, unlike the atmosphere or many modeling studies with a single idealized ridge (e.g. , the ACC is often punctuated by bathymetry. That is, soon after its interaction with the Shackleton Fracture Zone, the PF must navigate the Scotia Arc and the SAF is steered strongly northward by the South American continental slope. Upstream of the Shackleton Fracture Zone, the ACC also encounters the Phoenix Ridge near 66 • W. Here, it appears that barotropic processes, diagnosed as W H and suggested by its convergence, are important in the maintaining the offset between EPE (produced through horizontal eddy buoyancy flux in the region of high baroclinicity and observed through W z ) and EKE. Moreover, , using an idealized numerical simulation of flow over a ridge, show that mixed barotropic-baroclinic instability is important for the dynamics of Southern Ocean storm tracks. In the conventional eddy energy budgets, EKE is produced in two ways: through the baroclinic pathway by vertical eddy buoyancy flux that converts EPE to EKE or through the barotropic pathway by horizontal eddy momentum flux that converts mean kinetic energy to EKE. It remains unclear here which of these two processes is responsible for the EKE in Drake Passage or what the relative contribution of each process is to the total production of EKE. In order to properly parameterize global circulation and climate models to accurately simulate the transfers of energy and enstrophy, i.e. wave activity, through the ACC system, all the processes responsible for those transfers must first be understood.

Conclusion
In this study, stationary wave activity flux (W ) and eddy energy (EKE and EPE) are presented in the eddy-rich inter-frontal zone between the SAF and PF in  Figure 3.6. Case study of wave activity flux and its horizontal divergence (top and bottom row, respectively) and eddy energies, EPE (second row) and EKE (third row). The ψ anomaly field (deviation from 90-day low-passed mean field) is contoured, with ψ > 0 in black and ψ < 0 in gray. An SSH contour representative of the PF (SSH=-0.3 m) is shown in brown. The horizontal wave activity flux vectors are plotted at every other grid point in each panel for orientation.