RESEARCH ARTICLE
10.1029/2025JC022960
Key Points:
•		Eddy heat flux divergence along the Norwegian Atlantic Slope Current (NwASC) offsets more than 70% of heat flux convergence by the mean flow
•		Eddy heat flux divergence in the NwASC peaks subsurface and near the steep Lofoten Escarpment
•		Eddy heat flux divergence in the NwASC remains stable on interannual timescales, although there is strong seasonality
Supporting Information:
Supporting Information may be found in the online version of this article.
Correspondence to:
D. Jian, d.jian@uea.ac.uk
Citation:
Jian, D., Zhai, X., Stevens, D. P., & Renfrew, I. A. (2026). Oceanic heat transport along the Norwegian Atlantic Slope Current and the role of eddies. Journal of Geophysical Research: Oceans, 131, e2025JC022960. https://doi.org/10. 1029/2025JC022960
Received 4 JUN 2025
Accepted 13 JAN 2026
Author Contributions:
Conceptualization: Dong Jian, Xiaoming Zhai, David P. Stevens, Ian A. Renfrew
Formal analysis: Dong Jian
Funding acquisition: Dong Jian, Xiaoming Zhai, Ian A. Renfrew Investigation: Dong Jian, Xiaoming Zhai, David P. Stevens, Ian A. Renfrew Methodology: Dong Jian, Xiaoming Zhai, David P. Stevens, Ian A. Renfrew Supervision: Xiaoming Zhai, David P. Stevens, Ian A. Renfrew Visualization: Dong Jian
Writing – original draft: Dong Jian Writing – review & editing: Dong Jian, Xiaoming Zhai, David P. Stevens, Ian A. Renfrew

© 2026. The Author(s).
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Oceanic Heat Transport Along the Norwegian Atlantic Slope Current and the Role of Eddies
Dong Jian1 , Xiaoming Zhai1 , David P. Stevens2 , and Ian A. Renfrew1
1School of Environmental Sciences, University of East Anglia, Norwich, UK, 2School of Engineering, Mathematics and Physics, University of East Anglia, Norwich, UK
Abstract The poleward warm Atlantic Water and returning cold water in the Nordic Seas play a crucial role in regulating the Northern Hemisphere climate. While previous studies have recognized the importance of mesoscale dynamics, a quantitative assessment of the role of mesoscale eddies in poleward heat transport is lacking. Our study investigates the role of eddies in poleward oceanic heat transport in the Nordic Seas using an ocean model where eddies are well represented. Using a novel configuration of the MITgcm ocean‐ice model, we analyze 21 years of simulation. We show that eddy heat flux divergence offsets more than 70% of heat flux convergence induced by the mean flow along the Norwegian Atlantic Slope Current. Eddy heat flux divergence peaks at a depth of about 400 m near the thermocline and reaches a maximum near the steep Lofoten Escarpment. A temporal decomposition reveals that eddy heat flux divergence is stable on interannual timescales, although there is strong seasonality. Our study emphasizes the significant role of eddies in reducing poleward heat transport by diverting heat out of the Norwegian Atlantic Current into the Nordic Seas.
Plain Language Summary In the Nordic Seas, warm Atlantic water flows northward along the Norwegian coast and brings heat toward the Arctic. Using a high‐resolution ocean model, we analyze 21 years of data and find that eddies (swirls in the ocean) are responsible for more than two‐thirds of the total heat loss from the Norwegian Atlantic Slope Current. These ocean swirls divert heat zonally, especially westward near the steep slope off the Lofoten Islands along the northern coast of Norway, mainly below the surface and during winter. This heat leakage remains steady over the years and significantly reduces the amount of heat reaching the Arctic.
1.		Introduction
Oceanic heat transport by the North Atlantic Current toward the Arctic, and the return flow of cold water toward the equator, are crucial to climate (Chafik et al., 2025; Årthun & Eldevik, 2016). Its northernmost extension, the Norwegian Atlantic Current (NwAC), channels warm, saline Atlantic Water (AW) across the Greenland‐Scotland Ridge (GSR) into the Arctic. AW influences sea ice dynamics, biogeochemical cycles, and deep water formation in the Nordic Seas, processes critical to the Atlantic Meridional Overturning Circulation (Chafik et al., 2015; Chafik & Rossby, 2019; Tsubouchi et al., 2021). Despite its importance, the variability of NwAC and its downstream implications remain insufficiently understood (Smedsrud et al., 2022). A key factor in this uncertainty is the influence of mesoscale and submesoscale eddies, which are abundant along the AW pathways and are believed to modulate poleward heat transport, sea ice variability, and the Arctic heat budget (Isachsen et al., 2012; Årthun et al., 2012; von Appen et al., 2022).
Earlier studies used surface drifters to examine the NwAC and its subbranches, leading to the widely accepted three‐branch schematic of Atlantic inflow into the Nordic Seas (Hansen & Østerhus, 2000; Koszalka et al., 2011; Poulain et al., 1996). These branches include the North Icelandic Irminger Current (NIIC), the Norwegian Atlantic Front Current (NwAFC), and the Norwegian Atlantic Slope Current (NwASC), which transport Atlantic inflow across the GSR, as schematized in Figure 1. Subsequent work has revealed strong topographic constraints through subsurface drifters and mid‐depth RAFOS floats (Rossby, Prater, & Søiland, 2009; Søiland et al., 2016). Although these Lagrangian tracers have provided useful information on large‐scale circulation, their nonuniform spatiotemporal sampling limits their ability to fully resolve mesoscale variability, particularly in regions with strong seasonal fluctuations (Isachsen et al., 2012). Satellite altimetry offers near‐global coverage; however, its coarse resolution and the smoothing required to reduce noise introduce limitations in eddy detection in the Nordic Seas (Bashmachnikov et al., 2023; Chelton et al., 2011).

Figure 1. Model domain, horizontal grids (sampled at every 8 × 8 points), bathymetry, and schematized surface circulation of the Nordic Seas. Horizontal resolution gradually increases from 4.5 to 1 km poleward, as labeled on the map. Red arrows show the three main Atlantic Water (AW) inflow branches: the North Icelandic Irminger Current, the Norwegian Atlantic Front Current, and the Norwegian Atlantic Slope Current. A minor coastal inflow via the European Shelf is omitted due to its small volume and different origin. The northward flow in the Fram Srait is referred to as the West Spitsbergen Current. As AW circulates through the Nordic Seas, portions recirculate and return southward along the East Greenland Current (EGC, shown in blue arrow). Key sections including the Greenland‐Scotland Ridge, the Barents Sea Opening, the Fram Strait, and other bathymetry features are labeled.

Although both the NwAFC and NwASC feature eddy generation, the strongest eddy activity and the densest in situ measurements occur along the eastern NwASC (Fer et al., 2020; Huang et al., 2023; Orvik, 2022; Orvik & Niiler, 2002). The NwASC is tightly constrained by topography along the Norwegian continental slope and can be traced northward toward the Arctic. In contrast, the NwAFC is a shallower and more variable baroclinic jet; its pathway and northward continuity along the Mohn Ridge remain debated (Orvik & Niiler, 2002; Ypma et al., 2020); its dynamical role is often framed as maintaining the hydrographic front between warm AW in the Norwegian Sea and colder water in the Greenland Sea, rather than the heat supply toward the Arctic (Håvik et al., 2017). Hence, we focus on the onshore slope branch, the NwASC.
Realistic ocean models with ∼4 km horizontal resolution can partially resolve mesoscale dynamics, such as the quasi‐permanent Lofoten Vortex in the Lofoten Basin (Volkov et al., 2015). However, slightly coarser models (∼4.5 km) struggle to consistently represent the Lofoten Vortex and heat distribution (Wekerle, Wang, Danilov, et al., 2017; Treguier et al., 2021). This limitation may arise from the inability to fully resolve the Rossby radius of deformation north of ∼60°N, which has average annual and regional values ranging from 4.3 km in the Iceland Sea to 6.9 km in the Norwegian Sea (Nurser & Bacon, 2014). Following Hallberg (2013), resolving mesoscale eddies requires at least two grid points per Rossby radius, implying targeted horizontal spacings of ∼2–3.5 km.
Compounding these challenges are uncertainties in oceanic boundary conditions, atmospheric forcing, and bathymetry representation, which may distort key fields and dynamics, such as volume transport across the GSR, the NwAFC, sea surface temperature (SST), marginal sea ice, and overflow (Huang et al., 2023; Treguier et al., 2021). Although localized eddy‐resolving models (∼800 m) have been applied to specific regions such as the Lofoten Basin and the Fram Strait (FS) (Hattermann et al., 2016; Trodahl et al., 2020), it is desirable to better capture mesoscale processes on a basin‐wide scale. Increasing model resolution to explicitly resolve eddy fluxes is essential to advance the understanding of regional ocean dynamics in the Nordic Seas (Spall, 2010; Spall, 2011; Wekerle, Wang, von Appen, et al., 2017).
Recent observational and numerical studies present conflicting perspectives on oceanic heat transport in the Nordic Seas. For example, Tsubouchi et al. (2021) use a mass‐balance inverse model and report increased heat transport into the Nordic Seas after 2001, while observational records at the Svinøy section indicate no long‐term trend, but rather fluctuations in different phases (Orvik, 2022). The contrasting perspectives arise from the intrinsic limitations of each methodology. Observations often suffer from nonuniform spatiotemporal coverage and are typically limited to a few monitoring locations (Isachsen et al., 2012; Orvik, 2022), making it challenging to capture the full variability of Atlantic inflow. On the other hand, numerical approaches, such as data‐ assimilated reanalysis, mass‐balanced inverse model, or one‐dimensional mixed layer models, often lack the resolution or physical representation needed to fully diagnose mesoscale processes (Asbjørnsen et al., 2019; Huang et al., 2023; Treguier et al., 2021; Tsubouchi et al., 2021).
Despite these methodological differences, there is a consensus that oceanic heat transport in the Nordic Seas exhibits strong interannual to decadal variability, driven by changes in volume transport, temperature anomalies, and associated atmospheric forcing (Asbjørnsen et al., 2019; Smedsrud et al., 2022; Årthun & Eldevik, 2016). This variability underscores the complexity of the subarctic heat budget and highlights the need for a deeper understanding of heat transport mechanisms in the region. Although previous studies have recognized the importance of eddies in heat transport (Huang et al., 2023; Isachsen et al., 2012), their conclusions are either drawn from surface fluxes during winter or inferred from the differences between observations and model. A rigorous, closed heat budget is lacking due to challenges in ocean modeling for this region. A realistic, heat‐ balanced, high‐resolution model is therefore needed to assess how eddy‐induced heat transport compares to air‐sea heat fluxes and heat transport by the mean flow.
In this study, we aim to assess the role of eddies in poleward oceanic heat transport, using a high‐resolution ocean‐ ice coupled model of the Nordic Seas. Our approach integrates state‐of‐the‐art atmospheric forcing and optimized boundary conditions to minimize biases in SST, sea ice extent, and volume transport. The key novelties are as follows:
1.		We apply cosine‐weighted horizontal grids to increase horizontal resolution from 4.5 to 1 km toward higher latitudes (Figure 1). This approach aligns horizontal resolution with the latitudinal contraction of the first baroclinic Rossby radius (Chelton et al., 2011), which governs the scale of eddies. It also avoids elongated grid cells in high latitudes and is thus superior to existing models using regular longitude/latitude grids. The improved horizontal resolution enables the model to skillfully simulate an eddying field (Figure S1 in Supporting Information S1).
2.		We focus on an 80‐km‐wide corridor along the NwASC, capturing eddies generated by the mean current before migrating into interior basins. Although previous analyses emphasize heat content in the broader AW domain or budgets across key gateways (Asbjørnsen et al., 2019; Tsubouchi et al., 2021; Årthun & Eld- evik, 2016; Østerhus et al., 2019), our work addresses akey gap by focusing on lateral eddy‐driven processes. These are hypothesized to be important, as inferred by a mixed‐layer model and coarse‐resolution data (Bashmachnikov et al., 2023; Huang et al., 2023), but a solid budget analysis using a realistic simulation in the Nordic Seas is lacking.
3.		We disentangle the eddy‐driven heat convergence from other parts using budget analysis and Reynolds decomposition. The methods enable a robust, quantitative assessment of the spatial distribution and temporal variability of eddy contributions. In doing so, we build upon and extend earlier studies focused primarily on the Lofoten Basin (Isachsen et al., 2012; Volkov et al., 2015), by embedding the heat budget within a high‐ resolution ocean model that provides greater spatial coverage and longer temporal duration.
2.		Data and Methods
2.1.		Model
Our Nordic Seas model uses a regional configuration of the Massachusetts Institute of Technology General Circulation Model (MITgcm; Marshall et al. (1997)), coupled with the sea ice model (Losch et al., 2010). The horizontal grids adopt cosine‐weighted latitudinal spacings to gradually increase resolution from 4.5 to 1 km poleward, which is finer than the local Rossby radius in deep basins estimated by Nurser and Bacon (2014). Vertically, the model has 72 layers, with thickness ranging from 2 m at the surface to 150 m at depth, using a rescaled z* coordinate that accounts for free surface displacement (Adcroft et al., 2004). It employs the equation of state by McDougall et al. (2003), bulk formula for calculating surface fluxes, and K‐profile parameterization for vertical mixing (Large et al., 1994). Additionally, bottom drag coefficients, which vary according to topographic roughness, are applied.
Initial and open boundary conditions are obtained from the global 1/12°reanalysis GLORYS12V1 (Jean‐Michel et al., 2021) for oceanic variables and TOPAZ4 (Xie et al., 2017) for sea ice. Both data sets have assimilated observational data and are available at daily temporal resolution. Atmospheric forcing uses hourly ERA5 data for heat and momentum (Hersbach et al., 2020). A comprehensive evaluation of surface meteorology and fluxes over the Iceland and Greenland Seas in ERA5 suggests that it performs well (Renfrew et al., 2021). Freshwater fluxes from Bamber et al. (2018) are evenly scaled from monthly to daily resolution. These fluxes cover only Greenland and are supplemented with JRA55‐do data (Tsujino et al., 2018) to fill data gaps in other regions. No surface restoration is applied. Bathymetry is obtained from the high‐resolution RTopo‐2.0.4 (Schaffer et al., 2019).
The model is initialized in August 1993 from reanalysis products in a near‐balanced state and undergoes a 2.5‐ year spin‐up period to allow the ocean dynamics to adjust. All subsequent analyses are insensitive to this spin‐up period. Five‐day averaged diagnostics together with snapshot fields taken every 5 days are saved for analysis, following Piecuch (2017). The results presented below are based on 21 years of model output, from 1996 until model completion at the end of 2016.
2.2.		Observations
Observational data sets across multiple scales and locations are used to validate the model performance. On large scales, we compare simulated surface circulation, SST, and sea ice extent from gridded products, including surface geostrophic velocities from SSALTO/DUACS altimetry (Pujol et al., 2016) and SST/sea ice extent from the OSTIA reanalysis (Good et al., 2020). Local‐scale validation uses AW volume transport measurements across the GSR (Østerhus et al., 2019) and long‐term moored measurements from the Svinøy section (Orvik, 2022), as well as downstream validations across the Barents Sea Opening (BSO) and the FS.
On basin scales (Figure 2), the model successfully reproduces the three branches of AW inflow, including the NIIC, the offshore NwAFC, and the onshore NwASC. It also captures key mesoscale features, such as the quasi‐ permanent Lofoten Vortex. Time‐mean surface currents and SST compare well with gridded products. Seasonal sea‐ice extent is also realistic, with 30% concentration isolines for March (orange) and September (green) closely matching satellite observations. Although amplitude differences are expected owing to the smoothing and effective coarse resolution of gridded altimetry, the surface geostrophic eddy kinetic energy (EKE) exhibits the observed spatial pattern. The elevated EKE mainly occurs along AW pathways and quiescent areas in the Greenland and Iceland Sea, agreeing with mooring‐based EKE estimates (von Appen et al., 2022).
At local scales (Figure 3), the simulated AW volume transport across the GSR is consistent with mooring‐based estimates (Østerhus et al., 2019). We acknowledge that the AW volume transport is calculated across full‐depth monitoring sections (thick blue lines in Figure 2a) with a criterion of temperature T > 4°C, following Rossby et al. (2018), whereas observational estimates are based on moorings calibrated with altimetry. Alternative land‐ to‐land estimates across the GSR yield comparable results (not shown). The model also reproduces temperature and velocity anomalies at 100 m depth near the Svinøy section with high fidelity, capturing both seasonal cycles and interannual variability, in agreement with in situ measurements (Orvik, 2022). Additional downstream validations across the BSO and the FS also compare favorably with observations (Figure S2 and S3 in Supporting Information S1). Together, these assessments indicate that the model skillfully represents the large‐scale circulation and the local temperature/velocity variability required to diagnose oceanic heat transport along the NwASC.

Figure 2. (a) Observed and (b) modeled time‐mean (2008–2013) sea surface temperature and surface geostrophic velocity. Orange and green contours mark the 30% monthly mean sea ice concentration in March and September, respectively. The northward flow along the Norwegian Atlantic Slope Current is outlined in a gray “strip” region and is further segmented into three subdomains based on topography; Thick blue lines denote sections used to estimate Atlantic Water volume transports shown in Figure 3, where the long‐term in situ monitoring has been established. Svinøy section is marked with a green cross. (c) Altimeter‐based and (d) model‐simulated surface geostrophic eddy kinetic energy (EKE) averaged between 2008 and 2013. EKE definition follows Reynolds decomposition that removes seasonal climatological cycle, as described in the Methods section. A log10 scale is applied to the EKE color bar.

2.3.		Methods
2.3.1.		Study Region
The study region is denoted in a gray “strip” in Figure 2. We first identify surface velocity maxima along the current and then extend the domain zonally to 80 km width, ensuring the inclusion of the mean current. A sensitivity test with a 50 km width shows that the findings are not affected by our choice (Table S1 in Supporting Information S1). The chosen north‐south extent focuses on the basin scale and remains sufficiently distant from the model boundaries. This targeted region allows for the isolation of lateral heat advection and eddy fluxes generated by the current. Given that the northward flow is topographically steered and bounded by the Norwegian continent, the BSO, and the Svalbard Archipelago, the study region is further segmented into three subdomains based on topography: Norwegian Shelf, Norway‐to‐Svalbard, and Svalbard Shelf. These subdomains are depicted in Figure 2a.

Figure 3. (a) Modeled Atlantic Water (AW) volume transport across the Greenland‐Scotland Ridge, compared to long‐term observational estimates (summation of three branches AW inflows measured across three sections) from January 1996 to July 2016 (Østerhus et al., 2019). The AW criterion used is temperature T > 4°C. (b) Modeled temperature and (c) velocity anomalies at 100 m depth near the Svinøy section, compared to long‐term moored measurements (Orvik, 2022). All time series are smoothed with a 3‐month running mean. Summary statistics are provided.

2.3.2.		Volume and Heat Budget
We assess the heat budget within a finite, full‐depth control volume bounded by four vertical transects, referred to as the “strip.” To facilitate the interpretation of the heat budget, we first introduce the volume conservation constraint. Starting with the mass continuity equation:
∇ ⋅ V = 0,
where ∇⋅ is the divergence vector operator and V is the three dimensional velocity vector. Integrating over the control volume V and applying the divergence theorem, Equation 1 becomes:

∇ ⋅ V dV =

∫V⋅
A

n dA = 0,

where n is the outward unit normal vector on the control area A, which is bounded by six walls: the southern, northern, western, and eastern vertical boundaries, the ocean surface, and the ocean bottom. Volume transport across the ocean bottom is zero and can be dropped. Although we retain the surface term for completeness, it can be neglected because the surface vertical velocity resulting from the net freshwater fluxes (precipitation–evaporation + runoff) is very small. The discrete form of the volume budget is:
∫V⋅ndA + ∫V⋅ndA + ∫V⋅ndA + ∫V⋅ndA + ∫V⋅ndA =0. ⏟̅̅⏞⏞̅̅⏟ ⏟̅̅⏞⏞̅̅⏟ ⏟̅̅⏞⏞̅̅⏟ ⏟̅̅⏞⏞̅̅⏟ ⏟̅̅⏞⏞̅̅⏟

South

North

West

East	Surface

Figure 4. (a) Time series and (b) time‐mean of volume budget closure for the “strip.” (c) Time series and (d) time‐mean of heat budget closure for the “strip.” (e) Time series and (f) time‐mean of oceanic heat transport convergence across four lateral boundaries with Tref = 0°C. All time series are smoothed using a 12‐month running mean. The “strip” is shown in the right panels and gray dots mark the three subdomains introduced in Methods.

The temporal evolution for each term in Equation 3, along with the total convergence, is explicitly plotted in Figure 4a and demonstrates that the volume budget is closed. This ensures that the heat budget is evaluated in a volume‐conserving domain.
The heat budget is derived from the conservation of temperature, given by:
∂T
ρCp ∂t = ρCp [-∇ ⋅ (VT) - ∇ ⋅ Fdiff] + Qatm,
where ρ is seawater density, Cp is specific heat capacity, and T is potential temperature. This equation states that temporal changes in temperature within a grid cell are balanced by the divergence of advective heat fluxes (-∇ ⋅ (VT)), the divergence of diffusive fluxes (-∇ ⋅ Fdiff), and the net air–sea heat fluxes Qatm. The heat diffusion term represents explicit and parameterized diffusive mixing processes and the atmospheric term includes both turbulent and radiative fluxes. Integrating over the control volume V yields:

ρCp∫ ∂T dV = ρCp∫ -
V ∂t	V

∇⋅(VT)dV+ρCp

- ∇ ⋅ Fdiff dV +

∫Qatm dS, S

hereafter we drop the heat diffusion term because its volume integration is minimal and can be neglected, as demonstrated in Figure 4c. Applying the divergence theorem to the control volume yields:

ρCp∫V∂∂TtdV=ρCp ⏟̅̅̅̅⏞⏞̅̅̅̅⏟	⏟̅̅̅
OHC tendency
∫VT⋅ndA +ρCp∫VT⋅ndA +ρCp∫VT⋅ndA
South	North	West
+ρ
p∫VT⋅ndA+ ∫Qatm dS, S
̅̅̅̅̅̅̅⏞⏞̅̅̅̅̅̅̅⏟ ⏟̅⏞⏞̅⏟
East	Surface
(6)

where the left‐hand side represents the heat content tendency in a closed volume, balanced by the right‐hand side: convergence of advective oceanic temperature fluxes across four lateral boundaries and integrated air‐sea fluxes over the surface S. The temporal evolution for each term and the residual is explicitly plotted in Figure 4c to demonstrate heat budget closure. Note that oceanic heat transport across individual boundaries adopts a reference temperature Tref = 0°C for simplicity, following previous observational practices and modeling works (Rossby et al., 2018; Smedsrud et al., 2022; Årthun et al., 2012). This enables a direct comparison with observational estimates. Alternative choices of Tref would shift the calculated values by an amount of ±ρCp ∫ VTref ⋅ n dA, but the total convergence/divergence is independent of the choice of reference temperature. We thus primarily frame the interpretation in a convergence/divergence framework. Note that “heat convergence” is used in the figures, while in the text we distinguish between “heat convergence” (positive values) and “heat divergence” (negative values).
2.3.3.		Reynolds Decomposition
We apply standard Reynolds decomposition to distinguish the eddy contributions to the heat budget. This method separates the potential temperature T and velocity vector V into their seasonal climatological cycle (denoted by a subscriptclim) and fluctuating components (denoted by a prime ′):
T=Tclim+Tʹ,V=Vclim+Vʹ. (7)
Here the seasonal climatological cycle uses 21‐year (1996–2016) averages over December–February (DJF), March–May (MAM), June–August (JJA), and September–November (SON). In doing so, we establish a baseline that minimizes variability from interannual anomalies and emphasizes deviations from the steady state. This approach allows us to effectively isolate and analyze the contributions of mesoscale eddies to heat transport in the long term. Inserting Equation 7 in the oceanic advective heat transport term and applying temporal averaging over 1996–2016 (denoted by 〈〉) yields:
ρCp∫ 〈∂T〉 dV = ρCp∫ - ∇ ⋅ 〈Vclim Tclim〉 dV + ρCp∫ - ∇ ⋅ 〈VʹTʹ〉 dV + ∫〈Qatm〉 dS.
V ∂t	V	V	S
⏟̅̅̅̅̅̅⏞⏞̅̅̅̅̅̅⏟	⏟̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ̅⏞⏞̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ̅⏟	⏟̅̅̅̅̅̅̅̅̅̅̅̅̅̅⏞⏞̅̅̅̅̅̅̅̅̅̅̅̅̅̅⏟ ⏟̅̅̅⏞⏞̅̅̅⏟
OHC tendency	Mean	Eddy	Air‐sea fluxes
Here, the OHC tendency is balanced by seasonal climatological mean, eddy components, and air‐sea fluxes. The cross terms, for example, 〈VʹTclim〉 and 〈VclimTʹ〉, vanish because the temporal average of deviation components, for example, 〈Vʹ〉, is zero. Over long‐term averages, the ocean can be considered in steady state, such that the time‐mean OHC tendency is small and can be neglected, yielding a balance between the last three terms.
3.		Results
3.1.		Budgets Closure
The net volume convergence within the “strip”, resulting from lateral and surface volume fluxes, remains near zero over the full record, confirming volume conservation (Figure 4a; 12‐month running mean applied). The dominant inflow occurs through the southern (red) and western (blue) boundaries, with the core of the NwASC via the southern boundary providing the bulk of volume import. The eastern (cyan) and northern (magenta) boundaries show relatively stable outflow. The anti‐phase relationship between boundary fluxes indicates temporal variations in current orientation and path, likely associated with meanders; for instance, around 2014, a reduction in southern inflow is offset by an increase along the western boundary. Nevertheless, the near‐zero
Table 1
Heat‐Budget Closure and Decomposition for the Norwegian Atlantic Slope Current Strip (TW)
Region	Advective heat convergence	Air‐sea heat fluxes	Eddy/Mean (%)	Air‐sea/Mean (%)	
	Mean(W/E/S/N)	Eddy(W/E/S/N)	Total(W/E/S/N)				
Norwegian Shelf	35(-2/ 19/ 110/ - 92)	-29(-30/ - 1/2/0)	6(-32/ 18/ 112/ - 92)	-6	-83%	-17%	
Norway to Svalbard	22(54/ - 72/92/ - 52)	-14(-8/ - 5/0/ - 1)	8(46/ - 77/ 92/ - 53)	-8	-64%	-36%	
Svalbard Shelf	10(-4/ - 3/ 52/ - 35)	-6(-6/ - 1/ 1/0)	4(-10/ - 4/ 53/ - 35)	-4	-60%	-40%	
Whole NwASC “strip”	67(48/ - 56/ 110/ - 35)	-49(-44/ - 7/2/0)	18(4/ - 63/ 112/ - 35)	-18	-73%	-27%	
Note. (i) Advective heat convergence Total = Mean + Eddy. Values are time means over 1996–2016. (ii) Heat fluxes across boundaries are listed as (West/East/South/ North), computed relative to Tref = 0°C. The convergence is independent on reference temperature. (iii) Eddy/Mean = 100% × Eddy/ Mean; Air‐sea/ Mean = 100% × Air ‐ sea/ Mean.

volume convergence confirms volume closure over time. The time‐mean volume budget for 1996–2016 (Figure 4b) shows net inflows of 3.2 Sv (1 Sv = 1 × 106 m3/ s) from the south and 2.3 Sv from the west, balanced by net outflows of 3.5 Sv to the north and 2.0 Sv to the east.
The temporal evolution of heat budget terms demonstrates heat closure within the volume‐conserving “strip” (Figure 4c). After applying a 12‐month running mean to remove the seasonal cycle, interannual variations in ocean heat content (OHC; orange) are balanced by ocean heat convergence (black) and net air‐sea fluxes (green), yielding a negligible residual (gray). Interannual variability in OHC is primarily driven by advective heat convergence (correlation coefficient r = 0.90), whereas its correlation with the net air‐sea fluxes is weaker (correlation coefficient r = 0.44). The time‐mean heat budget over 1996–2016 (Figure 4d) reveals that an average oceanic heat convergence of 18 TW within the “strip” is balanced by an equivalent 18 TW of net heat loss to the atmosphere, yielding a negligible long‐term OHC change.
The advective heat convergence in a volume‐conserving domain is independent of the reference temperature. However, to diagnose the source contributions to this convergence, we partition the 18 TW heat convergence into heat fluxes across boundaries using a reference temperature of 0°C. The largest contribution arises from the southern boundary (red), which delivers the bulk of poleward heat transport. The western boundary (blue) is more variable, showing both positive and negative values depending on the year. In contrast, the eastern (cyan) and northern (magenta) boundaries display relatively weak and stable heat fluxes over time (Figure 4e). Time‐mean contributions to the 18 TW total ocean heat convergence are: +112 TW from the south, +4 TW from the west, -35 TW to the north, and -63 TW to the east. Note that heat transports across lateral boundaries, calculated relative to 0°C for consistency with observation‐based estimates, sum to the total convergence of +18 TW; in this context, 112 TW of time‐mean heat poleward from the southern boundary of the “strip” is consistent with observational time‐mean estimates of 126 TW measured across the upstream Svinøy section (Skagseth et al., 2008), and 140 TW farther upstream at the Faroe–Shetland Channel (Hansen & Østerhus, 2000). While the choice of reference temperature alters the magnitude of individual boundary heat fluxes, the net advective heat convergence within a volume‐conserving domain remains invariant.
3.2.		Reynolds Decomposition
Applying Reynolds decomposition to total heat transport convergence in a finite controlled volume, total heat transport is partitioned into climatological mean and eddy components (Equation 8). Within the “strip” and its subdomain, the heat budget reflects a three‐way balance between heat convergence by mean flow, eddy‐induced heat divergence, and local surface heat loss to the atmosphere, providing a quantitative assessment of the relative importance of each term in different regimes (Table 1).
Over the whole NwASC “strip,” the advective heat convergence by the mean flow ( +67 TW) is largely offset by eddy heat flux divergence (-49 TW), leading to anet convergence of +18 TW that is balanced by -18 TW of net air–sea heat loss. This closed budget highlights the critical role of mesoscale eddies in laterally exporting heat and reducing 73% of the warming brought by mean flow heat convergence, which is ∼2.7 times the heat loss induced by air‐sea fluxes.
Among the subdomains, the most significant eddy heat flux divergence appears along the Norwegian Shelf subdomain (-29 TW). Eddy heat flux divergence gradually decreases northward, along with the weakening mean heat convergence, suggesting progressive cooling of the poleward heat through eddy and atmospheric processes. The heat loss due to eddy and atmospheric fluxes is evaluated relative to the heat gain from mean flow heat convergence. The resulting ratios indicate that eddies are more effective than local air–sea fluxes in removing heat from the mean current, with eddy‐induced cooling exceeding atmospheric heat loss by a factor of 1.5–2.5 depending on subdomain. Overall, eddy‐induced heat leakage plays a leading role in regulating ocean heat loss along the NwASC.
3.3.		Spatial Pattern
The spatial structure of the full‐depth integrated horizontal convergence of the advective heat fluxes is shown for (a) the mean flow, (b) the eddy component, along with (c) air‐sea heat fluxes and (d) eddy heat flux vectors (Figure 5). Positive values indicate net full‐depth column warming, negative values cooling. The eddy heat vectors indicate the horizontal direction and relative magnitude of eddy temperature transport. While our primary focus is on lateral processes within the defined “strip”, additional diagnostics confirm that volume and heat budgets are also closed over the broader eastern Nordic Seas (5°W–20°E, 60–80°N, Figure S4 in Supporting Information S1), supporting the interpretation of the mapped patterns beyond the “strip” itself.
The eddy heat flux divergence generally mirrors the heat convergence by the mean flow but with the opposite sign, at roughly 70% of its magnitude. Here we focus on the interpretation of the eddy component. The eddy heat flux divergence induced cooling is dominant along the NwASC, captured mainly within our defined “strip,” as well as less significant cooling elsewhere indicated by blue patches. The eddy‐induced warming appears on the western flank of the “strip”, particularly west of the Norwegian Shelf and the Svalbard Shelf subdomain. A pronounced eddy‐driven warming maximum occurs west of the Lofoten Islands/Lofoten Escarpment, indicating a primary pathway that transfers heat out of the slope current and into the interior basin. This hot spot is consistent with prior in situ and modeling studies of eddy activity in the region (Fer et al., 2020; Isachsen et al., 2012; Köhl, 2007).
The time‐mean net air–sea heat fluxes reveal surface cooling over the broad eastern Nordic Seas. The strongest cooling occurs over the northern Norwegian Sea and the FS, and slight warming appears over the Iceland and Greenland Sea, consistent with ERA5 data and previous model results (Spall et al., 2021). Integrating over the “strip” gives consistent numbers: the eddy heat flux divergence of -49 TW largely offsets the mean flow heat flux convergence of 67 TW, leaving 18 TW balanced by the net air–sea heat loss over the “strip.” In comparison, an integration over the central Lofoten Basin (2°W–10°E, 68.5–72°N, constrained by the 3,000 m isobath) yields eddy heat flux convergence of 10.5 TW, heat flux divergence by the mean flow of -2.5 TW, resulting in 8 TW that is balanced by a net air–sea heat loss of ∼8 TW, closing the local heat budget. Hence, the heat resident in the central Lofoten basin is mostly brought by the eddy component rather than the mean flow component (10.5 TW vs. -2.5 TW), and is then lost to the atmosphere. This heat stored in the Lofoten Basin resulting from the eddy heat flux convergence must be replenished by the eddy heat flux divergence from the lateral boundary currents, both the NwAFC and the NwASC, with a major contribution from the onshore NwASC indicated by the vector map.
While quantitative warming/cooling is assessed with the convergence/divergence map (Figure 5b), the qualitative indicators of preferred lateral eddy transport pathways and magnitude can be noticed from eddy heat flux vectors (Figure 5d), as discussed in previous studies (Isachsen et al., 2012; Spall, 2010). Itis important to note that the flux vectors are visually useful to suggest preferred eddy pathways, but their rotational component does not alter the temperature (Isachsen et al., 2012). The vector map exhibits two distinct branches, one following the NwAFC, another following the NwASC, consistent with upper‐layer circulation schematics of the Nordic Seas (Orvik & Niiler, 2002). It indicates time‐mean eddy transport pathways within the AW domain, with evident lateral exchanges between NwASC and NwAFC. The offshore branch generally follows the ridge system northward, aligned with the Arctic front, where warm and saline AW in the Norwegian Sea interacts with cold and fresh Arctic Water in the Greenland Sea (Raj et al., 2019). Notably, westward eddy heat flux vectors along the NwASC point from areas of eddy heat flux divergence (blue patch; cooling) to areas of eddy heat flux convergence (red patch; warming). Those eddy heat flux vectors are preferentially oriented westward as the boundary current flows along the slope. In particular, the vectors along the Norwegian Shelf point nearly normal to the western boundary

Figure 5. Full‐depth integrated horizontal convergence of the advective heat fluxes for (a) the mean flow
(ρCp ∫ - ∇ ⋅ 〈Vclim Tclim〉 dz) and (b) the eddy component (ρCp ∫ - ∇ ⋅ 〈VʹTʹ〉 dz). (c) Time mean net air‐sea fluxes (Qatm). (d) Full‐depth integrated eddy heat flux vectors (ρCp ∫ 〈VʹTʹ〉 dz).

of our defined “strip”, consistent with the significant eddy temperature fluxes reported in Table 1. A dominant route extends from the Lofoten Escarpment (∼69°N) to the quasi‐permanent Lofoten Vortex in the Lofoten Basin. This pathway likely maintains the longevity of the Lofoten Vortex, as evidenced by models, surface drifters, mid‐ depth RAFOS floats, and altimetry (Andersson et al., 2011; Köhl, 2007; Koszalka et al., 2011; Søiland et al., 2016; Volkov et al., 2015). The primary eddy pathway diverts westward from the Lofoten Escarpment, with secondary branches veering into the basin north of Lofoten Island, in agreement with established gyre circulation

Figure 6. (a) Vertical profiles of heat flux convergence for the mean flow (orange) and eddy component (blue) averaged over the “strip”; positive denotes convergence (warming), negative divergence (cooling). (b) Eddy heat flux divergence averaged along an 80 km‐wide zonal extent and depth. Vertical profiles of time‐mean (c) temperature, (d) temperature anomaly variance, and (e) eddy kinetic energy averaged along an 80 km‐wide zonal extent following the path of the Norwegian Atlantic Slope Current. The latitudes of three subdomains are labeled.

patterns. Eddy heat fluxes near FS are mainly westward, indicating eddy‐induced westward advection of heat/ temperature (Hattermann et al., 2016; Hofmann et al., 2021).
Eddy heat flux vectors include not only cross‐stream (lateral exchange) but also along‐stream (up‐ or down‐ gradient) components. In most places they align with the mean current, reflecting down‐gradient fluxes associated with baroclinic instability. However, in the southern NwASC, eddy heat fluxes oppose the northward mean flow. A similar pattern appears in an idealized Nordic Seas model (Figure 11 horizontal eddy temperature flux at 275 m depth in Spall (2010)) but was not discussed, suggesting that this is a robust feature. Our diagnostics indicate that those counter‐stream oriented fluxes are predominantly subsurface, likely associated with thermocline slope at depth. We put an explanation forward in the next section.
3.4.		Depth Dependence
To quantify its vertical structure and latitudinal dependence, we diagnose eddy heat‐flux convergence/divergence as a function of depth and latitude (Figures 6a and 6b). Eddy‐induced heat flux divergence (blue) peaks at intermediate depths (∼450 m) rather than at the surface. The depth of maximum heat convergence by mean flow (orange) is shallower, displaying double maximum in the mean profile. This is because the profile is averaged along the full path of the current, which bifurcates near BSO, producing two zones of enhanced convergence. In depth dimension, the heat flux convergence by mean flow slightly exceeds the eddy heat flux divergence, consistent with the volume integrated heat budget. Latitudinally, the eddy heat flux divergence is largest and most variable along the Norwegian Shelf subdomain, with pronounced extrema near the steep Lofoten Escarpment, which gradually weakens northward toward Svalbard.
The vertical and latitudinal structures align with both observational and modeling studies. Lagrangian studies report that a greater proportion of subsurface RAFOS floats, compared to surface drifters, have entered the Lofoten Basin from the NwASC (Rossby, Ozhigin, et al., 2009). Modeling studies have found that the eddy fluxes examined in the Lofoten Basin supplying heat from the NwASC are centered at approximately 700 m depth (Dugstad et al., 2019), indicating a deepening process that features merging and vertical stacking of lighter eddies en route (Trodahl et al., 2020). These findings imply that eddies generated along the slope current have subsurface‐intensified cores that gradually deepen as they propagate into the basin interior, where they act to cool the upper warmer ocean brought by the heat convergence by mean flow.
To explain the ∼400 m subsurface maximum in eddy heat flux divergence, we examine vertical profiles of time‐ mean temperature, temperature anomaly variance, and EKE averaged over 80 km zonal extent of the NwASC domain (Figures 6c–6e). There are two distinct regimes, separated by a transition. Between 65°N and 72°N, the thermocline gradually deepens, along with the peaks in temperature anomaly variance and EKE. North of 72°N, extending to about 78°N, the thermocline shoals (upshoaling pattern) and the temperature anomaly variance and EKE weaken. Observational hydrographic data corroborate this deepening‐to‐shoaling transition. Huang et al. (2023) present the vertical profiles of temperature (300–550 m; in their Figure 2a) and salinity (their Figure S2a in Supporting Information S1) that confirm the deepening‐shoaling pattern.
Between 300 and 700 m depth south of 72°N, elevated temperature anomaly variance indicates vigorous eddy activity and enhanced mid‐depth eddy‐induced heat transport, as eddies redistribute warm and cold heat anomalies laterally. While surface forcing and mixed‐layer variability imprint temperature variance in the top upper ocean, it is at intermediate depths where eddy stirring of the thermoclines/isopycnals is most effective. This corresponds to the steep vertical temperature gradient ∂T/∂z around the 400–500 m depth range (Figure 6c), where baroclinic instability can efficiently convert mean potential energy into eddy energy. EKE is also significantly elevated slightly downstream of the Lofoten Escarpment (69–72°N), consistent with the idea that eddies require some growth and advection before reaching peak intensity. This region, a known hotspot of baroclinic instability (Fer et al., 2020), also exhibits the deepest thermocline and strongest temperature variability at depth, underscoring a tight coupling between eddy dynamics and subsurface heat transport.
This two‐regime structure along the NwASC is indicative of eddy heat vectors along the stream presented earlier in Figure 5d. Baroclinic instability extracts potential energy from the mean flow and transfers it into both EKE and eddy potential energy (Vallis, 2017). A central manifestation is the down‐gradient eddy temperature/buoyancy flux, such that the horizontal temperature flux changes sign across the thermocline. This means that the eddy temperature flux vector in the vertical dimension is southward above the thermocline and northward below, that is anticlockwise south of 72°N. This leads to net southward temperature fluxes, opposing heat transport carried by the northward mean flow. This pattern reverses north of 72°N as the thermocline reverses its slope; eddy heat flux vector is northward above the thermocline and southward below, which leads to net northward heat transport.
3.5.		Temporal Variability
To study how the eddy processes modulate the heat budget through time, we examine seasonal and interannual variability in eddy heat flux divergence within the “strip” (Figures 7a and 7b). The volume‐integrated eddy heat flux divergence within the “strip” is shown every five days (blue) and a 12‐month running mean (orange). Interannual variability is taken from the 12‐month running mean; the seasonal variability is shown as monthly climatology over 1996–2016.
The five‐day time series is highly intermittent, with bursts occasionally exceeding -100 TW, reflecting synoptic variability embedded in eddy shedding or meandering events. Despite this high frequency variability, the 12‐ running mean remains at around -49 TW, suggesting limited interannual variability. The interannual fluctuations are small compared with the climatological mean of -49 TW itself, and there is no robust trend over 1996– 2016. However, the seasonal cycle appears pronounced. Eddy heat flux divergence peaks at -68 TW in February and weakens to -40 TW in July, with amplitude exceeding half of the eddy heat flux divergence. The wintertime

Figure 7. (a) Time series of eddy heat flux divergence integrated over the “strip” shown as 5‐day averages (blue) and 12‐ month running mean (orange). (b) Monthly climatology of eddy heat flux divergence integrated over the “strip.” (c) Time series of estimated Eady growth rate shown as every 5‐day averages and 12‐month running mean. (d) Monthly climatology of estimated Eady growth rate.

intensification in eddy heat flux divergence coincides with stronger winds and elevated EKE in winter (Fer et al., 2020).
The finding that the eddy‐induced cooling has relatively low interannual variability is intriguing, as one might expect stronger eddy heat fluxes during periods of enhanced mean volume transport, when sharper velocity shear and density gradients could favor baroclinic instability. We further calculate the Eady growth rate averaged along the “strip”, a theoretical measure of baroclinic instability. Previous linear stability analyses have shown consistently large growth rates along the steep slope of the NwASC, for example, the Lofoten Escarpment, but temporal variability is lacking (Isachsen, 2015; Spall, 2010; Trodahl & Isachsen, 2018). Following the methodology described in von Appen et al. (2016), we compute the spatially averaged Eady growth rate along the NwASC (Figures 7c and 7d). The results reveal pronounced seasonal variability, with peak instability in winter and a marked reduction in summer, yet little interannual variation. In simple terms, the NwASC becomes more unstable and generates more eddies in winter, but is less unstable and thus generates fewer eddies in summer. The overall rate of eddy shedding remains stable from year to year over the 1996–2016 period. In fact, the observational eddy census supports this finding, where Bashmachnikov et al. (2023) report a small interannual variability in the number of the generated eddies from the NwASC based on coarse resolution altimetry and hydrography.
Overall, eddy heat flux divergence features a stable heat leakage across the NwASC that is seasonally modulated but shows limited interannual variability. Its seasonality closely resembles that of the Eady growth rate, with both fields showing winter maxima and summer minima. Their shared seasonal modulation is consistent with the expectation that enhanced baroclinic instability in winter promotes stronger eddy activity and thus larger eddy heat flux divergence. After applying a 12‐month running mean, the remaining interannual variability in both the eddy heat flux divergence and Eady growth rate is small. This indicates that most of the temporal variability arises from the seasonal cycle, while the interannual component is weak.
4.		Discussion
4.1.		Eddy‐Induced Cooling
Our study underscores the critical role of eddy‐driven heat leakage with greater confidence, supported by a rigid heat budget analysis in an improved high‐resolution model. It demonstrates that eddy‐induced cooling of the NwASC en route toward the Arctic is underestimated when relying solely on surface‐based diagnostics (Isachsen et al., 2012). Consistent with Isachsen et al. (2012), who suggested that eddy‐induced cooling is comparable to (or larger than) the local atmospheric heat loss. Our full‐depth, volume‐conserving heat budget demonstrates a substantially larger eddy contribution relative to atmospheric heat loss. Over 1996–2016, the time mean eddy heat flux divergence is -49 TW within our defined “strip”, offsetting 73% of the +67 TW heat convergence by the mean flow, and leaving +18 TW balanced by net atmospheric heat loss. In other words, the eddy cooling effect is approximately 2.7 times that of surface heat loss to the atmosphere, substantially damping poleward heat transport toward the Arctic. The heat budget fills a gap in previous works and corroborates an earlier study based on a one‐ dimensional mixing model, where differences between model results and observations were attributed to unresolved lateral processes, thereby inferring their dominant role along the NwASC (Huang et al., 2023).
The spatial distribution of the eddy heat flux convergence/divergence in our model closely follows bathymetric features and mean current pathways. Along the offshore NwAFC, eddy heat flux divergence follows the Mohn Knipovich Ridge system, but is much weaker than that along the onshore NwASC. Baroclinic instability intensifies where the NwASC flows over steep and narrow topography (Fer et al., 2020), leading to vigorous eddy shedding that cools the current and warms surrounding regions. A prominent example is the steep Lofoten Escarpment, where eddy heat flux divergence channels heat fluxes into the central Lofoten Basin, making the basin more susceptible to atmospheric heat loss. Additional westward pathways north of Lofoten Island, eastward pathways via Bear Island and Storfjordrenna troughs, and enhanced eddy‐induced westward advection of heat near the FS further diminish poleward heat propagation. These eddies extract heat from the boundary current, diverting it into broad interior basins where air‐sea fluxes cool and densify the water, with cascading impacts on deep water formation and overturning circulation in the Nordic Seas (Huang et al., 2023).
Previous underestimation may be traced to the eddy heat flux divergence maxima centered around 400 m depth, rather than at the surface. This depth dependence is consistent with Lagrangian studies and implies that surface drifters may not fully capture mesoscale variability in heat transport (Dugstad et al., 2019; Rossby, Prater, & Søiland, 2009). Moreover, we pinpoint the steep Lofoten Escarpment and the thermocline depth (rather than the surface) as hotspots for lateral heat transport.
4.2.		Interannual Variability
Intriguingly, our high‐resolution model indicates that interannual variability in the eddy heat flux divergence along the NwASC remains small. Eddies persistently leak heat into the Norwegian Sea year‐round, primarily driven by local baroclinic instabilities associated with steep topography (Fer et al., 2020; Trodahl & Isach- sen, 2018). Previous studies have shown localized intensification of baroclinic instability along steep slopes (Isachsen, 2015; Trodahl & Isachsen, 2018), a spatial pattern confirmed by our model‐based Eady growth rate estimates. The temporal evolution reveals pronounced seasonality, stronger in winter and weaker in summer, but with weak interannual variability. While the seasonal signal is evidenced by mooring data from the West Spitsbergen Current (von Appen et al., 2016), interannual variability has remained largely unquantified. Our results indicate that interannual fluctuations in Eady growth rate averaged along the NwASC are not significant, consistent with and likely explaining the stable interannual eddy heat flux divergence and eddy‐induced heat transport observed in the region (Bashmachnikov et al., 2023).
5.		Conclusion
Mesoscale eddies in the Nordic Seas, as resolved by our high‐resolution model, play a significant role in extracting heat from the NwASC. These eddy‐driven fluxes divert and redistribute heat from the boundary currents as the NwASC advances toward the Arctic. We find that eddies dominate the heat budget: eddy heat flux divergence along the current offsets more than two‐thirds of the heat flux convergence brought by the mean flow and exceeds the contribution from atmospheric heat loss. This eddy‐driven heat leakage is strongest below the surface and peaks in winter, particularly near the steep topography of the Lofoten Escarpment. These patterns highlight the need for targeted subsurface, temporally homogeneous, and topographically focused in situ observations to capture eddy dynamics.
Despite substantial seasonal variations, the magnitude of eddy heat divergence remains remarkably stable from year to year. This implies that mesoscale eddies and associated lateral heat transport along the NwASC are governed more by local topography, stratification, and instability than by upstream forcing. Throughout the 21‐ year simulation, we do not detect a significant long‐term trend in the total heat convergence within the study region. However, recent years show indications of rapid shifts in heat partition among individual lateral
boundaries, as well as changes in the net atmospheric heat fluxes (Figure 4). These emerging signals underscore the importance of extending the analysis to include the offshore NwAFC and to quantify heat transports through the BSO and FS in future work, to better understand their impacts on the Arctic heat budget.
Conflict of Interest
The authors declare no conflicts of interest relevant to this study.
Data Availability Statement
The SSALTO/DUACS altimetry, OSTIA product, GLORYS, and TOPAZ4 reanalysis are available via CMEMS portal at https://marine.copernicus.eu/. ERA5 data were obtained from the European Centre for Medium‐Range Weather Forecasts. Bathymetry is obtained from RTopo‐2.0.4 (Schaffer et al., 2019). Temperature and velocity measurements are obtained from Orvik (2022) and are available from the Norwegian Marine Data Centre (NMDC; at http://metadata.nmdc.no/UserInterface/#/). Observational volume transports across the GSR (Østerhus et al., 2019) are available at https://www.ocean‐ops.org/oceansites/tma/gsr.html. The processed model output required to reproduce the results and Python scripts used to generate the figures in this study are archived at the Zenodo repository (Jian, 2025).

Acknowledgments
D.J. acknowledges funding from the China Scholarship Council, the University of East Anglia (UEA), doctoral training support from the ARIES Doctoral Training Partnership, and a travel award from the Challenger Society for Marine Science. I. A.R. acknowledges partial support from the UK's Natural Environment Research Council Grant (NE/N009754/1). We thank Mattia Almansi and Thomas Haine, whose prior work (Spall et al., 2021) provided the foundation upon which our model is built. We are also grateful to the reviewers for their constructive remarks. The model simulations and post‐processing were conducted on the High‐Performance Computing Cluster supported by the Research and Specialist Computing Support service at UEA.

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