Barotropic vorticity balance of the North Atlantic subpolar gyre in an eddy-resolving model

. The circulation in the North Atlantic Subpolar gyre is complex and strongly inﬂuenced by the topography. The gyre dynamics is traditionally understood as the result of a topographic Sverdrup balance, which corresponds to a ﬁrst order balance between the planetary vorticity advection, the bottom pressure torque and the wind stress curl. However, this dynamics has been studied mostly with non-eddy-resolving models and a crude representation of the bottom topography. Here we revisit the barotropic vorticity balance of the North Atlantic Subpolar gyre using a high resolution simulation ( ≈ 2-km) with topography- 5 following vertical coordinates to better represent the mesoscale turbulence and ﬂow-topography interactions. Our ﬁndings highlight that, locally, there is a ﬁrst order balance between the bottom pressure torque and the nonlinear terms, albeit with a high degree of cancellation between each other. However, balances integrated over different regions of the gyre – shelf, slope and interior – still highlight the important role played by nonlinearities and the bottom drag curls. In particular the topographic Sverdrup balance cannot describe the dynamics in the interior of the gyre. The main sources of cyclonic vorticity are the non 10 linear terms due to eddies generated along eastern boundary currents and the time-mean nonlinear terms from the Northwest Corner. Our results suggest that a good representation of the mesoscale activity along with a good positioning of the Northwest corner are two important conditions for a better representation of the circulation in the North Atlantic Subpolar Gyre. currents driven instead by nonlinear effects. The comparison between balances in the interior and slope regions indicates that the NL term helps to redistribute vorticity from the boundary toward the interior of the gyre. dynamics of the North Atlantic Subpolar gyre in a numerical model with, for the ﬁrst time, terrain following coordinates and a mesoscale-resolving resolution ( ∆ x ≈ 2 km). The combination of the high resolution with σ -levels allows

The aim of this paper is to investigate the dynamics of the SPG by analysing the barotropic vorticity balance in a truly eddy-resolving σ-level coordinate model. To our knowledge no study of the SPG dynamics has ever been conducted at this resolution with this kind of vertical coordinates. The switch in vertical coordinates combined with eddy-resolving resolution might help to resolve smaller scale processes and allow a better representation of flow-topography interactions overall. The paper is organised as follows: The simulation setup is presented in section 2. The mean currents characteristics and variability in the simulation are confronted to observations in section 3. The barotropic vorticity balance is analyzed for the full SPG in section 4. The balances corresponding to the different parts of the gyre are further described in section 5. To better understand what is hidden inside the non linear term we analuze it more in details in section 6. Conclusions are presented and discussed in section 7.

Model and set-up
To investigate the impact of the topography on the circulation, it is essential to have a good representation of the flow-70 topography interactions. To do so, we use a terrain-following coordinate model: the Regional Oceanic Modelling System (ROMS, Shchepetkin and McWilliams (2009)) in its CROCO (Coastal and Regional Ocean Community) version (Debreu et al., 2012). It solves the hydrostatic primitive equations for velocity, temperature and salinity, using a full equation of state for seawater McWilliams, 2009, 2011).
To achieve a kilometric resolution at a reasonable cost, we use a one way nesting approach by defining two successive 75 horizontal grids with resolutions ∆x ≈ 6 km for the parent grid covering the North Atlantic ocean (NATL) and ∆x ≈ 2 km for the child grid covering the SPG (POLGYR). The parent North Atlantic domain is identical to the one in Renault et al. (2016).
It has 1152 × 1059 points with a horizontal resolution of 6-7 km. The child grid has 2000 × 1600 points and a horizontal resolution of 2 km. It allows the simulation to be truly eddy resolving in most of the area, as the Rossby deformation radius varies between 10 and 20 km over the region (Chelton et al., 1998). The domains are shown in figure 1. 80 The bathymetry for both domains is constructed from the SRTM30 PLUS dataset (available online at http://topex.ucsd. edu/WWW_html/srtm30_plus.html) based on the 1 min Sandwell and Smith (1997) global dataset and higher resolution data where available. A Gaussian smoothing kernel with a width 4 times the topographic grid spacing is used to avoid aliasing whenever the topographic data are available at higher resolution than the computational grid and to ensure the smoothness of the topography at the grid scale. Also, to avoid pressure gradient errors induced by terrain-following coordinates in shallow 85 regions with steep bathymetric slopes (Beckmann and Haidvogel, 1993), we locally smooth the bottom topography h to ensure that the steepness of the topography does not exceed a factor r = 0.2, where the local r-factor is defined in the x and y directions by r x = h(i,j)−h(i−1,j) h(i,j)+h(i−1,j) and r y = h(i,j)−h(i,j−1) h(i,j)+h(i,j−1) , (i,j) representing the grid index. Initial and lateral boundary data for the largest domain are taken from the Simple Ocean Data Assimilation (SODA, Carton and Giese (2008)). The NATL simulation is run from January 1st, 1999 to December 31st, 2009. It is spun up for 2 years, 90 and the following 8 years are used to generate boundary conditions for the child grid. Our focus is the barotropic vorticity dynamics, characterized by time scales on the order of months, such that a year of spin up is sufficient for the kinetic energy to   The North Atlantic and subpolar gyre simulations have 50 and 80 vertical levels, respectively. Vertical levels are stretched at the surface and bottom (Lemarié et al., 2012) to have a better representation of the surface layer dynamics at the top and flow-topography interactions at the bottom. The depth of the transition between flat z levels and terrain-following σ levels is h cline = 300 m. The two parameters controlling the bottom and surface refinement of the grid are σ b = 2, σ s = 7 for the parent grid and σ b = 3, σ s = 6 for the child grid, corresponding to strongly stretched levels at the surface and bottom (Figure 2).

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The vertical mixing of tracers and momentum is done by a k-model (GLS, Umlauf and Burchard (2003)). The effect of bottom friction is parameterized through a logarithmic law of the wall with a roughness length Z 0 = 0.01 m.

Mean circulation
Before investigating what is driving the SPG dynamics, we first need to validate the mean circulation in our simulations. Mean 105 velocities from the two simulations (NATL and POLGYR) at the surface and 1000-m depth are shown in figure 3. We present at the bottom of figure 3 (e,f) the amplitudes of the currents from the NOAA drifter climatology (Laurindo et al., 2017) at the surface and from the ARGO-based ANDRO dataset at 1000-m depth (Ollitrault and Rannou, 2013;Lebedev et al., 2007). The ANDRO data have been binned on a 0.25 • × 0.25 • grid and cells with less than 10 data points have been removed.
The North Atlantic Current (NAC) represents a boundary between the subtropical and the subpolar gyres. Oceanic models 110 have difficulties in reproducing its dynamics and particularly its Northern extension known as the NorthWest Corner (Bryan et al., 2007;Hecht and Smith, 2008;Drews et al., 2015), which is centered at 50 • N, 48 • W (Lazier, 1994). These difficulties lead to the apparition of the so called "cold-bias", which can reach up to 10 • C (Griffies et al., 2009;Drews et al., 2015), and which plays a role in the Atlantic low frequency variability (Drews and Greatbatch, 2017). The NorthWest Corner is well reproduced in our simulations, and the temperature bias at this location is less than a degree.

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After turning eastward, the NAC splits into three branches, which are strongly constrained by topography (Bower, 2008).
They cross the Mid Atlantic Ridge (MAR) through three deep fracture zones: the Charlie-Gibbs Fracture Zone (CGFZ, 52.5 • N), the Faraday fracture zone (50 • N) and the Maxwell fracture zone (48 • N) (Bower et al., 2002). In both surface and 1000 m observations (Fig. 3(e),(f)), the Northern branch of the NAC is more intense and corresponds to the main pathway across the MAR. The three branches are well represented in the simulations with, at the surface, an overestimation of the southern 120 branch and an underestimation of the northern branch. At depth, ANDRO data depict an intense branch crossing the MAR at the CGFZ while the amplitude of the two Southern branches is smaller. This feature might be related to the Labrador Sea Water passing into the Eastern Basin through the CGFZ in this depth range, while in the Faraday and Maxwell Fracture zones the flow is more surface intensified. The circulation in POLGYR is closer to the observations with a better representation of the flow in the CGFZ at 1000 m.

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After crossing the MAR, the three branches head North with the two Northern ones feeding the interior of the Iceland basin and the Rockall Trough (RT) (Daniault et al., 2016). The water coming from the Maxwell fracture zone recirculates southward in the West European Basin (Paillet and Mercier, 1997). As most of the models (Treguier et al., 2005;Deshayes et al., 2007),  This structure is detectable in the ANDRO dataset around 55 • N, 12 • W (Fig. 3(f)). It is not present in NATL while it appears in POLGYR, albeit with too intense velocities. In NATL at depth, there is a strong southward flow in the western part of the RT due to the wrong representation of the Faroe Bank channel. As the topography is strongly smoothed, the channel is not properly 135 represented and does not allow the dense water coming from the Nordic Seas to pass through it and feed the Iceland Scotland Overflow Water properly (Hansen et al., 2016;Kanzow and Zenk, 2014). Thus, the water is recirculating in the western part of the RT, creating a spurious pattern ( Fig. 3(b)). The problem is solved by increasing the horizontal resolution and improving the representation of the topography, which corresponds to a wider opening of the channel and allows a more realistic circulation in the RT.

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Further north, part of the flow continues to the Nordic Seas (Rossby and Flagg, 2012), while the other part follows the Reykjanes Ridge (RR). A common bias in models east of RR is a too intense southward flow at the surface (Treguier et al., 2005). This bias is present in NATL but disappears at higher resolution in POLGYR, which is closer to the circulation observed by the drifters. On the western side of the RR the signal of the strong northward Irminger current visible in observations is well resolved by the simulations (Fig. 3).

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At 1000-m depth, Argo floats reveal a continuous current following the Eastern RR flank until reaching the CGFZ, with some of the flow crossing the ridge North of 57.3 • N and some crossing at the Bight Fracture Zone (56-57 • N). This is coherent with the results from Petit et al. (2018), which observed that water at this depth (their layer 3) was more likely to cross the ridge North of 56 • N. This southwestward flow is present in our simulations, with too intense velocity amplitudes in NATL, but realistic amplitudes at higher resolution in POLGYR. In both cases, we clearly see the flow crossing the ridge north of 56 • N.

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On the western side of RR, the velocity in the simulations is too strong compared to observations. The mean subpolar gyre intensity in the model (Fig. 4), computed as the cumulative transport from Iceland to 53.15 • N along the crest of the RR, is equal to -25 Sv and compares well with the -21.9 ± 2.5 Sv monthly average in Petit et al. (2018).
Numerous recirculations are present in the SPG, many of them occurring near the intense boundary currents along Greenland and around the Labrador sea (Reverdin, 2003;Flatau et al., 2003;Cuny et al., 2002). The recirculation cells are present in the 155 Labrador sea (Lavender et al., 2000;Cuny et al., 2002) and extend to the Irminger basin (Holliday et al., 2009). Theses features are mainly driven by the topography and the wind as described in Käse et al. (2001); Spall and Pickart (2003), and are stable in time (Palter et al., 2016). Some models are unable to reproduce correctly the recirculation cells, especially the one in the center Labrador Sea (Treguier et al., 2005). In our case, this recirculation is well represented (Figure 3  EKE amplitudes in the NATL simulation are weaker than in observations, but the eddy activity is enhanced when the reso-170 lution is increased. The POLGYR simulation displays similar EKE patterns than observational data in every basins (Labrador, Irminger and Iceland) with close amplitudes over most of the SPG. The EKE patterns corresponding to the generation of Irminger Rings have higher magnitudes in POLGYR than in the NOAA drifters data.
A way to quantify the mesoscale activity at depth is to look at the vertical isopycnal displacements. When referenced to a mean, it represents the Eddy Available Potential Energy (EAPE) or the amount of energy stored in the potential energy reservoir 175 due to mesoscale activity (Lorenz, 1955). This quantity is a proxy of the baroclinic activity in the interior of the ocean. We compare EAPE from the simulations with the atlas of Roullet et al. (2014) constructed from Argo data (Fig. 5(f)). In NATL (at 6 km resolution) most of the baroclinic activity already seems well resolved. However, observations highlight an EAPE maximum on the western flank of the RR that is missing in NATL, but appears only in POLGYR (at 2 km resolution). On the contrary, strong patches of EAPE are visible along the boundary currents of the western half of the SPG in NATL, but are 180 not visible in observations. Interestingly these patterns weaken in POLGYR, potentially pointing to a change in the vertical structure of the currents at higher resolution. Another factor to take into consideration is the lack of Argo measurements close to the boundaries, which might cause an underestimation of EAPE at these locations. The barotropic vorticity equation is obtained by integrating the momentum equations in the vertical and cross-differentiating them (Gula et al., 2015): where the vorticity Ω is the curl of the vertically integrated components of the velocity between the bottom and the surface: The overbar defines a vertically integrated quantity: with η(x, y, t) the free surface height and h(x, y) the topography. It is possible to decompose the planetary vorticity advection with V the vertically integrated meridional component of velocity, if we consider a mean over a long enough time period such that ∂η ∂t ≈ 0. The non linear term can be written as: The expression for A Σ is similar to the one shown in Schoonover et al. (2016) (their equation (2) In the subtropical gyre, the barotropic vorticity balance is close to a Sverdrup balance away from the boundaries (βV ≈ ∇ × τ wind ρ0 ), while the closure of the northward branch of the gyre at the western boundary is done primarily through BPT ) (Schoonover et al., 2016).
The barotropic vorticity balance in the SPG is slightly more complex due to the strong impact of the topography. Along the northern and western boundaries of the SPG, the first order balance is between meridional advection and BPT (βV ≈ J(P b ,h) In our simulations, the BPT balances the advection of vorticity at leading order everywhere in the domain (Fig. 6). This is qualitatively different from the vorticity balances shown in Yeager (2015), but it is similar to the results of Gula et al. (2015) in the Gulf Stream region with the same ocean model and a similar horizontal resolution. This highlights the fact that locally the flow is able to follow isobaths due to an equilibrium between the NL term (making the flow cross isobaths) and the bottom pressure anomaly.

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Both terms exhibit small scales related to topographic features, but with a high degree of cancellation between each other.
The sum of the BPT and NL terms (Fig. 6 (c) is often an order of magnitude smaller than the amplitude of the terms considered individually and exhibits patterns and amplitudes matching the advection of planetary vorticity. This cancellation is also clear in Wang et al. (2017), their Figure 3, where the transport driven by mean flow advection balances the one driven by the BPT, both having amplitudes larger than the wind stress curl-driven transport.

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To facilitate the interpretation of maps of NL and BPT terms, the impact of small topographic scales has to be reduced by smoothing with a large enough length scale. NL terms in particular are expected to be smoothed out on scales larger than 1-2 • (Hughes and De Cuevas, 2001). Figure 7 shows all terms smoothed with a gaussian kernel of 1 • radius. Even with such smoothing, the BPT and NL terms are still significantly larger than the corresponding results from the 0.1 • simulation of Yeager (2015). However, their sum J(P b ,h) ρ0 + A Σ (Fig. 7 (f)) is of the same order of magnitude than the βV (Fig. 7 (a) ) and 235 the Bottom Drag Curl (BDC, Fig. 7 (e)).
The curl of the wind stress in POLGYR has the same pattern and amplitude than in Yeager (2015). It is mostly positive with the strongest signal on the Eastern coast of Greenland. The amplitude of the βV term is slightly stronger in our model than in coarser resolution simulations. In the simulations of Hughes and De Cuevas (2001) and Yeager (2015), the patterns of the βV term seems to indicate much wider currents. Here, the patterns correspond to thinner and more intense currents, closely 240 following the continental slopes, in agreement with the observations.   Following Mertz and Wright (1992) and Yeager (2015), the BPT can be further decomposed into: which illustrates that the bottom geostrophic currents that appears in the expression of BPT are the sum of a vertically averaged part and a baroclinic part directly related to the JEBAR term. The term f h u g · ∇h highlights regions where the depth-averaged flow is crossing isobaths, and the h(JEBAR) term where the baroclinic effects are playing a role to decouple the bottom 265 flow from the barotropic flow through the geostrophic shear. In Fig. 8 (c) the geostrophic velocity has been computed from the thermal wind balance referenced at the surface.  Along the continental slopes, on the western and northern part of the gyre, the flow is close to barotropic and the f h u g · ∇H term has similar patterns and amplitudes than the BPT. This contrasts with results from Yeager (2015), who found that the h(JEBAR) term was almost an order of magnitude larger than the BPT in these regions. However over the southern and 270 eastern part of the gyre, it is clear that the structure of the flow is much more baroclinic and the f h u·∇h and h(JEBAR) terms are both an order of magnitude larger than the BPT.
5 Integrated vorticity balance for the shelf, slope and interior of the gyre

Gyre integrated barotropic vorticity balances
The maps of the barotropic vorticity terms, with various degrees of smoothing, can help identify the locally dominant terms, 275 but do not enable us to identify the important balances at the gyre scale. Spatial integrations are performed inside different gyre contours (Fig. 9) to better understand the main contributions to the circulation of the subpolar gyre.
We distinguish the shelf area from the gyre using a contour of barotropic streamfunction of -3 Sv. This contour is chosen because it corresponds to the largest possible closed contour of the barotropic streamfunction. We can check that the term −∇.(f u) ≈ −βV integrates to zero over such a contour (Fig. 9 (c). The shelf thus defined corresponds to an area with a mean 280 depth of 290 meter and is extending from the South of Iceland to Flemish cap (blue area in Fig. 9 (b)). When integrated inside the -3 Sv contour (which means excluding the shelf area, Fig. 9 (c)), the main sources for the cyclonic circulation of the gyre are the wind and the BPT. They are balanced by the BDC. The wind input does not contribute much locally (Fig. 7), but becomes significant when integrated spatially over the whole gyre. The BPT is the major source of positive vorticity and helps the flow move cyclonically around the gyre. The BDC and NL terms act as sinks of vorticity, but the NL 285 term is much smaller than the BDC. The BDC is very intense where the current flows close to a steep topography, as in the case of the Labrador Current (LC) and the West Greenland Current.
When integrated over the whole gyre ( Fig. 9 (a)), the balance is slightly different. The wind is still a major contributor for the cyclonic circulation and the BDC still represents the major sink of vorticity. However, the NL term replaces the BPT as a source of cyclonic vorticity for the gyre. In this interpretation, both the wind and the NL term forces the gyre cyclonically, 290 while the BDC and BPT balance this input.
The difference between the two balances is highlighted by looking at the balance in the region in-between the two contours, which covers the upper slope and the shelf. It corresponds to a balance between BPT, NL and bottom drag. This balance is close to the one described in Csanady (1978) and evokes a buoyancy driven flow in this area (Chapman and Beardsley, 1989). Indeed, with a switch to (n,s) coordinates system with n the right handed coordinates (here oriented toward shallower water) and s the 295 distance along flow, the BPT can be written J(P b ,h) ρ0 = − ∂P b ∂s ∂h ∂n . A negative value of BPT then means ∂P b ∂s < 0 corresponding to a buoyancy driven current. Figure 10. Integration of the barotropic vorticity terms in the slope area (a, defined between the barotropic streamfunction contour -3 Sv and the 3000-m isobath) and interior (b).

Barotropic vorticity balance in the interior of the gyre
It is clear from the patterns of the different terms of the barotropic vorticity balance that the local balances over the boundary currents are very different than what is happening in the interior of the gyre. The classical picture of a gyre interior (far from 300 the boundaries) in a quasi-Sverdrup balance that applies in the subtropical gyre, does not seem to apply anywhere in the SPG.
To better understand what drives the interior part of the subpolar gyre, we further divide the domain into an interior and a boundary part, as represented in Figu. 10. The two domains are defined using the -3 Sv line as previously, and the 3000 m isobath. What is between the -3 Sv line and the 3000 m isobath is considered as the slope region and the rest is considered as the interior area. The choice of the 3000 m isobath is somehow subjective but the results are not sensitive to the choice of a 305 specific isobath.
In the slope region, the main source of cyclonic vorticity is the BPT. The curl of the wind and the βV are also positive. The strongly negative NL term indicates advection of cyclonic vorticity outside of this domain toward the shelf or the gyre interior.
In the interior, the NL term represents the major contribution to the cyclonic circulation. It is balanced by the BDC, the BPT and the βV terms. Contributions from the BDC are of similar magnitude in the interior and the slope area. The wind input of 310 vorticity is smaller than in the slope region, as the major wind source of vorticity is located along the Greenland area (Fig. 7 (d)) and not uniformly distributed over the gyre. It confirms that the gyre interior in not in Sverdrup balance at the first order, which would imply a dominant balance between a negative βV and a positive input from the curl of the wind stress, but is driven instead by nonlinear effects. The comparison between balances in the interior and slope regions indicates that the NL term helps to redistribute vorticity from the boundary toward the interior of the gyre.

Balance in the slope area
The main source of cyclonic vorticity inside the gyre is related to the NL term, which helps transferring the vorticity from the boundary toward the inside. But which boundary regions are the main contributors of vorticity to the interior?
Several type of regions can be identified by looking at the dominant terms in the barotropic vorticity balance (Fig. 11): The western boundary areas in cyan, which include the Western Labrador Sea (WLS), Eastern Greenland (EG) and Eastern 320 Reykjanes Ridge (ERR); the eastern boundary regions in yellow, which include the Western Greenland (WG), the Western Reykjanes Ridge (ERR) and the eastern part of the Iceland Basin; and the Northwest regions in green, which include the extension of the Denmark Strait and Iceland Scotland overflows, and the northwestern part of the Labrador Sea.
The barotropic vorticity balance in the western boundary areas (cyan in Fig. 11) is close to the typical equilibrium of Western Boundary Currents (WBC) (Schoonover et al., 2016;Gula et al., 2015) with an equilibrium between the planetary vorticity 325 and the BPT. For the WLS, the deviation from WBC dynamics is small and is related to a bottom drag signal. We excluded the Southern part near Flemish Cap (48 • N, 46 • W) (not shown) where the dynamics is driven by a positive input of planetary vorticity and BPT balanced by the NL term. The case of the ERR is slightly different with no net meridional transport in this area. The main input of vorticity is provided by the NL term, which is related to inertial effects from the current following the Iceland Shelf. In this area the input of positive vorticity is mainly balanced by topography and the drag corresponding to a 330 local dissipation of vorticity. From this we can infer that western boundary areas do not provide cyclonic vorticity to the gyre interior.
Three regions (green in Fig. 11) have in common a dominant contribution from the bottom drag. Vertical sections of the mean along-stream current ( Fig. 12 (a),(c),(e)) in these areas reveal strong intensified bottom current (especially near the Iceland shelf and the Denmark Strait). In comparison, WBCs have a more surface intensified structure with reduced amplitudes near 335 the bottom (Fig. 12 (b),(d),(f)). In Fig. 12, vorticity balances are indicated. They differs from Fig. 11 because the integration is restricted to the boundary current, excluding recirculations. In Fig. 12 (a),(c),(e) the BPT amplitudes are reduced (and even change sign) compared to Fig. 11. This reflects the sensitivity of the vorticity balance on the location of the boundary on the continental slope. The -3 Sv contour used in Fig. 11 does not coincide everywhere with the top of the continental slope used in Fig. 12. 340 The dynamics in the extension of the Denmark Strait and Iceland Scotland overflows is a balance between the NL term and BDC, while in the Northwestern Labrador sea, the BDC balances the β-effect. As the BDC is the main sink of vorticity and only acts locally, no advection of positive vorticity toward the inside of the gyre can come from these locations.
In Eastern boundary regions (yellow in Figure 12), most of the cyclonic vorticity is provided by flow-topography interactions through the BPT and is balanced by the NL term. These regions are located where a strong eddy activity is observed ( Figure   345 5), which might be responsible for the high amplitude of the NL term. This negative NL signal implies an export of positive vorticity toward either the shelf or the gyre interior.

Characterisation of the nonlinear term
The NL term is locally important and balances the bottom pressure torque at small scales (Fig. 6). When integrated over the gyre it plays a role in exporting cyclonic vorticity from the boundary toward the interior of the gyre. The NL term is however 350 quite difficult to interpret as many processes are hidden inside the vertical and time integrals.
By decomposing the velocity in a barotropic and baroclinic part (u = u + u ) the NL advection term can be written as: where the barotropic part can be written as A(u, v) = uΩ x + vΩ y which is the advection of the barotropic vorticity by the barotropic flow. 355 We show these terms integrated over the slope area and interior (same as Fig. 10) in Fig. 13. Over the slope area, both terms are negative and contribute to export cyclonic vorticity. The barotropic part is much larger than its baroclinic counterpart and export most of the vorticity, as can be expected from the barotropic structure of the currents over the slope. In the interior, both terms are positive, corresponding to an input of cyclonic vorticity for the interior (Fig. 13), but the NL term is evenly divided between its barotropic and baroclinic contributions. The North West corner provides about half of this baroclinic NL input, 360 while the remaining part comes mostly from the South-Eastern boundary. The exchange of barotropic vorticity is only due to the barotropic NL term between the slope region and the interior. It is also possible to decompose the NL term into a time mean and eddy part by writing u = u + u * where • is the time average and the star denotes the fluctuation part. By putting this in the non linear operator A Σ we have: The ε part is the residue of the cross product and its value is negligible compared to both the mean and eddy parts.
When integrated over the slope area (Fig. 13), the eddy component dominates over the mean one. In the interior area, the supply of barotropic vorticity is also mainly due to the eddy component but the mean component contributes about a third of the total. Almost all of this mean signal is coming from the North West corner, consistent with Wang et al. (2017), while the eddy part is dominant over the rest of the interior. 370 We can identify several processes providing cyclonic barotropic vorticity to the subpolar gyre. The most important is the eddy contribution coming from the boundary area that is associated with a barotropic contribution. Barotropic vorticity is also provided through a mean-baroclinic signal coming from the NWC. In comparison, in the lower resolution simulation (not shown) most of the vorticity is advected inside the gyre by mean-barotropic processes but the amplitude of the NL term is cut by half. The nonlinear term is the main forcing for the interior part of the gyre, overcoming the effects of the wind curl and bottom 400 pressure torque. This is putting forward the failure of the classical Sverdrup balance or even of a topographic Sverdrup balance in the interior of the Subpolar gyre, and emphasizing the importance of the inertial effects to obtain a more realistic Subpolar gyre circulation.