What Causes the Subsurface Velocity Maximum of the East Australian Current?

Peter R. Oke aCSIRO Environment, Hobart, Tasmania, Australia

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Tatiana Rykova aCSIRO Environment, Hobart, Tasmania, Australia

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Bernadette M. Sloyan aCSIRO Environment, Hobart, Tasmania, Australia

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Ken R. Ridgway aCSIRO Environment, Hobart, Tasmania, Australia

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Abstract

The East Australian Current (EAC) system includes a poleward jet that flows adjacent to the continental shelf, a southward and eastward extension, and a complex eddy field. The EAC jet is often observed to be subsurface intensified. Here, we explain that there are two factors that cause the EAC to develop a subsurface maximum. First, the EAC flows as a narrow current, carrying low-density water from the Coral Sea into the denser waters of the Tasman Sea. This results in horizontal density gradients with a different sign on either side of the jet, negative onshore and positive offshore. According to the thermal wind relation, this produces vertical gradients in southward current that are surface intensified onshore and subsurface intensified offshore. Second, we show that the winds over the shelf are mostly downwelling favorable, drawing the surface EAC waters onshore. This aligns the region of positive horizontal density gradients with the EAC core, producing a subsurface velocity maximum. The presence of a subsurface maximum may produce baroclinic instabilities that play a role in eddy formation and EAC separation from the coast.

Significance Statement

Observations of the East Australian Current (EAC) show that the strongest currents are often below the surface at about 100-m depth. Two factors cause this subsurface maximum. First, because the EAC is a narrow jet, carrying warm water southward from the Coral Sea, the density gradient across the jet changes sign, causing surface-intensified currents onshore and subsurface-intensified currents offshore. Second, the wind field over the shelf often pulls the shallow waters shoreward, shifting the waters that cause subsurface intensification to align with the center of the jet, resulting in a subsurface maximum of the EAC. This process may be responsible for the generation of eddies in the Tasman Sea.

For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Peter R. Oke, peter.oke@csiro.au

Abstract

The East Australian Current (EAC) system includes a poleward jet that flows adjacent to the continental shelf, a southward and eastward extension, and a complex eddy field. The EAC jet is often observed to be subsurface intensified. Here, we explain that there are two factors that cause the EAC to develop a subsurface maximum. First, the EAC flows as a narrow current, carrying low-density water from the Coral Sea into the denser waters of the Tasman Sea. This results in horizontal density gradients with a different sign on either side of the jet, negative onshore and positive offshore. According to the thermal wind relation, this produces vertical gradients in southward current that are surface intensified onshore and subsurface intensified offshore. Second, we show that the winds over the shelf are mostly downwelling favorable, drawing the surface EAC waters onshore. This aligns the region of positive horizontal density gradients with the EAC core, producing a subsurface velocity maximum. The presence of a subsurface maximum may produce baroclinic instabilities that play a role in eddy formation and EAC separation from the coast.

Significance Statement

Observations of the East Australian Current (EAC) show that the strongest currents are often below the surface at about 100-m depth. Two factors cause this subsurface maximum. First, because the EAC is a narrow jet, carrying warm water southward from the Coral Sea, the density gradient across the jet changes sign, causing surface-intensified currents onshore and subsurface-intensified currents offshore. Second, the wind field over the shelf often pulls the shallow waters shoreward, shifting the waters that cause subsurface intensification to align with the center of the jet, resulting in a subsurface maximum of the EAC. This process may be responsible for the generation of eddies in the Tasman Sea.

For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Peter R. Oke, peter.oke@csiro.au

1. Introduction

The East Australian Current (EAC) is the southward-flowing western boundary current of the South Pacific Ocean. The EAC jet normally flows as a continuous, strong, narrow boundary current adjacent to the continental shelf between about 18° and 32.5°S. The path of the jet is often evident in satellite sea surface temperature (e.g., https://oceancurrent.aodn.org.au/), as a narrow tongue of warm water flowing from the Coral Sea into the cooler waters of the Tasman Sea (e.g., Fig. 1). At 32.5°S, the EAC often separates from the coast and flows either eastward, toward New Zealand along its eastward extension (e.g., Fig. 1b; Godfrey et al. 1980b; Oke et al. 2019a,b), or southward along its southern extension (e.g., Fig. 1a), sometimes flowing around Tasmania and toward the Indian Ocean, along a path that is often referred to as the Tasman Leakage (e.g., Ridgway and Dunn 2003; van Sebille et al. 2012). The EAC system is also characterized by a complex eddy field after separation (e.g., Suthers et al. 2011; Everett et al. 2012; Rykova et al. 2017). The EAC influences the transport of heat (e.g., Sloyan et al. 2016), freshwater (e.g., Rykova and Oke 2015), and marine biota (e.g., Baird et al. 2008; Suthers et al. 2011).

Fig. 1.
Fig. 1.

Example maps of 6-day composite SST image, using night-only SST, produced by the Bureau of Meteorology for the Integrated Marine Observing System (IMOS) on a 0.09° grid for (a) 23 Sep 2016 and (b) 2 Feb 2020 (accessed on 1 Dec 2023 from https://oceancurrent.aodn.org.au/).

Citation: Journal of Physical Oceanography 54, 2; 10.1175/JPO-D-23-0128.1

Many elements of the EAC system have been studied using both observations and models. Early studies provided descriptions of the EAC system, based on sparse observations, with insights that proved to be remarkably accurate (e.g., Boland and Hamon 1970; Nilsson and Cresswell 1980; Boland and Church 1981; Cresswell 1982). More contemporary studies exploited models and more complete observing systems to provide refined descriptions of the EAC system (e.g., Marchesiello and Middleton 2000; Ridgway and Dunn 2003; Kerry et al. 2016). These studies have focused on EAC eddies (e.g., Oke and Griffin 2011; Everett et al. 2012; Macdonald et al. 2013; Rykova and Oke 2015, 2022; Rykova 2023), EAC separation (e.g., Godfrey et al. 1980b; Marchesiello and Middleton 2000; Oke and Middleton 2001; Bull et al. 2017), the path of the EAC after separation (e.g., Tilburg et al. 2001; Hill et al. 2011; Cetina-Heredia et al. 2014; Pilo et al. 2015; Ypma et al. 2016), EAC volume transport (e.g., Mata et al. 2006; Sloyan et al. 2016; Zilberman et al. 2018), and characteristics of the horizontal structure of the EAC jet at the surface (e.g., Archer et al. 2017). Surprisingly few studies have investigated the subsurface structure of the EAC jet, with Kerry and Roughan (2020) a notable exception. Most studies that mention the jet stopped short of describing the subsurface structure, often presenting observations or model results, and analyzing some other aspect of the system, such as the variability of volume transport (e.g., Sloyan et al. 2016), or the impacts on upwelling (e.g., Cresswell et al. 1996; Oke and Middleton 2000; Roughan et al. 2003; Cresswell et al. 2017). The modeling study of Kerry and Roughan (2020) provides the most comprehensive analysis of the subsurface structure of the EAC. However, their analysis did not include a description of the elements of the EAC that are explored here, including the subsurface maximum, perhaps because it was not a prominent feature of their model results. Many other modeling studies also appear to fail to reproduce the subsurface maximum in the EAC jet (e.g., Marchesiello et al. 2000; Oke and Middleton 2000, 2001; Wilkin and Zhang 2007; Wijeratne et al. 2018), while others reproduce it, but do not fully describe or explain it (e.g., Gibbs et al. 2000; Roughan et al. 2003). Here, we investigate the EAC jet and provide a simple dynamical explanation for the subsurface maximum that has been observed on many occasions (Cresswell et al. 1996; Mata et al. 2000; Roughan and Middleton 2002; Sloyan et al. 2016).

The first evidence of a subsurface maximum in the EAC is reported by Hamon (1961, his Fig. 2), showing a profile of steric height between adjacent hydrographic profiles with a subsurface maximum at 50-m depth. In a subsequent early study, Hamon (1965) seems to have looked for evidence of a subsurface maximum, reporting that “there’s no evidence of a subsurface maximum in the current.” Similarly, Mata et al. (2000) report that some sections of velocity include a subsurface maximum, while others do not. A stocktake of published velocity sections from shipboard acoustic Doppler current profiler (ADCP) surveys that transit the EAC jet also reveal a mix of sections showing the EAC with a surface-intensified and subsurface intensified jet (e.g., Roughan and Middleton 2002; Oke et al. 2003). This survey indicates that the EAC core, here defined as where the southward currents associated with the EAC jet are strongest, is sometimes surface intensified and sometimes subsurface intensified.

This paper is organized as follows: section 2 summarizes past observations of the EAC with a subsurface maximum, and section 3 describes the model that we use here to understand when and where the EAC jet includes a subsurface maximum. The results are presented in section 4, followed by an analysis of results in section 5 and a discussion in section 6. We summarize our conclusions in section 7.

2. Observations

A selection of observations of the EAC jet with a subsurface maximum is reproduced in Fig. 2. This includes velocity sections at various latitudes off eastern Australia for different times using shipboard and moored ADCP observations. The northernmost observation of the EAC with a subsurface maximum is at 18°S (Ridgway et al. 2018, their Fig. 3, not shown here), based on observations with gliders.

Fig. 2.
Fig. 2.

Observed cross-shore sections of southward velocity (m s−1), showing the EAC jet at various latitudes off eastern Australia, including observations based on (a) a deep-water mooring array at 27°S [adapted from Sloyan et al. (2016), their Fig. 5], along with shipboard ADCP measurements at (b)–(d) 28.7°S and (e),(f) 29.2°S [adapted from Cresswell et al. (2017), their Fig. 9]; (g) 30°S and (h) 31°S [adapted from Roughan and Middleton (2002), their Fig. 5]; and (i)–(k) 30°S [adapted from Mata et al. (2000), showing the ADCP sections in their Fig. 7].

Citation: Journal of Physical Oceanography 54, 2; 10.1175/JPO-D-23-0128.1

Although Hamon (1961) presented the first observational evidence of a subsurface maximum in the EAC jet, he did not explicitly describe the feature. Godfrey et al. (1980a) presented a velocity section with a subsurface maximum, derived from surface current estimates and subsurface temperatures. The first direct measurements of a subsurface-intensified EAC jet were presented by Cresswell et al. (1996, their Fig. 3), using shipboard ADCP observations at 29°S using the same data that are reproduced here in Fig. 2f, and republished by Cresswell et al. (2017, their Fig. 9). These synoptic ADCP sections are supported by Sloyan et al. (2016), who observed a subsurface jet in an 18-month mean section at 27°S from a mooring array. In all data presented in Fig. 2, the core of the EAC jet has a subsurface maximum. To balance this, we note that other observations of the EAC include evidence of a surface-intensified jet (e.g., Mata et al. 2000; Roughan and Middleton 2002; Oke et al. 2003).

Time series of monthly-averaged southward velocities from moored ADCP observations are presented in Fig. 3, showing data from the top 350 m that are described by Sloyan et al. (2021). All time series show a subsurface-intensified southward current for most of the record. Data in Figs. 3a and 3b are near the core of the EAC jet, and show the southward maximum often between 50- and 150-m depth. Data in Figs. 3c and 3d are farther offshore, sampling the seaward flank of the EAC, and show the southward maximum often around 200 m and sometimes deeper.

Fig. 3.
Fig. 3.

Time series of meridional velocity (negative is southward; blue) observed at about 27.3°S from moorings (a) EAC500, (b) EAC2000, (c) EAC3200, and (d) EAC4200, from the CSIRO/IMOS EAC Deep Water array. The numbers ending each mooring name denote the water depth of each mooring. The depth of the southward maximum velocity is denoted by the black line. Year labels are for the middle of each year.

Citation: Journal of Physical Oceanography 54, 2; 10.1175/JPO-D-23-0128.1

Most of the observed velocity sections referred to above and elsewhere include three features that are of particular interest for this study. First, all sections show a subsurface maximum for the EAC core. In each case, the maximum is between 50- and 200-m depth. Second, in many sections, most clearly Figs. 2b, 2f, 2i, and 2j, the structure of the subsurface jet leans in toward the shelf, with the vertical axis that is slanted with depth. Third, most velocity sections that extend offshore include a broad bulge on the seaward flank of the EAC jet, with a deepening subsurface maximum offshore.

The bulge on the seaward flank of the EAC is the most subtle feature considered here. The bulge in the velocity sections occurs because the vertical profile of the southward velocity includes a subsurface maximum, and the depth of the subsurface maximum tends to increase offshore. In Fig. 2a, the core is at about 50-m depth. At about 153.3°E the strongest current is at about 75-m depth, and at 154.6°E the strongest current is about at 150-m depth. Similarly in Fig. 2f, the core is at 100-m depth; and at 154.9°E, the strongest current is at 150-m depth. The 1 m s−1 velocity contour in Fig. 2e tracks seaward from the surface to about 150-m depth, highlighting this bulge. Furthermore, the average depth of the maximum southward velocity in the moored ADCP data (Fig. 3) increases offshore, from 71 m at EAC500, 73 m at EAC2000, 89 m at EAC3200, and 106 m at EAC4200. This deepening of the seaward flank of the EAC is also clear in the sections of absolute geostrophic velocity, presented by Mata et al. (2000, their Fig. 7), and in many other geostrophic velocity sections of the EAC jet (e.g., Kessler and Cravatte 2013, their Fig. 13a)., including sections produced using Argo and expendable bathythermograph data (e.g., Zilberman et al. 2018, their Figs. 5 and 7).

Each feature of the EAC jet described above is evident in previously published observations. Despite these observations, no dynamical explanation has yet been provided for any of these features of the EAC jet, including the subsurface-intensified EAC jet, the leaning in of the jet, and the deep, seaward bulge. We provide an explanation for all of these features in this study.

3. Model

To better understand the subsurface structure of the EAC jet, we use monthly-averaged fields of temperature, salinity, and velocity from the Ocean Forecasting Australia Model, version 3 (OFAM3; Oke et al. 2013a). OFAM is a near-global, eddy-resolving model with a horizontal grid spacing of 1/10° and 51 vertical levels with 5-m spacing near the surface, 10-m spacing at 200-m depth, and coarser spacing below that. Here, we use data from the last 11 years (2011–21) of a 54-yr run, including monthly-mean fields, averaged over 11 years to represent the model’s seasonal cycle. OFAM3 is forced using 3-hourly fields from ERA-Interim (Dee et al. 2011). The horizontal resolution of fields from ERA-Interim is approximately 79 km. Fields from ERA-Interim are interpolated to the 1/10° resolution OFAM3 grid, and wind stress is calculated every time step, using a constant drag coefficient, and using the difference between the 10-m winds and the surface ocean currents from the model using the bulk formula described by Large and Yeager (2009). This produces wind stress with sub-79-km scales, due to the higher resolution in the model. We might regard the derived surface fluxes as a downscaled version of the ERA-Interim fluxes that takes into account ocean currents. The model is also forced with realistic surface heat and freshwater fluxes, as described by Oke et al. (2013a), along with all other aspects of the model configuration. Results from OFAM3 have been used for several previous studies of the EAC (e.g., Rykova and Oke 2015; Pilo et al. 2015). Although OFAM3 is often run with data assimilation (e.g., Schiller et al. 2008; Oke et al. 2013b; Chamberlain et al. 2021), the model fields used here are from a free model run, with no data assimilation.

The focus of this study is to determine the dynamics that explain the EAC jet subsurface velocity maximum and offshore slanted velocity structure. Ordinarily, a model with 1/10° resolution would not be considered a suitable choice for such a study. Similarly, the coarse resolution of the surface forcing fields applied here would not usually be regarded as sufficient for studies of continental shelf processes. However, we show here that the features of interest, including specific characteristics of the EAC’s subsurface structure, are surprisingly well reproduced by OFAM3. This indicates that despite the relatively coarse resolution of the model and the coarse resolution of the surface forcing fields, the key dynamical processes are included in this model. This finding is itself of value for this study and helps identify the simplest explanation for the features of interest (consistent with Occam’s razor), indicating that we need not pursue a model with greater complexity to explain the underlying dynamics.

4. Results

Figure 4 shows the seasonal cycle of potential density (referenced to the surface), averaged over the top 100 m (Figs. 4a–d) and between 325- and 425-m depth (Figs. 4e–h), based on an 11-yr mean from OFAM3. Throughout the year, the EAC is evident near the surface as a tongue of low-density water (Figs. 4a–d), with denser water shoreward and seaward of the jet. OFAM3 correctly simulates the EAC jet as a narrow current, carrying the light waters from the Coral Sea into denser waters of the Tasman Sea. An important characteristic of the EAC over these shallow waters is that the zonal density gradient, ∂ρ/∂x, where ρ is potential density referenced to the surface and x is the zonal direction, has a different sign on either side of the jet. Moreover, the amplitude of the ∂ρ/∂x is greater on the shoreward side of the jet than on the seaward side, evident from the more closely spaced contours on the shoreward side of the low-density tongue (Figs. 4a–d).

Fig. 4.
Fig. 4.

Seasonal cycle of potential density, ρ, averaged between (a)–(d) the surface and 100-m depth and (e)–(h) between 325- and 425-m depth, with contour intervals of 0.1 kg m−3, showing fields averaged for Austral summer (December–February; labeled DJF), autumn (March–May; MAM), winter (June–August; JJA), and spring (September–November; SON), from OFAM3.

Citation: Journal of Physical Oceanography 54, 2; 10.1175/JPO-D-23-0128.1

The potential density at greater depths does not include the same narrow density minimum aligned with the EAC (Figs. 4e–h). Rather, the seasonal cycle of the depth-averaged potential density between 325- and 425-m depth shows that density generally decreases offshore, with a broad pool of lower-density water extending offshore from the continental slope. This is what we expect for an idealized subtropical gyre with lighter water toward the center of the gyre, resulting from the deepening of isopycnals by downward Ekman pumping in response to a basinwide positive wind stress curl (in the Southern Hemisphere).

The patterns of density in Fig. 4 are an outcome of the South Pacific subtropical gyre structure (Ridgway and Dunn 2003). The location of the tongue of light water is set by the position of the EAC, flowing over the continental slope, and largely constrained to follow the contours of constant potential vorticity. The different characteristics of the density field at different depths arise because the gyre is “tilted,” with shallow flow of the gyre positioned farther north than the deeper flow (Roemmich and Cornuelle 1990; Ridgway and Dunn 2003; Kessler and Cravatte 2013). This means that a shallow eastward flow in the offshore surface layer overlays a westward flow at greater depth producing the distribution of density that is evident in Fig. 4.

Across-shore sections of the meridional velocity, potential density, and ∂ρ/∂x at 27°S from OFAM3 are presented in Fig. 5 for examples when the core of the EAC is subsurface intensified, in May (Figs. 5a,c), and when it is surface intensified, in December (Figs. 5b,d). For both velocity sections, the EAC jet leans in toward the coast, with an axis of the EAC jet that departs from the vertical. Both velocity sections also have a bulge on the seaward flank of the EAC, with the strongest southward currents below the surface. In general, when ∂ρ/∂x at the surface is negative, the southward current is strongest at the surface; when ∂ρ/∂x at the surface is positive, the depth of the maximum southward velocity, for each vertical profile, deepens farther offshore following the depth at which ∂ρ/∂x changes sign. The point where ∂ρ/∂x changes sign corresponds to the deepest point of each isopycnal for the section shown. Together with the subsurface-intensified core, these are the key features noted in observations in section 2 and evident in Fig. 2. Close inspection of the slope of the shallow isopycnals (shallower than about 100-m depth) reveals that the position where ∂ρ/∂x changes sign, highlighted by the thick gray contour in Fig. 5, is shoreward of the EAC core when there is a subsurface-intensified core (Figs. 5a,c) and seaward of the EAC core when there is a surface-intensified core (Figs. 5b,d). The sections of ∂ρ/∂x (Fig. 5) show that ∂ρ/∂x is generally negative shoreward of the EAC core, and below about 100–200-m depth offshore of the core, where isopycnals slope downward to the east, and is positive above 100–200-m depth offshore of the core, where isopycnals slope upward to the east. In this study, we show that these characteristics of ∂ρ/∂x, including the across-shore position and the depth of the point at which ∂ρ/∂x changes sign, are critical to the development of all three features investigated here.

Fig. 5.
Fig. 5.

Cross sections of (a),(b) meridional velocity and (c),(d) ∂ρ/∂x for examples when the EAC has (left) a subsurface-intensified jet in May and (right) a surface-intensified jet in December and at 27°S, using fields from the model’s seasonal cycle. Panels (a) and (b) show meridional velocity in color, with contour intervals of 0.05 m s−1, with the four strongest southward contours highlighted in black and potential density in white, with contour intervals of 0.2 kg m−3, with the 24, 25, and 26 kg m−3 isopycnals denoted by the thick magenta, cyan, and blue lines. Panels (c) and (d) show ∂ρ/∂x in color, with contour intervals of 0.5 × 10−5 kg m−3 m−1, where blue is negative, red is positive, and the thick, gray contour shows where ∂ρ/∂x is zero, with the four strongest southward velocity contours in black.

Citation: Journal of Physical Oceanography 54, 2; 10.1175/JPO-D-23-0128.1

The full seasonal cycles of across-shore sections of the meridional velocity and potential density at 27° and 30.5°S are presented in Figs. 6 and 7, respectively. At 27°S (Fig. 6), the core of the EAC jet, where the southward currents are strongest, is surface intensified between September and December, and subsurface intensified from February to August. Throughout a typical year, the axis of the EAC jet leans in toward the coast, and the broad, deep seaward flank of the EAC has vertical profiles of velocity that are strongest at depth. Similarly, for the section at 30.5°S (Fig. 7), the core of the EAC jet has a subsurface maximum between March and August; the EAC jet also shows the leaning in of the currents’ axis, and the velocities in the deep seaward flank of the EAC have maxima that are below the surface and aligned with the point at which ∂ρ/∂x changes sign. Again, these are the key features noted in observations in section 2, evident in Fig. 2, and described in detail above, with reference to Fig. 5.

Fig. 6.
Fig. 6.

(a)–(l) Cross section of meridional velocity (color, with contour intervals of 0.05 m s−1, with the four strongest southward contours highlighted in black) and potential density (white, with contour intervals of 0.2 kg m−3, with the 24, 25, and 26 kg m−3 isopycnals denoted by the thick magenta, cyan, and blue lines), showing the seasonal cycle of the EAC jet at 27°S. The thick, white contour shows where ∂ρ/∂x is zero. Above each cross section (a′)–(l′) is the cross-shore profile of the seasonally-averaged wind stress curl (N m−3; black), ∂τy/∂x (red), and τy (blue).

Citation: Journal of Physical Oceanography 54, 2; 10.1175/JPO-D-23-0128.1

Fig. 7.
Fig. 7.

As for Fig. 6, but at 30.5°S.

Citation: Journal of Physical Oceanography 54, 2; 10.1175/JPO-D-23-0128.1

Consistent with the cross sections presented in Fig. 5, most sections in Figs. 6 and 7 that have a subsurface maximum in the EAC core have the same characteristic, with the change of sign of ∂ρ/∂x (aligned with the maximum depths of isopycnals and the thick white contour) located slightly shoreward of the EAC core. This is least clear in July and August at 27°S (Fig. 6) when the modeled EAC core starts transitioning back to being surface intensified.

To understand why the position where ∂ρ/∂x changes sign is often shoreward of the EAC core, we examine the seasonal cycle of the wind stress and the wind stress curl (∇ × τ = ∂τy/∂x∂τx/∂y, where τx and τy are the zonal and meridional components of wind stress, in the x and y directions) in the vicinity of the EAC (Fig. 8). The zonal profiles of τy, ∇ × τ and τy/∂x at 27° and 30.5°S are presented above the velocity sections in Figs. 6 and 7, in panels (a′)–(l′), for easy reference. The alongshore wind stress is downwelling-favorable (positive) throughout much of the year and strongest between February and August. The amplitudes of ∇ × τ over the shelf are large, with values often exceeding 10−6 N m−3. This wind stress curl corresponds to a downward Ekman pumping velocity, ∇ × τ/(ρ0f), of up to 2 m day−1. By comparison, the average amplitude of ∇ × τ between 160°E–180° and 15°–45°S, toward the center of the basin and responsible for driving the subtropical gyre, is ∼6 × 10−8 N m−3, with a corresponding Ekman pumping velocity of 0.05–0.08 m day−1. The wind stress curl includes contributions from the zonal gradient of meridional wind stress (∂τy/∂x), and meridional gradients of zonal wind stress (∂τx/∂y). The large values of ∇ × τ, shown in Fig. 8, are almost entirely due to zonal gradients in meridional wind stress (see the red lines in Figs. 6a′l′ and 7a′l′). Close inspection of the vectors of wind stress shows that for much of the year the northward, downwelling-favorable wind stress is weaker nearer the coast and increases offshore, consistent with the profiles of ∂τy/∂x in Figs. 6 and 7. As imposed by the application of the bulk formula, small-scale (sub-79-km scale) spatial structure of the wind stress field over the shelf is due to the spatial structure of the surface currents associated with the EAC (for reference, 1° of longitude at 26°S is about 100 km, and 95 km at 30.5°S).

Fig. 8.
Fig. 8.

Seasonal cycle of wind stress curl (contours) off eastern Australia, with wind stress overlaid (showing every second vector in the zonal direction, and every fifth vector in the meridional direction), showing monthly climatological averages over the 11-yr model run used in this study. The magenta contour denotes the 500-m isobath. The white gaps adjacent to the coast arise because the location of the model’s coastline is not perfectly coincident with the actual coastline (the thick gray line). Wind stress is based on the application of winds from ERA-Interim to OFAM3.

Citation: Journal of Physical Oceanography 54, 2; 10.1175/JPO-D-23-0128.1

5. Analysis

a. Thermal wind

The presence of a subsurface core in the EAC jet can be understood by considering the thermal wind relation, expressed here for meridional geostrophic velocity υ:
υz=gfρ0ρx,
where x and z are the zonal and vertical directions, g is gravity, f is the Coriolis parameter, ρ is density, and ρ0 is the background density. Derivation of the thermal wind relation assumes a geostrophic balance for momentum and the hydrostatic approximation for pressure. According to the thermal wind relation, in the Southern Hemisphere, where ∂ρ/∂x is negative, a southward current is stronger nearer the surface. Conversely, where ∂ρ/∂x is positive, a southward current is stronger at depth. As described in section 4, shoreward of the EAC jet, ∂ρ/∂x is generally negative, and so the shoreward flank of the EAC jet is surface intensified. Over the top 200 m or so, offshore of the EAC jet, ∂ρ/∂x is generally positive, with denser water offshore (where isopycnals slope upward to the east), and so southward currents are subsurface intensified in seaward flank of the EAC. Below about 200 m, offshore of the EAC jet, ∂ρ/∂x is negative, with lighter water offshore (where isopycnals slope downward to the east), and so the southward velocity becomes weaker with depth.

The change in the sign of ∂ρ/∂x over depth, on the seaward flank of the EAC, explains the seaward bulge in the velocity section that is evident in observations described in section 2 and presented in Figs. 2 and 3 and the model results (Figs. 57). Where isopycnals slope upward to the east, offshore of the EAC, the southward velocity profiles are subsurface intensified; where isopycnals slope downward to the east, the southward velocity decreases with depth. As a result, the strongest southward velocities are at the depth where ∂ρ/∂x changes sign, which tends to be deeper offshore (denoted by the thick white contours in Figs. 6 and 7). This produces vertical profiles of velocity that have a subsurface maximum, producing velocity sections with a bulge in the seaward flank of the EAC.

The explanation for the lean in the EAC jet is the same as that for the bulge, described above. The contour where ∂ρ/∂x changes sign deepens to the east. Above this contour, the southward current is stronger at greater depth, and below this contour, the southward current is stronger at shallower depths. Like the seaward bulge, the maximum subsurface southward velocity aligns with the contour of zero ∂ρ/∂x. When this contour deepens to the east, the depth of the strongest southward current in the EAC jet also deepens. This produces velocity sections with the characteristic lean that is evident in the observations (e.g., Figs. 2b–f) and the model results (Figs. 57).

For both the lean of the jet near the surface and the bulge of the current on the seaward flank, the dynamical explanation is the same. For both features, the angle of the lean and the angle of the deepening of the bulge are set by the turning point of density, the zero-contour of ∂ρ/∂x. When the zero-contour of ∂ρ/∂x is near vertical (e.g., over the top 100 m in June at 30.5°S, Fig. 7f), the lean of the jet is only clearly evident well below the surface. Similarly, when the zero-contour of ∂ρ/∂x extends deeper offshore (e.g., below 200 m in October at 20.5°S, Fig. 7j), the bulge is deeper, with the strongest southward currents at greater depths for each longitude.

b. The role of the wind over the shelf

What is the impact of the downwelling-favorable wind stress and the strong, positive wind stress curl over the shelf on the subsurface structure of the EAC jet? Off eastern Australia, a northward wind stress drives a shoreward Ekman transport. Moreover, in the Southern Hemisphere, when ∇ × τ is positive, the wind-driven Ekman transport is convergent, resulting in a downward Ekman pumping velocity that deepens isopycnals in the ocean interior. On basin scales, downward Ekman pumping sets up pressure gradients that drive the ocean gyres. However, on smaller scales, Ekman pumping can also drive localized upwelling or downwelling (e.g., Qu et al. 2007; Chelton and Xie 2010). Over the continental shelf, off eastern Australia, there is a persistent, strong, positive wind stress curl (Fig. 8), with maxima between 25°–27°S and 30°–31°S. The zonal profiles of ∇ × τ at 27° and 30.5°S are presented along with the velocity sections in Figs. 6a′l′ and 7a′l′. As reported in section 4, this drives an Ekman pumping velocity of up to 2 m day−1, potentially sufficient to deepen isopycnals from the surface to the shelf break over 2–3 months. The alongshore wind stress is also downwelling-favorable for much of the year, driving a shoreward Ekman transport over the shelf. The downwelling forced by these characteristics of the wind field over the shelf is partially “fed” by shallow waters from the EAC jet being drawn shoreward. The result of this shoreward movement of shallow waters is evident in the position where shallow isopycnals are deepest within the EAC’s jet (Figs. 6 and 7), as noted above, with reference to Fig. 5. This also explains why the zonal density gradient across the shelf, in shallow waters, is stronger on the shoreward side of the EAC jet than on the seaward side, as noted in section 4 with reference to Fig. 4. Additionally, the density sections in Figs. 6 and 7 show well-mixed density over the shelf to about 50-m depth, between March and September at 27°S and between May and September at 30.5°S. High mixing over the shelf is a characteristic associated with wind-driven downwelling (e.g., Allen and Newberger 1996). This detail significantly alters the subsurface structure of the EAC jet, resulting in a subsurface maximum in the EAC core. When the region of positive ∂ρ/∂x aligns with the EAC core, the core develops a subsurface maximum, as evident in Figs. 57.

Consider the sections at 27°S (Fig. 6). When τy is strong and downwelling-favorable and when ∇ × τ is large and positive, shoreward of the EAC, the EAC core is subsurface intensified. See, for example, the zonal profiles of τy and ∇ × τ between February and July in Fig. 6. In each case, positive τy and strong, positive ∇ × τ over the shelf corresponds to a well-defined subsurface core. The period of downwelling-favorable winds and strong, positive ∇ × τ over the shelf typically starts in February, when the modeled EAC jet develops a subsurface maximum. Then, when τy and ∇ × τ weaken in August–September, the subsurface structure of the EAC core reverts to becoming surface intensified by September. Consider also the sections at 30.5°S (Fig. 7). Again, when τy and ∇ × τ are strong and positive over the shelf, between April and August, the EAC core is clearly subsurface intensified. At other times, there is sometimes evidence of a subsurface-intensified core (e.g., October), but this is less clear. We expect that as the wind stress over the shelf changes, the shallow waters of the EAC may shift offshore. However, the time scale of this “relaxation” is unclear.

Time series of the depth of the EAC core in the model is shown in Fig. 9, along with time series of the mean τy and ∇ × τ shoreward of the EAC core over the shelf at 27° and 30.5°S. At both latitudes, the EAC core is subsurface intensified for 69% of the 11-yr period being examined here. For comparison, the ADCP observations presented in Figs. 3a and 3b suggest that the maximum southward velocities in the EAC jet (at EAC500 or EAC2000) are at the top one or two bins for 13%–18% of the record, suggesting that the measured EAC is subsurface intensified for 82%–87% of the time. However, we note that the moored ADCP data, presented in Figs. 3a and 3b, does not always measure the core of the EAC jet (i.e., the across-shore position of the EAC core was not necessarily aligned with any of the moorings), so a direct comparison of the time series of the depth of the core between the model and observations is problematic.

Fig. 9.
Fig. 9.

Time series of the 3-month-averaged depth of the EAC core (black), the mean ∇ × τ shoreward of the EAC core (red), and the mean alongshore wind stress τy shoreward of the EAC core (blue) at (a) 27°S and (b) 30.5°S in OFAM (year labels are for the middle of each year).

Citation: Journal of Physical Oceanography 54, 2; 10.1175/JPO-D-23-0128.1

The close relationship between the depth of the modeled subsurface maximum and the wind over the shelf is clear in the time series (Fig. 9). The correlation between the depth of the core and the mean ∇ × τ (τy) over the shelf is 0.64 (0.68) at 27°S and 0.73 (0.73) at 30.5°S. The 1-month lagged correlation between the depth of the core and the mean ∇ × τ (τy) over the shelf is 0.74 (0.76) at 27°S and 0.73 (0.74) at 30.5°S. The correlation between τy and ∇ × τ is high (exceeding 0.94), and so the consistent correlations reported here are because these metrics are not independent. The amplitude of the wind stress curl at 27°S is smaller than it is at 30.5°S. The typical depth of the subsurface maximum of the EAC jet at 27°S is also smaller than it is at 30.5°S. When the downward Ekman pumping over the shelf is stronger, the shoreward shift of the shallow EAC waters is greater, and the EAC core is aligned with waters with stronger ∂ρ/∂x, producing a deeper subsurface maximum. This is evident in the position where ∂ρ/∂x changes sign, relative to the EAC core, at 30.5°S (Fig. 7e is perhaps the clearest example).

During periods of strong positive ∇ × τ, the average curl across the shelf at 27° and 30.5°S, shoreward of the EAC core, is typically 50–100 × 10−8 N m−3, respectively (Fig. 9). This wind stress curl translates to an average downward Ekman pumping velocity of about 0.6 and 1.1 m day−1, respectively. When surface waters are pumped downward, those surface waters could potentially be replaced by waters drawn from any direction. But because the positive curl extends right up to the coast and along the entire coastline (Fig. 8), we expect most of the downward transport to be replaced by waters drawn from offshore. If we presume the downward transport is entirely balanced by the shoreward transport over the shallow layers of the EAC to a depth of ΔZ:
×τ/(ρ0f)ΔXΔY=UbalanceΔZΔY,
where ∇ × τ/(ρ0f) is the downward Ekman pumping velocity; ΔX and ΔY are the zonal and meridional distances over which the wind stress curl is applied; and Ubalance is the average shoreward velocity between the surface and ΔZ m depth, needed to balance the downward transport. We can then estimate the value of Ubalance needed to balance the downward Ekman pumping by
Ubalance=×τ/(ρ0f)ΔX/ΔZ.
At 27° and 30.5°S, the core of the EAC is typically about 60 and 50 km from shore, respectively. We do not expect surface waters over the shallow parts of the shelf to be efficiently pumped into the ocean interior. If we conservatively presume that the positive ∇ × τ pumps surface waters downward over a 10–20-km region shoreward of the core (ΔX = 10–20 km, to only include the deeper portion of the shelf and upper slope), and assuming the top 50–150 m of EAC is drawn shoreward (ΔZ = 50–150 m), then Ubalance at 27°S is ∼40–260 m day−1 (1.2–7.8 km month−1), and at 30.5°S is ∼80–470 m day−1 (2.4–14.1 km month−1). Under these assumptions, it seems reasonable to expect that the positive ∇ × τ over the shelf is sufficient to shift the EAC surface waters far enough shoreward to align the EAC core with the region of positive ∂ρ/∂x. For the examples in Fig. 5, the distance between the ∂ρ/∂x contour near the surface in May and December, is about 6 km (less than the model grid spacing of ∼10 km, because the fields in Figs. 57 are averages over 11 months; monthly means, averaged over 11 years of the model run). This level of detail is not resolved by the model, but these calculations indicate that the across-shore position of this turning point does not need to move very far to produce a significant change in the structure of the EAC core.
A similar calculation to that presented above, based on alongshore wind stress, produces a consistent picture. The Ekman transport T is
T=ΔZ0UEkmandz
=τy/(ρ0f),
where UEkman is the wind-driven Ekman velocity in the surface layer, of depth ΔZ. The average alongshore wind stress when the EAC’s core is subsurface intensified is about 0.05 N m−2 (Figs. 69), producing an Ekman transport of T = −0.75 m2 s−1, with a corresponding depth-averaged UEkman of ∼400–1300 m day−1 (12–39 km month−1), assuming ΔZ is 50–150 m. These calculations confirm that the amplitude of the downwelling-favorable wind stress is sufficient to explain the shoreward shift of surface waters of the EAC so that the region of positive ∂ρ/∂x aligns with the EAC core.

c. Comparison of scenarios

To break down the cause of each feature of the EAC jet that we have described here, we present a series of idealized calculations of geostrophic velocity for different density fields (Fig. 10). For each velocity section, we prescribe a Gaussian cross-shore profile of depth-averaged velocity with a maximum southward velocity of 1 m s−1, and a half-width of 50 km (Fig. 10a). We then use the thermal wind relation to derive the vertical profile of meridional velocity that corresponds to density fields for different cases. Cases presented include the following:

  • ρ/∂x = 0, producing a barotropic jet (Fig. 10b).

  • ρ/∂x is constant and negative, producing a surface-intensified jet (Fig. 10c).

  • ρ/∂x changing sign at the core of the jet over all depths, with ∂ρ/∂x < 0 onshore of the core, and ∂ρ/∂x > 0 offshore of the core, consistent with an EAC with a deep, narrow, low-density tongue. Geostrophic velocities using the prescribed depth-averaged velocity profile include a surface-intensified jet shoreward of the core, and a subsurface-intensified jet seaward of the core (Fig. 10d).

  • ρ/∂x changing sign at the core of the jet, with ∂ρ/∂x < 0 onshore and below 150 m, and ∂ρ/∂x > 0 offshore, above 150-m depth, consistent with an EAC with a shallow, narrow, low-density tongue, and lighter water toward the center of the basin at intermediate depths. Geostrophic velocities using the prescribed depth-averaged velocity profile are quite realistic, with a surface-intensified jet that leans in toward the coast, and with a subsurface bulge on the seaward flank (Fig. 10e).

  • ρ/∂x changing sign 10 km shoreward of the core of the jet (to represent the shoreward advection of shallow EAC waters in response to wind over the shelf), with ∂ρ/∂x < 0 onshore and below 150 m, and ∂ρ/∂x > 0 offshore and above 150-m depth. Geostrophic velocities using the prescribed depth-averaged velocity profile are quite realistic, with a subsurface-intensified jet, with a surface expression that leans in toward the coast, and with a subsurface bulge on the seaward flank (Fig. 10f).

Fig. 10.
Fig. 10.

Idealized cases for the EAC jet. (a) The cross-shore profile of the prescribed depth-averaged velocity. Velocity and density sections for different cases (with velocity in color, with contour intervals of 0.1 m s−1, and density in white contours, with contour intervals of 0.25 kg m−3 and thick contours indicating every 1 kg m−3). Cases presented include (b) ∂ρ/∂x = 0, (c) ∂ρ/∂x is constant and negative, (d) ∂ρ/∂x changing sign at the core for all depths, (e) ∂ρ/∂x changing sign at the core above 150-m depth, and (f) ∂ρ/∂x changing sign 10 km shoreward of the core above 150-m depth. The insets are intended to be a key for each case, showing the density section (black; with 1 kg m−3 contour intervals), with the area where ∂ρ/∂x > 0 shaded in gray and the zonal position of the core denoted by the dashed line.

Citation: Journal of Physical Oceanography 54, 2; 10.1175/JPO-D-23-0128.1

The characteristics evident in Figs. 10e and 10f resemble many of the observed and modeled velocity sections in Figs. 2 and 57. In general, the velocity sections with a surface-intensified core resemble the velocity fields in Fig. 10e, and the velocity sections with a subsurface-intensified core resemble the velocity field in Fig. 10f. These idealized calculations further support the explanations offered here to explain the subsurface-intensified EAC jet, the leaning of the jet toward the coast, and the deep velocity bulge in the seaward flank of the EAC.

6. Discussion

a. What causes the subsurface maximum?

Based on the analyses presented above, we conclude that the subsurface maximum in the core of the EAC is caused by two factors. First, because the EAC flows as a narrow current, carrying low-density water from the Coral Sea into the denser waters of the Tasman, the horizontal density gradient shoreward and seaward of the EAC jet has a different sign. As a result, according to the thermal wind relation, the vertical shear in the southward velocity is generally surface intensified shoreward of the EAC jet and subsurface intensified seaward of the EAC jet. Second, as a result of the downwelling-favorable winds over the shelf, the surface waters of the EAC jet are drawn shoreward, shifting the region of subsurface-intensified current into the region of the EAC core, resulting in an EAC jet with a subsurface core.

b. Reflections on other model results

As noted in the introduction, many modeling studies of the EAC appear to fail to reproduce a subsurface-intensified jet (e.g., Marchesiello et al. 2000; Oke and Middleton 2000, 2001; Wilkin and Zhang 2007; Wijeratne et al. 2018; Kerry and Roughan 2020). Here, we consider why these models may have failed to reproduce this element of the EAC.

Some of these models are configured with no wind forcing (Marchesiello et al. 2000; Oke and Middleton 2000, 2001). As a result, those models do not include the necessary forcing fields to draw the surface waters of the EAC shoreward to align the waters with positive ∂ρ/∂x with the core. That is, they did not include the necessary forcing to produce a subsurface maximum.

Other models that do not appear to produce a subsurface-intensified core do include wind forcing, but they are regional models of the Tasman Sea, with a northern boundary positioned off central eastern Australia (Wilkin and Zhang 2007; Kerry and Roughan 2020). The boundary forcing at their northern boundary prescribes fields from either climatology (Wilkin and Zhang 2007) or from a data-assimilating global model (Kerry and Roughan 2020). Perhaps the prescribed fields do not include a subsurface-intensified EAC jet, perhaps the boundary forcing has the EAC core at an incorrect position, or perhaps the boundary forcing interferes with the model dynamics that are required to produce a subsurface maximum. We note that although a subsurface maximum is not clearly evident, or explicitly described by Kerry and Roughan (2020), some of their analysis hints at a subsurface maximum and a lean of various modes of variability in their model (e.g., their Figs. 10 and 11), so we cannot be sure that their model does not reproduce a subsurface-intensified EAC jet. They showed time averages of the EAC, as did Wilkin and Zhang (2007), without separating out different seasons. It is possible that the EAC jet is subsurface intensified sometimes, and surface intensified at other times, and that the mean field includes a surface-intensified jet (note that the annual mean from OFAM at both 27° and 30.5°S is surface intensified; not shown). Their results clearly show the bulge of the seaward flank of the EAC (Kerry and Roughan 2020, their Fig. 5).

Another model that does not appear to reproduce a subsurface-intensified EAC jet is the model presented by Wijeratne et al. (2018). This model appears to include all of the necessary elements to produce a subsurface core, but the published results do not describe such a feature and the figures do not clearly show it. However, we note that the velocity sections presented therein are not focused on the EAC jet, showing sections between the surface and 3000-m depth (their Fig. 3). So perhaps the subsurface core is present in their model, but just not clearly evident in the published figures.

We also noted in the introduction that some models do reproduce an EAC jet with a subsurface-intensified core. Gibbs et al. (2000) describe a two-dimensional, cross-shelf model that is initialized with a surface-intensified EAC jet and is forced with downwelling-favorable winds. Their model develops a subsurface-intensified EAC jet. We suggest that the ocean’s response to the downwelling-favorable winds is sufficiently to align the water with positive ∂ρ/∂x with the EAC core. Roughan et al. (2003) present results from a model that includes an EAC with a subsurface-intensified core. Their model is run in a “diagnostic” mode, solving for the momentum equations using a time-invariant density field as input to diagnose the velocity field. They did not force their model with any winds, but presumably the prescribed density field that was based on climatology, and includes the characteristics required for generation of a subsurface-intensified EAC core. Schiller et al. (2008) present results from a near-global ocean reanalysis, using an earlier version of the model used for this study. They did not describe the EAC as having a subsurface-intensified core, but close inspection of their results (and analysis of their archived data, not shown) confirms that their data-assimilating model reproduces an EAC jet with a subsurface core (their Fig. 18d).

There are many other published papers that describe models of the EAC. However, many do not include figures that show velocity sections of the EAC jet (e.g., Tilburg et al. 2001; Oke and Griffin 2011; Macdonald et al. 2013; Sloyan and O’Kane 2015; Ypma et al. 2016; Bull et al. 2017; Sandery and Sakov 2017), so we cannot comment on whether those models produced an EAC jet with a subsurface-intensified core.

c. Comparison with other boundary currents

Many velocity sections in other western boundary currents show similar bulging of the current, with a broad subsurface maximum, on the seaward flank of the current, and often with evidence of the jet leaning in toward the coast. This includes sections in the Florida Current at 27°N (Leaman et al. 1987, their Fig. 2b), the Gulf Stream at 35°N (Berezutskii et al. 1991, their Fig. 3), the Kuroshio at 27°N (Wei et al. 2015, their Fig. 2), and the Mindanao Current at 8°N (Zhang et al. 2014, observed subsurface velocity maximum). Other examples in the literature include sections produced from shipboard ADCP (e.g., Wei et al. 2015; Andres et al. 2020), from geostrophic estimates using hydrography (e.g., Halkin and Rossby 1985; Berezutskii et al. 1991; Pickart and Lindstrom 1994), and from mooring arrays (e.g., Bower and Hogg 1996). ADCP sections of the Kuroshio at 27°N (Wei et al. 2015, their Fig. 2) also show an instance when the core of the Kuroshio had a subsurface maximum. However, we have not examined the density fields or the wind stress fields to assess whether the explanations we offer for the EAC are also applicable to other WBCs. Such an investigation is a worthwhile endeavor for future investigations but is beyond the scope of this study.

More generally, the dynamics that explain the subsurface velocity maximum of the EAC may apply to any current system where the across-shore position of the core of the jet is constrained by topography; and where the position of the shallow density gradients is influenced by wind forcing. The Leeuwin Current, for example, is characterized by a warm, low-density tongue of water, flowing poleward in the core of a current adjacent to the continental shelf (e.g., Ridgway and Condie 2004). Observations of the cross-shore profile of the Leeuwin Current seem to mostly show a surface-intensified current (e.g., Cresswell 1996; Feng et al. 2003), but there are examples of shipboard ADCP sections with a clear subsurface maximum (Cresswell and Griffin 2004, their Fig. 7b). Again, we have not examined the corresponding wind forcing to determine whether the horizontal density gradients associated with the low-density tongue may have been shifted with respect to the core of the Leeuwin Current. Such an analysis is also worth pursuing in a future study.

d. Implications of a subsurface maximum

The presence of a subsurface maximum likely produces baroclinic instabilities that play a role in eddy formation and EAC separation from the coast. When the subsurface velocities are stronger than surface velocities, the net southward transport of heat may also have a subsurface maximum, or may be reduced as the jet transports deeper, cooler water. This may partially explain the subsurface maxima in the sections of temperature and salinity anomalies off Sydney, reported by Ridgway et al. (2008, their Fig. 3). We speculate that as warm, light water is transported from the low-density Coral Sea into the denser waters of the Tasman Sea, the merged water masses may become unstable. So it is possible that the development of a subsurface maximum in the EAC core may precede baroclinic instabilities downstream, initiating the development of more eddies in the Tasman Sea. This suggestion appears consistent with the analysis of the baroclinic conversion rate of eddies in the Tasman sea, presented by Xu et al. (2022, their Fig. 9).

7. Conclusions

The EAC has often been reported to have a subsurface maximum, centered at approximately 100-m depth (e.g., Godfrey et al. 1980a; Cresswell et al. 1996; Sloyan et al. 2016). To date, even though many studies have observed or modeled the subsurface maximum, none have offered any dynamical explanation for this prominent feature. Here we show that two factors cause the EAC jet to develop a subsurface maximum. First, the EAC flows as a shallow, narrow, low-density tongue, producing horizontal density gradients with a different sign on either side of the jet. The different sign of ∂ρ/∂x results in a surface-intensified southward current onshore, and a subsurface-intensified current offshore, according to the thermal wind relation. Second, the alongshore wind stress and wind stress curl over the shelf often drives a downwelling and downward Ekman pumping that is strong enough to draw surface waters shoreward, aligning the EAC core with the region of positive ∂ρ/∂x, producing a subsurface maximum. Both factors influence the development and position of a horizontal density gradient ∂ρ/∂x, in the vicinity of the EAC, and both factors are essential for the development of the subsurface-intensified core. Model results suggest that the core of the EAC is subsurface intensified for about 70% of the time. Similarly, observations indicate that the EAC jet is sometimes surface intensified and sometimes subsurface intensified (e.g., Mata et al. 2000; Sloyan et al. 2016).

The change of sign of ∂ρ/∂x across the shelf also causes the jet to lean in toward the coast, a characteristic also regularly observed (e.g., Cresswell et al. 2017). As highlighted in Fig. 5, ∂ρ/∂x increases offshore, immediately offshore of the point at which ∂ρ/∂x changes sign, the southward current becomes increasingly subsurface intensified, with the depth of the subsurface maximum generally increasing offshore, following the contour of zero ∂ρ/∂x. In the vicinity of the core, this contour tends to follow a diagonal path, from the surface near the center of the EAC, and becoming deeper offshore. This characteristic causes the EAC jet to appear to lean in toward the coast.

The depth at which ∂ρ/∂x changes sign in the offshore flank of the EAC generally deepens offshore. The depth of the strongest southward current on the seaward flank aligns with the depth at which ∂ρ/∂x changes sign, resulting in southward currents that increase with depth in shallower water, where ∂ρ/∂x is positive, and southward currents that decrease with depth in deeper water, where ∂ρ/∂x is negative (Fig. 10). This results in a distinct seaward bulge in the velocity sections and is really just a seaward extension of the lean of the EAC jet summarized above. A similar bulge is evident in most observed and modeled velocity sections that span the seaward flank (e.g., Sloyan et al. 2016) and is evident 100% of the time in moored ADCP observations that measured the flank (Figs. 3c,d).

Features similar to those investigated here for the EAC, including the subsurface maximum, the leaning in of the jet, and the subsurface bulge, are also evident in other WBCs (e.g., Pickart and Lindstrom 1994; Wei et al. 2015), presumably for the same reasons outlined here. The presence of a subsurface maximum may produce baroclinic instabilities and may play a role in eddy formation and in the separation of boundary currents from the coast. These speculations warrant more investigation.

Acknowledgments.

Model data used in this study are from the Bluelink suite of global models (https://dapds00.nci.org.au/thredds/catalog/gb6/BRAN/catalog.html). Model runs used resources and services from the National Computational Infrastructure (NCI), which is supported by the Australian government. Moored ADCP data were sourced from the CSIRO Data Access Portal (https://doi.org/10.25919/kr1g-ew82). The EAC Deep Water mooring array was supported by CSIRO and the Integrated Marine Observing System (https://www.aodn.org.au). IMOS is a national collaborative research infrastructure, supported by the Australian government. The authors gratefully acknowledge David Griffin for discussions that led to improvements in this study.

Data availability statement.

Data used for this study are from a spinup run of OFAM3. Data are available online (https://dapds00.nci.org.au/thredds/catalogs/gb6/catalog.html; follow links to OFAM3_BGC_2021). ADCP data presented in Fig. 3 are from CSIRO Data Collections (https://doi.org/10.25919/kr1g-ew82) and were accessed on 6 July 2023.

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