Abstract

The relationship between Antarctic Circumpolar Current jets and eddy fluxes in the Indo–western Pacific Southern Ocean (90°–145°E) is investigated using an eddy-resolving model. In this region, transient eddy momentum flux convergence occurs at the latitude of the primary jet core, whereas eddy buoyancy flux is located over a broader region that encompasses the jet and the interjet minimum. In a small sector (120°–144°E) where jets are especially zonal, a spatial and temporal decomposition of the eddy fluxes further reveals that fast eddies act to accelerate the jet with the maximum eddy momentum flux convergence at the jet center, while slow eddies tend to decelerate the zonal current at the interjet minimum. Transformed Eulerian mean (TEM) diagnostics reveals that the eddy momentum contribution accelerates the jets at all model depths, whereas the buoyancy flux contribution decelerates the jets at depths below ~600 m. In ocean sectors where the jets are relatively well defined, there exist jet-scale overturning circulations with sinking motion on the equatorward flank and a rising motion on the poleward flank of the jets. These jet-scale TEM overturning circulations, which are also discernible in potential density coordinates, cannot be attributed to Ekman downwelling because the Ekman vertical velocities are much weaker and their meridional structure shares little resemblance to the rapidly varying jet-scale overturning pattern. Instead, the location and structure of these thermally indirect circulations suggest that they are driven by the eddy momentum flux convergence, much like the Ferrel cell in the atmosphere.

1. Introduction

The Southern Ocean, which extends from Antarctica to 30°S, has a significant influence on the global oceanic circulation and the earth’s climate. The Antarctic Circumpolar Current (ACC) is known to play a critical role for the modulation of a global-scale meridional overturning circulation (MOC; Toggweiler and Samuels 1995; Marshall and Speer 2012). In spite of its importance, there are aspects of ACC dynamics that remain elusive in part because turbulent mesoscale eddies are important players in the general circulation of the Southern Ocean.

Mesoscale eddies influence the ACC circulation through eddy buoyancy and eddy momentum fluxes. During the past decade or so, the importance of the eddy buoyancy fluxes on the ACC dynamics has been firmly established. It has been shown that eddy buoyancy fluxes are important in determining the slope of isopycnal surfaces and setting the strength of the ACC and Southern Ocean MOC (Karsten et al. 2002; Marshall and Radko 2003; Olbers et al. 2004; Olbers and Visbeck 2005). In contrast, the role of eddy momentum fluxes in ACC dynamics remains less certain (Hughes and Ash 2001; Grezio et al. 2005). Stevens and Ivchenko (1997) found that when averaging over the entire ACC, the primary zonal momentum balance is between surface wind stress and bottom form stress, and the contribution by eddy momentum flux divergence–convergence is an order of magnitude smaller. However, at regional scales, eddy momentum flux may still be important. Close to the Macquarie Ridge–Campbell Plateau, Morrow et al. (1994) found that the eddy momentum flux convergence is significant and acts to accelerate the mean jet. Ivchenko et al. (1997) showed that eddy momentum flux convergence drives localized jets to the northeast of Drake Passage. Williams et al. (2007) found that in regions of topographic gaps, the vorticity flux (which is equivalent to the sum of the zonal and meridional convergence of eddy momentum flux) acts to accelerate (decelerate) the mean current at the entrance (exit and downstream) region. Stewart et al. (2015) found that eddy anisotropy, which is an indication of eddy forcing of the time-mean flow, is relatively large along the ACC. Although not directly relevant for the ACC jets, the eddy momentum flux is found to be important for reinforcing the idealized western boundary current jets (Waterman and Jayne 2011; Waterman and Hoskins 2013).

In the atmosphere, polar front jets are driven by meridional convergence of eastward eddy momentum flux (Starr 1948; Williams 1979; Palmén and Newton 1969; Lee and Kim 2003). These eddies are primarily baroclinic eddies. Consistent with the finding that almost the entire Southern Ocean is baroclinically unstable (Smith 2007), as was mentioned above, similar eddy-driven oceanic jets also exist. In the atmosphere, the same eddy momentum flux also drives the Ferrel cell across the eddy-driven jet with a rising motion poleward and a sinking motion equatorward of the jet. To the best of our knowledge, the existence of similar momentum flux–driven overturning circulations has not been investigated for the ocean. It is worthwhile to explore this possibility because such jet-scale overturning circulations, if they exist, can help promote the vertical exchange of zonal momentum and water mass.

The first goal of this study is thus to investigate the relationship between eddy fluxes and jets and between the jets and possible overturning circulations. Because our hypothesis is inspired by the atmospheric midlatitude circulation where jets are primarily zonal, as a first step to test our hypothesis, we restrict our analyses to a limited region in the Indo–western Pacific Southern Ocean where no major bathymetry exists and the jets are relatively zonal.

Compared with the atmosphere, however, the relationships among the ACC jets, eddy fluxes, and the overturning circulation are somewhat more complex because scales of the ACC jets are approximately the same as that of the eddies (e.g., Sokolov and Rintoul 2007), while the meridional scale of the eddy buoyancy flux is much greater and of the ACC scale (Thompson and Naveira Garabato 2014). This scale difference raises the possibility that the eddy buoyancy flux is poleward not only at the latitudes of the jets, but also at the latitudes of interjet regions. These supposed buoyancy flux characteristics are reminiscent of those simulated by a two-layer quasigeostrophic (QG) model on a beta plane (Lee 1997) and also in a spherical model (Lee 2005). In model runs where multiple zonal jets are persistent, Lee (1997) found that growing baroclinic waves exist not only at the jet latitudes but also between the jets (hence “poleward” buoyancy flux at the interjet regions) and that the interjet waves export zonal momentum1 out of the interjet region. As illustrated schematically in Fig. 1, these interjet disturbances, while helping to maintain eddy-scale multiple zonal jets, also allow the eddy buoyancy flux to be poleward throughout the entire baroclinic zone, encompassing both the jets and interjet regions. Therefore, it is our second goal to investigate if such interjet disturbances exist at least in part of the ACC.

Fig. 1.

A schematic diagram of multiple zonal jets, baroclinic eddy structure, baroclinic eddy momentum flux [] [the notation is introduced in (4)], and baroclinic eddy buoyancy flux. This schematic is based on Fig. 5 of Lee (1997). The horizontal axis is either the zonal speed U of the flow or zonal phase speed c of the eddies; the eddies that grow at the jet latitudes propagate faster than the eddies that grow at the interjet region. The former eddies transport zonal momentum into the corresponding jet, while the interjet eddies export zonal momentum out of the interjet. As a result, the momentum flux by both eddies help maintain the multiple jets. However, the buoyancy flux has a meridional scale of the entire baroclinic zone that encompasses both the jets and the interjet region (notice that the vertical shear of the flow is positive everywhere).

Fig. 1.

A schematic diagram of multiple zonal jets, baroclinic eddy structure, baroclinic eddy momentum flux [] [the notation is introduced in (4)], and baroclinic eddy buoyancy flux. This schematic is based on Fig. 5 of Lee (1997). The horizontal axis is either the zonal speed U of the flow or zonal phase speed c of the eddies; the eddies that grow at the jet latitudes propagate faster than the eddies that grow at the interjet region. The former eddies transport zonal momentum into the corresponding jet, while the interjet eddies export zonal momentum out of the interjet. As a result, the momentum flux by both eddies help maintain the multiple jets. However, the buoyancy flux has a meridional scale of the entire baroclinic zone that encompasses both the jets and the interjet region (notice that the vertical shear of the flow is positive everywhere).

The remainder of this paper is organized as follows: In section 2, we offer a more detailed description of the aforementioned circulation features and relevant theories. The model and the data will be described in section 3. The results will be presented in section 4, and conclusions will follow in section 5.

2. Theories on indirect circulations: Eddy momentum flux and its imprint on the transformed Eulerian mean circulation

The analogy between the atmospheric Ferrel cell and the Southern Ocean overturning circulation had been drawn previously. Karoly et al. (1997) described that the Deacon cell, with its rising (sinking) branch being poleward (equatorward) of ~45°S as being analogous to the atmospheric Ferrel cell with rising (sinking) motion occurring at around 60° (30°) latitude. Both circulations are indirect in the sense that less (more) buoyant fluid appears to rise (sink) across horizontal density surfaces. In analogy with Edmon et al. (1980) for the atmosphere, in the transformed Eulerian mean (TEM) framework where the resulting circulation describes Lagrangian motion, Karoly et al. (1997) showed that the indirect Deacon cell disappears and is replaced by a direct circulation. The reason is that while the TEM includes the effect of a zonally varying eddy buoyancy flux, this effect is unaccounted for in the Eulerian mean. We schematically illustrate this distinction in Fig. 2a for a hypothetical situation where the eddy buoyancy flux contribution is present and the eddy momentum flux contribution is negligible.

Fig. 2.

(a),(b) Schematic diagrams of atmospheric meridional overturning circulations. Blue (gray) lines and arrows with shading denote the thermally direct (indirect) overturning circulations in height z coordinates, that is, Hadley and Polar cells (Ferrel cell). Black lines and arrows indicate the TEM circulation in height coordinates or the overturning circulations in isentropic ϑ coordinates when (a) only eddy buoyancy flux is present and (b) both eddy fluxes of buoyancy and momentum are present and the momentum flux is strong enough to overcome the effect of the buoyancy flux. The eddy momentum flux (→) drives the midlatitude jet (⊙). (c) A schematic diagram of an idealized meridional overturning circulations corresponding to the double jets driven by eddy momentum flux, as in Fig. 1.

Fig. 2.

(a),(b) Schematic diagrams of atmospheric meridional overturning circulations. Blue (gray) lines and arrows with shading denote the thermally direct (indirect) overturning circulations in height z coordinates, that is, Hadley and Polar cells (Ferrel cell). Black lines and arrows indicate the TEM circulation in height coordinates or the overturning circulations in isentropic ϑ coordinates when (a) only eddy buoyancy flux is present and (b) both eddy fluxes of buoyancy and momentum are present and the momentum flux is strong enough to overcome the effect of the buoyancy flux. The eddy momentum flux (→) drives the midlatitude jet (⊙). (c) A schematic diagram of an idealized meridional overturning circulations corresponding to the double jets driven by eddy momentum flux, as in Fig. 1.

However, there are a couple of subtle aspects to consider. Observations of the atmospheric circulation show that the TEM circulation is not composed of a single cell as illustrated in Fig. 2a. Instead, as indicated schematically in Fig. 2b, there is a midlatitude dip in the upper branch of the TEM with descent in the subtropics and ascent in the subpolar region. This midlatitude dip can be clearly seen in Fig. 6a of Edmon et al. (1980). Figure 2 in Karoly et al. (1997) shows that this dip is sufficiently deep that it extends to the surface.

The cause of this dip is that eddy momentum flux convergence/divergence is strong enough to overcome the eddy buoyancy flux effect (Robinson 2006). Unlike the eddy buoyancy flux contribution, the eddy momentum flux contribution to the three-cell structure does not disappear in the TEM framework. To help illustrate the key idea, we consider the equation developed under the QG scaling of the Boussinesq equations on the beta plane (Vallis 2006). In terms of the residual-mean meridional circulation——defined as

 
formula

the QG zonal momentum and buoyancy equations take the form of

 
formula

and

 
formula

where u, υ, and w are the zonal, meridional, and vertical velocities, respectively; b is the buoyancy; and N is the buoyancy frequency. Following the notation of Peixoto and Oort (1992), the bracket [⋅] denotes a zonal mean, and asterisks denote the deviation from the zonal mean. Neglecting frictional and heating terms (F and Q) and by requiring maintenance of thermal wind balance,

 
formula

and (2) and (3) are combined to yield the equation for the residual-mean meridional circulation:

 
formula

Equation (5) tells us that a positive forcing [on the right-hand side (rhs)] drives a counterclockwise TEM circulation in the yz plane. Likewise a negative forcing drives a clockwise circulation. In the midlatitude troposphere, the eddy momentum flux convergence in term A is positive, and it increases with z. Therefore, in the Northern Hemisphere (NH), where f0 > 0, term A is positive; hence, this term drives a counterclockwise circulation. In the Southern Hemisphere (SH) where f0 < 0, term A drives a clockwise circulation. In both hemispheres, these circulations are the thermally indirect Ferrel cell. The buoyancy flux in term B is poleward, so to the extent that vertical variations in N are negligible, term B is negative in the NH and positive in the SH. In other words, term B drives a thermally direct circulation in both hemispheres.

In the Eulerian zonal-mean circulation, the buoyancy flux term also drives thermally indirect circulation [Fig. 2a; the relevant equation was derived by Kuo (1956), and Pfeffer (1981) performed calculations using this equation with observational data], but this circulation disappears in the TEM, as we just analyzed and as was discussed elsewhere (Edmon et al. 1980; Andrews et al. 1987; Vallis 2006). However, as (5) indicates, the momentum flux (term A) drives a thermally indirect circulation even in the TEM framework. Therefore, the midlatitude dip in the TEM circulation (Fig. 2b) indicates that the eddy momentum flux effect is strong enough to “win” (Robinson 2006) and hence to enslave the buoyancy field. Moreover, the dip implies that the buoyancy field adjusts in a manner that the meridional buoyancy gradient, or baroclinicity, is enhanced. For the ocean, this adjustment would be manifested as adiabatic vertical motion that leads to isopycnal tilting. For the hypothetical multiple jet configuration of Fig. 1, (5) predicts that momentum flux alone would produce jet-scale overturning circulations, but together with the buoyancy flux effect, in TEM framework (or in the isopycnal coordinates), these jet-scale overturning circulations would manifest themselves as multiple dips (black curve in Fig. 2c) analogous to the midlatitude dip in the atmosphere.

To the best of our knowledge, the momentum-driven overturning circulation has not received any attention for the ocean. Perhaps one reason for this is that strong diabatic effects in the Southern Ocean are thought to be restricted to the surface mixed layers, and the interior ocean is quasi adiabatic. Therefore, a deep-reaching dip in the TEM circulation, which must be associated with diapycnal processes in the deep interior, was not considered. Moreover, eddying ocean models show the eddy momentum flux contribution to be negligible in zonal average. However, it is worth investigating whether, given the strong longitudinal variability of eddy fluxes in the ACC, such overturning circulations exist locally.

3. Model and data description

The data used in this paper are obtained from the eddy-resolving Los Alamos Parallel Ocean Program (POP) model (Smith et al. 1992). A Mercator grid is employed with a latitudinal grid spacing of ⅞° cos(φ), where φ is latitude. Over the Southern Ocean, the corresponding horizontal resolution ranges between 4 and 9 km. In the vertical, the POP model has 42 levels with the thickness ranging from 5 m at the surface to 250 m at 5500-m depth. The POP model successfully reproduces the mesoscale variations in sea surface height of the Southern Ocean (McClean et al. 2006).

The POP model run analyzed here was forced with synoptic CORE.v2 corrected interannually varying forcing, initialized from a spun-up ocean state (Maltrud et al. 2010) that used a repeating monthly climatology (normal-year CORE). This initial spinup period was found to be sufficient for mesoscale processes in the upper ocean to reach a quasi-equilibrium state. The results described in this paper are based on the period between 1994 and 2007.

All of the eddy flux analyses presented here are calculated with unsmoothed data, but for display purposes a Gaussian boxcar smoothing with 2.5° × 2.5° resolution is applied to horizontal fields of fluxes and velocity fields (e.g., as in Williams et al. 2007). For the vertical cross-section calculations, we used the unsmoothed values. For brevity, the Gaussian boxcar smoothing will be simply referred to as “smoothing.”

4. Results

We first examine the horizontal distribution of zonal current speed and assess how the ACC jets are simulated by the POP model. Figure 3a displays the unsmoothed annual-mean, depth-averaged (above 1 km) zonal current speed field. There are multiple, finescale, zonally elongated features, with the strongest values in the Indo-Pacific sector, from 30° to 180°E (Fig. 3a). With the spatial smoothing, a dominant jet feature emerges (contours in Fig. 3b). Figure 3b presents the zonal current speed that exceeds 6 cm s−1 and the topography in the Southern Ocean. The area 80°–100°W, located to the west of the Drake Passage, is routinely monitored (e.g., Gille et al. 2012). However, the ACC jets are relatively weak in this area. Instead, we analyze the Indo–western Pacific Southern Ocean domain (90°–145°E; dashed box shown in Fig. 3b) because the jets are relatively strong, zonal, and persistent, and the bottom topography is relatively deep and less complex.

Fig. 3.

(a) The 1994–2007 average zonal current speed (cm s−1) in the Southern Ocean from the POP model. The zonal current speed is depth averaged above 1 km, but no horizontal smoothing is used. The region enclosed by the dashed box indicates the Indo–western Pacific Southern Ocean domain (38°–56°S, 90°–144°E) analyzed in this study. (b) The colors indicate bottom topography (m) and the contours show Gaussian boxcar smoothed zonal current speed that exceeds 6 (gray) and 12 (black), and areas that exceed 18 cm s−1 are hatched but because of resolution cannot be seen here but are visible in (c). (c) As in (b), but the study region is enlarged. Pink and green dashed boxes, respectively, indicate sector A (45°–55°S, 120°–144°E) and sector B (39°–49°S, 90°–110°E).

Fig. 3.

(a) The 1994–2007 average zonal current speed (cm s−1) in the Southern Ocean from the POP model. The zonal current speed is depth averaged above 1 km, but no horizontal smoothing is used. The region enclosed by the dashed box indicates the Indo–western Pacific Southern Ocean domain (38°–56°S, 90°–144°E) analyzed in this study. (b) The colors indicate bottom topography (m) and the contours show Gaussian boxcar smoothed zonal current speed that exceeds 6 (gray) and 12 (black), and areas that exceed 18 cm s−1 are hatched but because of resolution cannot be seen here but are visible in (c). (c) As in (b), but the study region is enlarged. Pink and green dashed boxes, respectively, indicate sector A (45°–55°S, 120°–144°E) and sector B (39°–49°S, 90°–110°E).

a. Structures of eddy fluxes: Do baroclinic eddies drive the ACC jets through the meridional convergence of zonal momentum flux?

Figure 3c shows that the jets are notably zonal between 120° and 144°E. We refer to this subsector as sector A (red dashed box). In the remainder of this subsection, we present results from the zonal mean–eddy diagnostic framework because in sector A the jet is close to being zonal. In addition, because we are interested in studying the structure of baroclinic eddy fluxes, we divide the eddy flux into transient and stationary components and interpret the transient component as representing a baroclinic eddy flux, whereas the stationary component represents meanders that arise from stationary forcings, such as topography. Again, following the notation of Peixoto and Oort (1992), time-mean and zonal-mean flux of can be written as

 
formula

with the total eddy flux being divided into transient and stationary components:

 
formula

where the overbar and prime denote the time mean (1994–2007) and departure therefrom. As was defined in section 2, the bracket and asterisk represent the zonal mean and the departure from the zonal mean.

Figures 4a–c, respectively, show the meridional convergence of the transient eddy momentum flux , the zonal convergence of the total zonal momentum flux , and the transient eddy buoyancy flux . To aid the interpretation, the mean position of the primary and secondary jet maxima (interjet minimum) is indicated with white dotted–dashed (dashed) lines in Fig. 4. At the latitude of the primary jet core at ~48.7°S, the zonal convergence of the total zonal momentum flux into this sector is much smaller (Fig. 4b) compared with the meridional convergence of the eddy momentum flux (Fig. 4a). Therefore, although our domain is not periodic, the effect of the unequal zonal momentum flux at the boundaries is negligible compared with that of These findings indicate that the meridional convergence of the transient eddy momentum flux drives the primary jet (~48.7°S) in this sector. (The secondary jet at ~50.9°S is driven by both the meridional and zonal momentum flux convergences, whereas the meridional flux convergence again dominates the forcing of the tertiary jet at ~53.2°S.) However, as (2) indicates, the eddy buoyancy flux can also drive ACC jets (Johnson and Bryden 1989). Unlike the eddy momentum flux for which the stationary eddy contribution is negligible (not shown), even in the sector A where the flow is relatively zonal, the stationary eddy component cannot be ignored for the buoyancy flux. Therefore, in Fig. 4d, we show the buoyancy contribution to (2) by the total buoyancy eddy flux . A comparison between Figs. 4a and 4d shows that at the primary jet core (~48.7°S), while the eddy momentum flux contribution [in (2)] is positive at most depths, the buoyancy flux acts to decelerate the jet at depths below ~600 m. Moreover, it does not have the jet scale. These findings suggest for sector A that the eddy buoyancy flux generally opposes the formation of the multiple jet structure.

Fig. 4.

Vertical cross sections of sector zonal-mean fluxes (colors) with zonal current speed (cm s−1; contours) for sector A: (a) −∂[]/∂y (10−6 cm s−2), (b) −∂[]/∂x (10−6 cm s−2), (c) [] (10−1 cm2 s−3), and (d) ∂[(f0/N2)υ*b*]/∂z (10−6 cm s−2), where the overbar and prime denote the time mean and departure therefrom and the bracket and asterisk denote the zonal mean and departure therefrom. For the zonal current speed, the lowest contour value is 2 cm s−1, and the contour interval is 4 cm s−1. White solid–dotted lines represent the latitudes of primary (~48.7°S) and secondary (~50.9°S) jet cores, and the dashed line indicates the latitude of interjet minimum (~50.1°S). Hatched areas represent topography. The vertical axis for depth ≤ 1500 m is expanded for visualization. (a),(b) Positive (negative) values indicate the convergence (divergence) of momentum flux. (c) Positive (negative) values indicate equatorward (poleward) buoyancy transport. The red dots in (c) denote the local maxima. (d) Positive (negative) values indicate eastward (westward) acceleration by eddy buoyancy flux [see (2)].

Fig. 4.

Vertical cross sections of sector zonal-mean fluxes (colors) with zonal current speed (cm s−1; contours) for sector A: (a) −∂[]/∂y (10−6 cm s−2), (b) −∂[]/∂x (10−6 cm s−2), (c) [] (10−1 cm2 s−3), and (d) ∂[(f0/N2)υ*b*]/∂z (10−6 cm s−2), where the overbar and prime denote the time mean and departure therefrom and the bracket and asterisk denote the zonal mean and departure therefrom. For the zonal current speed, the lowest contour value is 2 cm s−1, and the contour interval is 4 cm s−1. White solid–dotted lines represent the latitudes of primary (~48.7°S) and secondary (~50.9°S) jet cores, and the dashed line indicates the latitude of interjet minimum (~50.1°S). Hatched areas represent topography. The vertical axis for depth ≤ 1500 m is expanded for visualization. (a),(b) Positive (negative) values indicate the convergence (divergence) of momentum flux. (c) Positive (negative) values indicate equatorward (poleward) buoyancy transport. The red dots in (c) denote the local maxima. (d) Positive (negative) values indicate eastward (westward) acceleration by eddy buoyancy flux [see (2)].

As was hypothesized in the introduction, Fig. 4c shows that the poleward transient eddy buoyancy flux, which presumably arises from baroclinic instability, is large not only along the main jet core but also along the interjet minimum. In fact, the eddy buoyancy flux maximum occurs at the interjet minimum. As a result, the eddy buoyancy fluxes have a much broader meridional scale than does the eddy momentum flux convergence. This also raises the possibility that there may be interjet baroclinic waves embedded in this part of the ACC jets, as in the multiple zonal jets in two-layer models (Lee 1997; 2005). To investigate this possibility, we next examine characteristics of the eddy heat–buoyancy flux and eddy momentum flux convergence as a function of zonal wavelength, period, and phase speed.

b. Eddy flux cospectra

What wavelengths, periods, and phase speeds account for the eddy fluxes? To address this question, we follow the analysis method described by Hayashi (1971): for each latitude, cospectra of the eddy fluxes are calculated as a function of zonal wavenumber k and frequency f and then for a given zonal phase speed (c = f/k); the sum of the contributing zonal wavenumbers and corresponding frequencies is calculated. This procedure yields a power spectrum in latitude–phase speed space (Fig. 7). To facilitate interpretation of this latitude–phase speed diagram, we also show eddy flux cospectra in latitude–wavelength (Fig. 5) and latitude–period (Fig. 6) spaces. The relationship between the information presented in Figs. 57 will be explained in the forthcoming paragraphs. The spectral analysis was performed for each year, and the results were averaged to produce the 14-yr mean. In addition, for the fluxes presented in Fig. 7, a normalized Gaussian filter with a window of 0.5 cm s−1 was applied. The fluxes shown in Figs. 5 and 6 are unsmoothed. To construct Fig. 7, it is necessary to discretize phase speed. We chose the phase speed interval to be 0.1 cm s−1. We repeated calculations with other intervals (i.e., 0.02, 0.05, 0.12, and 0.15 cm s−1) and found that the results are qualitatively insensitive to the choice.

Fig. 5.

Cospectra of depth-averaged (5 m to 6 km) transient eddy fluxes in latitude–wavelength (km) space for sector A: (a) −∂[]/∂y (10−6 cm s−2) and (b) [] (10−2 cm2 s−3). Black solid–dashed lines represent the latitudes of primary (~48.7°S) and secondary (~50.9°S) jet cores, and the dashed line indicates the latitude of the interjet minimum (~50.1°S). At latitudes within ±0.5° away from the jet center–interjet minimum, the cross × marks the averaged wavelength of eddies that contribute the most, and vertical solid lines indicate the averaged e-folding scale.

Fig. 5.

Cospectra of depth-averaged (5 m to 6 km) transient eddy fluxes in latitude–wavelength (km) space for sector A: (a) −∂[]/∂y (10−6 cm s−2) and (b) [] (10−2 cm2 s−3). Black solid–dashed lines represent the latitudes of primary (~48.7°S) and secondary (~50.9°S) jet cores, and the dashed line indicates the latitude of the interjet minimum (~50.1°S). At latitudes within ±0.5° away from the jet center–interjet minimum, the cross × marks the averaged wavelength of eddies that contribute the most, and vertical solid lines indicate the averaged e-folding scale.

Fig. 6.

As in Fig. 5, but for cospectra of transient eddy fluxes in latitude–period (days) space.

Fig. 6.

As in Fig. 5, but for cospectra of transient eddy fluxes in latitude–period (days) space.

Fig. 7.

As in Fig. 6, but for cospectra of transient eddy fluxes in latitude–phase speed (cm s−1) space. Pink (green) line indicates the sector zonal-mean zonal current speed at 918 (2625) m and shading denotes ±1 standard deviation of the zonal current speed. At the latitudes within ±0.5° away from the jet center and interjet minimum, the two crosses × mark the averaged phase speed of eddies that contribute the most, and vertical solid lines indicate the range that has the peak contribution that is consistent with the ranges of wavelength and the period analyzed with Figs. 5 and 6. The open circle (○) in (b) marks the secondary local minimum near the primary jet core (~48.7°S), which is attributed to the eddies with the same phase speed as the eddies shown in (a).

Fig. 7.

As in Fig. 6, but for cospectra of transient eddy fluxes in latitude–phase speed (cm s−1) space. Pink (green) line indicates the sector zonal-mean zonal current speed at 918 (2625) m and shading denotes ±1 standard deviation of the zonal current speed. At the latitudes within ±0.5° away from the jet center and interjet minimum, the two crosses × mark the averaged phase speed of eddies that contribute the most, and vertical solid lines indicate the range that has the peak contribution that is consistent with the ranges of wavelength and the period analyzed with Figs. 5 and 6. The open circle (○) in (b) marks the secondary local minimum near the primary jet core (~48.7°S), which is attributed to the eddies with the same phase speed as the eddies shown in (a).

Figure 5a shows that, in latitude–wavelength space, the cospectra is contributed by eddies with a broad range of zonal wavelengths. Close to the primary jet center (~48.7°S), the peak contribution comes from eddies with a zonal wavelength of 285 km. As a method of quantifying the peak range, we calculate the e-folding wavelength: At latitudes within ±0.5° away from the jet center, the wavenumber with the largest contribution is identified (indicated by × in the figure) and then using the peak value and the peak wavenumber, an e-folding wavenumber is calculated. The e-folding range (203–356 km) is indicated by the two vertical lines. Applying the same procedure, we find that at the interjet region (~50.1°S), larger-scale eddies of 237–475 km (centered at 356 km) are the main contributors to the jet deceleration. A similar scale difference between the jet center and interjet can also be seen in the spectra (Figs. 5b). At the primary jet center (~48.7°S), the 203–303-km (centered at 237 km) eddies contribute the most, while at the interjet region (~50.1°S), larger-scale eddies of 274–475 km (centered at 356 km) are the main contributors.

Figure 6 shows the and cospectra in latitude–period space. Following the same procedure as before, we identify the peak frequency and the corresponding e-folding range, and they are again indicated by × and two vertical lines. It shows that, for (Fig. 6a), the e-folding ranges are 66–365 days (centered at 182.5 days) at the primary jet center (~48.7°S) and 114–365 days at the interjet region (~50.1°S). For the spectra (Fig. 6b), the e-folding ranges are 69–365 days (centered at 182.5 days) at the primary jet center (~48.7°S) and 122–365 days at the interjet region (~50.1°S).

The and cospectra are shown in latitude–phase speed space (Fig. 7). The phase speed range that has the peak contribution is consistent with the ranges of wavelength and period analyzed in Figs. 5 and 6; assuming that the larger e-folding length scale corresponds to the longer e-folding period, and vice versa, we obtain a range of phase speeds. For (Fig. 7a), the resulting range, indicated by the two vertical lines, embodies the phase speed of maximum power (indicated by ×), evincing that the combinations of wavelengths and periods yield a range of fast wave phase speed at the primary jet center and slow wave phase speed at the interjet region. The main contribution to the jet acceleration (at ~48.7°S) is from eddies with phase speed of 0.65–6.21 cm s−1 (centered at 4.0 cm s−1), whereas 0.75–4.82 cm s−1 (centered at 2.75 cm s−1) eddies are responsible for maintaining the interjet minimum (at ~50.1°S). This range of phase speeds is consistent with the estimates from an eddy-tracking algorithm (Griesel et al. 2015).

The sector zonal-mean zonal current speed at 918 and 2625 m are superimposed on the diagram. The dotted area shows one standard deviation of the zonal current speed. For the primary jet, the standard deviation at 918 m is very small, indicating that the jet at that level is persistent. Although not shown, similar persistence is present at depths between 5 and 1875 m. At lower levels, where the jet is weak (Fig. 4), the zonal currents are less persistent, as evidenced by the greater standard deviation at 2625 m. For the remaining two jets (at 50.9° and 53.2°S) where the eddy–zonal mean flow relationship is weak or absent (refer to the above discussion pertaining to Fig. 4), the standard deviation is much greater even at the 918-m depth, suggesting that while the meridional convergence of eddy momentum flux may not be the only driver of the jet, it plays an important role for the jet persistence (Lee 1997; Yoo and Lee 2010). The jet persistence may be aided by critical layer dynamics. If the momentum flux divergence is caused by wave absorption at the critical latitudes (Randel and Held 1991; Lee 1997), from this diagram, it can be inferred that the levels where the fast wave propagation occurs are mostly between the depths of 918 and 2625 m. This is because the momentum flux divergence by the eddies (at 0.75–4.82 cm s−1) roughly coincides with the zonal current speed at these depths (see Fig. 7a), consistent with the steering level depth as determined from linear stability analysis in the same model simulation (Griesel et al. 2015). Although sector A takes up only 15% of the ACC, this is also consistent with the finding by Abernathey et al. (2010) that the steering level is at about 1-km depth.

The cospectra (Fig. 7b) reveal that at the main jet center (~48.7°S), the poleward fluxes are generated by eddies with phase speeds of 0.65–5.09 cm s−1 primarily centered at 2.15 cm s−1 and secondarily at 4.0 cm s−1. Therefore, the phase speed separation is less clear. However, consistent with the maximum in the eddy momentum flux convergence at the primary jet core (Fig. 7a), at the same phase speed, there is a secondary peak in the eddy buoyancy flux (indicated by ○).

Returning to Fig. 7a, the largest contribution to the eddy momentum flux divergence at the interjet region (~50.1°S) comes from the slow waves. Lee (1997) showed with linear stability analysis that there exists a baroclinically unstable normal mode (as evidenced by a poleward eddy buoyancy flux) with peak amplitudes at interjet regions. Since the ambient zonal-mean current speed is relatively low (hence interjet), the interjet mode has equally low zonal phase speeds. The interjet eddies in Fig. 7 show characteristics consistent with the properties of the interjet normal mode. Therefore, at least for sector A, we conclude that interjet disturbances exist and that they can help explain why the buoyancy flux structures seen in Fig. 4c are much broader than the jet scale.

c. Jet-scale overturning circulations

Given the evidence that the above eddy–mean flow relation resembles that of the atmospheric polar front jet, we further explore the apparent atmosphere–ocean analog by examining vertical motions. Figure 8a presents the horizontal distribution of a smoothed vertical velocity (color) and zonal current speed (contours) in the Indo–western Pacific Southern Ocean (90°–145°E). In the western end of the Indo–western Pacific domain, the jets are less zonal but are still strong. This region is referred to as sector B (90°–110°E; green dashed box). It can be seen that a band of sinking motion occurs following the equatorward flank of the primary jet, and rising motion is observed on the poleward flank of the jets in both sectors A and B. Figure 8b shows that transient eddy momentum flux convergence coincides with the jets not only in sector A but also in sector B. Therefore, although it is challenging to apply the zonal mean–eddy diagnostics to the flow in sector B, the eddy momentum flux convergence coincides with the jets and also with the jet-scale vertical motions. As will be described later in this subsection, more quantitative diagnostic results are presented for sector A (Fig. 10).

Fig. 8.

Horizontal plot of depth-averaged (above 1 km) Gaussian boxcar–smoothed (a) vertical velocity (10−4 cm s−1; colors) and zonal current speed (cm s−1; contours) and (b) transient eddy momentum flux convergence, −∂/∂y (10−6 cm s−2), in the Indo–western Pacific sector of the Southern Ocean (90°–145°E). Black contours show the smoothed zonal current speed that exceeds 6 (thin), 12 (thick), and 18 cm s−1 (hatched). Pink (green) box indicates the domain of sector A (B).

Fig. 8.

Horizontal plot of depth-averaged (above 1 km) Gaussian boxcar–smoothed (a) vertical velocity (10−4 cm s−1; colors) and zonal current speed (cm s−1; contours) and (b) transient eddy momentum flux convergence, −∂/∂y (10−6 cm s−2), in the Indo–western Pacific sector of the Southern Ocean (90°–145°E). Black contours show the smoothed zonal current speed that exceeds 6 (thin), 12 (thick), and 18 cm s−1 (hatched). Pink (green) box indicates the domain of sector A (B).

Figure 9a shows that jet-scale overturning circulations (JSOC) are indeed present in the sector A. Associated with the primary jet (~48.7°S), there is a thermally indirect overturning circulation with sinking (rising) motion on the equatorward (poleward) flank of the jet. A similar overturning circulation is also present associated with the secondary jet (~50.9°S) of sector A (Fig. 9a) and the primary jet (~44.3°S) of sector B (Fig. 9c). Analogous to the atmospheric circulation in isentropic coordinates (Fig. 2), the oceanic circulation in potential density coordinates can illustrate the net eddy effects on the mean meridional circulation and hence closely resemble the corresponding TEM. Similar to the momentum-driven midlatitude dip in Fig. 2b, and as was hypothesized for the idealized multiple jets (Fig. 2c), our oceanic JSOC is evident in the potential density–latitude space (Figs. 9b,d).

Fig. 9.

Vertical cross sections of zonal current velocity (cm s−1; colors), meridional velocity (cm s−1; vectors), and vertical velocities multiplied by L/D, where L is the meridional width and D is the depth of the domain (cm s−1; vectors) for (left) sector A and (right) sector B in (a),(c) TEM driven by transient eddies and (b),(d) isopycnal coordinates, respectively. Green contours in (a) and (c) indicate the potential density (kg m−3) surface. Hatched areas represent missing values.

Fig. 9.

Vertical cross sections of zonal current velocity (cm s−1; colors), meridional velocity (cm s−1; vectors), and vertical velocities multiplied by L/D, where L is the meridional width and D is the depth of the domain (cm s−1; vectors) for (left) sector A and (right) sector B in (a),(c) TEM driven by transient eddies and (b),(d) isopycnal coordinates, respectively. Green contours in (a) and (c) indicate the potential density (kg m−3) surface. Hatched areas represent missing values.

The individual momentum and buoyancy flux contributions to the rhs of (5) indicate that the JSOC is driven by the eddy momentum flux. Figure 10a shows that at the primary jet latitudes of sector A, the momentum flux contribution [term A in (5)] is negative throughout the entire depths. As was discussed in section 2, negative forcing drives a clockwise circulation, the direction of the JSOCs that hug the jets. At the latitudes of the interjet, the forcing is positive that drives a counterclockwise circulation. Again this is consistent with the direction of the JSOCs hugging the interjet region. On the other hand, the buoyancy flux contribution (Fig. 10b) shows a much broader meridional scale encompassing both the jets and interjet regions. This structure clearly cannot account for the JSOC. To this end, we note that the stationary component of the momentum flux [term A in (5)] is negligible, but it makes a substantial contribution to the buoyancy flux (term B). This means that the steady meander cannot be ignored in the buoyancy flux contribution. However, Fig. 10b shows that the meander is not responsible for driving the JSOC.

Fig. 10.

Eddy (a) momentum [−f0(∂/∂z)∂[u*υ*]/∂y] and (b) buoyancy [f02[(f0/N2)υ*b*]/∂z2] contributions (10−14 s−3) to the TEM circulation [see (5)]. Positive (negative) values drive counterclockwise (clockwise) circulations. Contours and white lines are same as Fig. 4.

Fig. 10.

Eddy (a) momentum [−f0(∂/∂z)∂[u*υ*]/∂y] and (b) buoyancy [f02[(f0/N2)υ*b*]/∂z2] contributions (10−14 s−3) to the TEM circulation [see (5)]. Positive (negative) values drive counterclockwise (clockwise) circulations. Contours and white lines are same as Fig. 4.

The foregoing analyses suggest that the JSOCs are driven by eddy momentum flux convergence. Nevertheless, since Ekman pumping is a critical player in the ocean, we examine if the sinking motions along the equatorward flank of the ACC jets are caused by Ekman downwelling. Figures 11a and 11b, respectively, show the model vertical velocities at various depths (green lines) and Ekman vertical velocities (red line) for sector A and B. In both sectors, within the latitudinal bands of the jets (red for the primary jets and gray for the secondary jet), the Ekman vertical velocities are often much weaker and their meridional structure shares little resemblance to the rapidly varying JSOC pattern. This finding indicates that the JSOCs cannot be attributed to Ekman downwelling.

Fig. 11.

Comparisons between vertical velocity (10−4 cm s−1; green lines) at various depths and Ekman vertical velocity (10−4 cm s−1; red line) for (a) sector A and (b) sector B. The Ekman vertical velocities are calculated from the POP. The zonal current speed (cm s−1; blue line) at 918 m is overlaid to show the location of the jets. Pink (gray) shading denotes the latitude band of the primary (secondary) jet.

Fig. 11.

Comparisons between vertical velocity (10−4 cm s−1; green lines) at various depths and Ekman vertical velocity (10−4 cm s−1; red line) for (a) sector A and (b) sector B. The Ekman vertical velocities are calculated from the POP. The zonal current speed (cm s−1; blue line) at 918 m is overlaid to show the location of the jets. Pink (gray) shading denotes the latitude band of the primary (secondary) jet.

5. Discussion and conclusions

We examined POP-simulated ACC jets in the Indo–western Pacific Southern Ocean (90°–145°E) where the jets are nearly zonal, and the bottom topographic heights are relatively low. In this region, transient eddy momentum flux convergence occurs at the latitude of the primary jet core, indicating that the jet is driven at least in part by mesoscale eddies. This finding complements earlier studies of local regions of the Southern Ocean (Hughes and Ash 2001; A. Klocker et al. 2016, unpublished manuscript). Compared with the eddy momentum flux, the poleward eddy buoyancy flux displays a broader meridional scale, and our spectral analysis offers a plausible explanation for this scale difference. Unlike for the atmosphere, the eddy length scale in the Southern Ocean is much smaller than its wind-driven baroclinic zone. For this reason, there are multiple eddy-driven jets within a single baroclinic zone. Consistent with the findings from idealized modeling studies (Lee 1997, 2005), our analysis indicates that there are baroclinic eddies not only at the latitude of the jets, but also in between the jets. At the same time, by exporting zonal momentum from the interjet region, these interjet baroclinic eddies also help to maintain the zonal jets. The analysis here shows that a broad band of buoyancy flux can occur even when the eddy momentum flux drives much smaller-scale multiple zonal jets.

Our findings are from a small sector and hence cannot be generalized for the entire ACC. For example, in the region of the ACC where topography generates substantial standing meanders, locally enhanced eddy buoyancy flux and eddy kinetic energy (oceanic storm tracks) can occur downstream of topography (Abernathey and Cessi 2014; Bischoff and Thompson 2014; Chapman et al. 2015). Thompson and Naveira Garabato (2014) concluded that the enhancement of eddy kinetic energy within the standing meanders is related to the increase in cross-stream buoyancy flux and enhanced mixing by mesoscale eddies. A. Klocker et al. (2016, unpublished manuscript) analyzed eddy momentum fluxes in regions downstream of Kerguelen Plateau and concluded that the control of baroclinic instability by the barotropic component of the flow vanishes downstream of topographic features, also leading to barotropic instability in our region; the momentum flux of the eddies that grow in the jet lean with the shear (barotropic stability), consistent with the geometric interpretation of eddy orientation as put forward in, for example, Marshall et al. (2012), sharpening the jet, while the interjet eddies also help maintain them (Lee 1997).

We also found evidence that these eddy-driven jets are associated with corresponding secondary, jet-scale overturning circulation. Coined here as jet-scale overturning circulation (JSOC), the circulation is composed of rising motion on the poleward and sinking motion on the equatorward flank of the jet. Analogous to the eddy momentum flux–driven portion of the atmospheric Ferrel cell that imprints itself in the TEM circulation, these JSOCs are discernible in potential density coordinates. Again, since our analysis is confined to a small region, the finding here cannot be generalized for the rest of the ACC. Our diagnostics of the eddy forcing of the TEM circulation confirms that it is the eddy momentum flux that drives the JSOCs. Thompson and Naveira Garabato (2014) also examined TEM eddy forcing but with a focus on regions where topography plays a major role. In addition, because they averaged over a meridional distance that encompasses multiple jets, the effect of the eddy momentum flux, even if it exists, cannot be seen in their analysis. Because the meridional extent of the ACC jet meander is much greater than the meridional scale of the individual jets, a zonal average over the entire ACC would obscure the small-scale overturning circulations. As Fig. 9 shows, the JSOC implies diapycnal transport in the water column in the interior. Diapycnal mixing in the POP simulation is associated with the subgrid-scale parameterizations [K-profile parameterization (KPP) and horizontal biharmonic diffusion] and may include spurious effects. However, there is observational evidence that diapycnal mixing in the Southern Ocean is intense and widespread (e.g., Naveira-Garabato et al. 2004; Wu et al. 2011). Therefore, for a future study, it would be worthwhile to investigate the relation between JSOCs and diapycnal mixing in more detail. In addition, Chapman and Morrow (2014) showed that near the Pacific–Antarctic Rise the ocean flow exhibits large temporal and spatial variability. Since this region partially overlaps with our study region, it would also be of interest to explore the sensitivity of our findings to the variability.

Acknowledgments

We thank Mat Maltrud for providing the tripole POP setup and grid and initial conditions. Many thanks to Elena Yulaeva for setting up the runs and providing data and to Julie McClean for suggesting this POP run and for initiating the collaboration between SL–QL and AG. SL and QL also appreciate comments by Cory Baggett and Steven Feldstein on the manuscript. QL and SL were supported by the National Science Foundation under Grant ATM-1139970. SL was also supported by Seoul National University, the Republic of Korea, through the Next Generation Distinguished Scholars Award. AG was supported by the Collaborative Research Centre TRR 181 on Energy Transfer in Atmosphere and Ocean funded by the German Research Foundation. An allocation of advanced computing resources OCE-0960914 provided by the National Science Foundation was instrumental in performing this research. The computations were performed on Kraken at the National Institute for Computational Sciences (http://www.nics.tennessee.edu/).

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Footnotes

1

There is no known precise rule that can predict the direction of baroclinically unstable eddy momentum flux. The direction not only depends on the stability of the background flow (Marshall et al. 2012; Maddison and Marshall 2013; Waterman and Hoskins 2013), but also on the shear and scale of the background flow (Held and Andrews 1983) and on the presence of critical latitudes (Yoo and Lee 2010).