In summer, the atmospheric forcing drives ice melt and freshwater input in the northern half of the domain, while the shortwave radiation warms the open ocean faster than the ice-covered ocean. The atmospheric forcing therefore generates a meridional density gradient in the ML. Within a few meters from the surface, the developing ML meridional density gradient is dominated by salinity as the released freshwater from ice melt is very buoyant (lighter water on the ice-covered ocean side; Fig. a). However, below this freshwater lens down to the bottom of the ML, the meridional density gradient is temperature-dominated, with relatively warm water in the open ocean and near freezing temperatures in the ice-covered ocean (Figs. a and a). The MLD is defined using the default MITgcm surface-referenced density criterion. As a consequence of the spreading of the melt freshwater lens near the surface, the MLD rapidly drops to a few metres in just a few days in both ice-free and ice-covered areas, though the ML remains weakly stratified below this (Fig. c).

Through baroclinic instability, SMLEs develop near the ice edge, where the meridional density gradient is the strongest. Figure a displays the Rossby number, clearly highlighting the SMLE vortices that have been energised through the ML instability. The Rossby number is on the border of the submesoscale range at Ro≈0.3. By day 50, eddies are well developed, as illustrated by a snapshot of SST (Fig. c). The vertical eddy buoyancy flux w′b′‾x (where overline x is a zonal mean at constant height, prime denotes departure from the zonal mean, w is the vertical velocity, and b=-gρ/ρ0 is the buoyancy) is shown at the surface and at depth z=-28.75 m in Fig. a. A time average of w′b′‾x is shown in Fig. a (the time average is taken over the whole simulation period of 110 d). If the vertical eddy buoyancy flux is positive (bringing light water up or dense water down), then the eddies act to restratify the ocean ML. As described above, the meridional density gradient is dominated by salinity near the surface and temperature below the surface. Figure a illustrates that (1) eddies do not reach the full meridional extent of the domain by the end of the simulation in summer, (2) at the surface (salinity dominated) the vertical eddy buoyancy flux can be negative (i.e., destratifying), and (3) below a few meters, it is strictly positive (i.e. restratifying) with the strongest effect near the ice edge. It is noteworthy that the SMLEs extend over the full initial MLD of 55 m for the entire simulation despite the MLD dropping to a few meters within days (more details in Sect. ). The weakly stratified ocean, from below the freshwater lens down to 55 m depth, remains prone to ML instability. The tendency of eddies to release available potential energy (PE), flatten isopycnals, and restratify the ML is therefore felt through the full depth of the initial ML. This is illustrated by comparing 2D and 3D density snapshots at day 50 (Fig. a and c). In the 2D run, the horizontal density gradient is more localised and stronger compared to that in the 3D run.

To evaluate the role of eddies, it is useful to explore the heat budget of the ML. We divide our domain into two boxes: an open ocean box from the southern solid wall to the middle of the channel (Yb=38 km) and an ice-covered box north of Yb=38 km. The two boxes extend from the ocean surface to a depth Zb=55 m (the summer initial MLD). For each of these regions of volume V, the volume-averaged ML heat budget in units of Wm-2 is: 2ρ0cwZbdTdt‾xyz︸storage=Qnet‾xy︸surface-ρ0cwwT|‾z=-Zbxy︸VHT-ρ0cwZbYbvT|‾y=Ybxz︸MHT+Fdiff, where dT/dt is the temperature tendency, cw is the heat capacity of seawater, and Qnet is the total surface ocean heat flux. Overlines denote spatial averages. The advective terms are the vertical heat transport (VHT) and the meridional heat transport (MHT). Because the box depth captures the vertical extent of SMLEs (being the initial MLD of 55 m in summer), the VHT across the box bottom is negligible. Fdiff are the net diffusive heat fluxes into the box. Qnet is the net air-sea or ice-sea heat flux at the surface (see Sect. 2.1).

Under summer conditions, Qnet dominates the heat budget in the open ocean (Fig. a). Warming due to FSWnet (O(102) Wm-2) dominates. However, the atmospheric temperature of approximately -10 °C brings about sensible cooling of the ocean (O(101) Wm-2), which increases in magnitude over time (from around 30 to 50 Wm-2) as the open ocean warms from (-1.8 to 3 °C). The increasing open ocean temperature also leads to a substantial increase in the magnitude of outgoing longwave radiation (-70 to -95 Wm-2). Overall, steady warming due to FSWnet (O(102) Wm-2) is partially compensated by (an increasing) cooling by FLWnet and FSH, leading to a decrease of Qnet over time (Fig. a).

The open ocean heat storage is mainly driven by Qnet, but with a significant contribution from MHT (Fig. a). MHT (negative, pushing heat from the open ocean to the ice covered region) peaks at -35 Wm-2 in the 3D simulation, but only -9 Wm-2 in the 2D simulation. This MHT is almost entirely due to the eddy-induced overturning. Figure a shows that the total overturning, ψiso, is dominated by ψeddy. ψeddy is maximum underneath the initial ice edge and extends from below the freshwater lens down to 50 m depth. As expected, ψeddy (clockwise) flattens the density front, by lifting lighter water on the open ocean side and pushing down denser water under the ice (i.e., removing the available PE that feeds baroclinic instability). Since density gradients over most of the initial MLD are temperature dominated, ψeddy realizes a northward MHT into the ice-covered ML.

VHT indicates a small exchange of heat between the ML and the deeper ocean (around 1 Wm-2 – not shown in Fig. ). Vertical mixing terms were found to be negligible through the bottom boundary Zb, and the surface correction term due to the linear free surface was also found to be negligible (not shown). Overall, the open ocean heat storage decreases by almost half over the 110 d (from 90 to 40 Wm-2) as Qnet reduces over time and negative MHT strengthens in magnitude.

In the ice-covered ocean region (Fig. b), the net surface heat flux is almost 2 orders of magnitude smaller (only a few Wm-2) than for the open ocean and changes little over time. All the heat flux components are much smaller in the ice-covered region than in the open ocean as expected, but there are also compensating effects. As the ice cover melts and thins (due primarily to heating from shortwave radiation), and the fraction of open water in this region increases, FSWnet into this region increases by an order of magnitude to O(101) Wm-2, but cooling via longwave radiation and sensible heat flux also increases too. The resulting surface heating is balanced by ice melt, maintaining the ocean surface temperature at the freezing point (only slightly increasing due to the salinity-dependence of the freezing point). However, the storage term over the full initial MLD in the ice-covered ocean is overwhelmingly dominated by warming of the ML below a few meters, which is driven by the MHT from the open ocean region.

The impact of eddies on the heat budgets of both regions is observed by comparing the 3D and 2D results in Fig. a and b. In the ice-covered region heat budget, by day 110, the MHT in the 3D simulation is three times larger than in the 2D simulation, resulting in a storage twice as large in 3D than in 2D (compare red solid and dashed lines in Fig. b). This can be traced back to the radically different streamfunctions in 2D compared to 3D (Fig. ). In 2D, there are no eddies and ψeddy is negligible (note that it is not exactly zero because of the transient component of the layer transport; see Sect. ). Therefore, in contrast to the 3D case, ψiso is approximately equal to ψ‾. Interestingly, the latter is almost twice as large as in the 3D simulation, scaling with the stronger lateral density gradient in the 2D simulation. However, this is not enough to compensate for the negligible eddy-induced overturning, and overall the MHT from open ocean to ice-covered ocean is much larger with than without eddies.

This increased eddy-induced MHT to the ice-covered ocean supports a larger ice melt in 3D compared to 2D. The ice melt, in turn, impacts air-sea fluxes: a positive feedback is created between ice melt and FSWnet as thinner and sparser ice coverage increases the fraction of ice-free ocean, and therefore the ML absorption of shortwave radiation (on average over the simulation, FSWnet is increased by 20 % in 3D compared to 2D). There is a partial cancellation of this effect by increased cooling by longwave radiation and sensible heat flux for that fraction, but shortwave radiation dominates.

Comparing the time series of sea ice volume over the entire domain for 3D and 2D Arctic summer simulations shows the net large impact of the eddy heat transport on the ice cover (Fig. a). We scaled up the 2D time series by the number of zonal grid points in 3D for a meaningful comparison. The difference in total ice volume between the 2D and 3D simulations increases over time, reaching 10 % by day 110. This metric, however, underestimates the impact of SMLEs, which is concentrated within the meridional extent of the eddies. Figure  displays the sea ice volume at day 110 in 3D and 2D Arctic summer summed in the zonal direction. It emphasizes that the impact of SMLEs on sea ice is tightly linked to their spatial scale and growth rate. When only considering this region (bordered by the blue dotted lines), the final 2D-3D sea ice volume difference rises to 17 %. In Sect. , we also show that thinner initial ice cover leads to a much larger effect.

Under winter atmospheric forcings, the ocean cools and ice forms within a few days. The rate of ice formation, which is associated with the rate of brine rejection, is faster in the open ocean, where ice is not already present or is thin. This is related to the conduction flux through ice which is inversely proportional to ice height. The salinity of the open ocean, therefore, increases faster than that of the ice-covered ocean (Fig. d). The developing winter ML density gradient (Fig. b) between the open and ice-covered regions is brought about by colder, saltier waters in the open ocean and warmer, fresher water in the ice-covered region (note that the density gradient is reversed compared to the summer case). That said, the gradient is salinity dominated as the ML is close to freezing point in both regions (the lateral temperature difference is less than 0.05 °C, compared to 3 °C in summer). This also implies that eddy buoyancy fluxes (Sect. ) are not accompanied by significant lateral eddy heat fluxes in winter compared to summer. As a consequence of the surface buoyancy loss, the ML deepens and warmer water is entrained from below the ML (Fig. d).

SMLEs develop through ML baroclinic instability near the sea ice edge as in the summer. Compared to the summer simulation, eddies develop and spread more rapidly, as well as reach higher Rossby numbers (Fig. b). The eddies spread heat and salinity anomalies laterally (Fig. d), extracting the available PE from the lateral density gradient. As expected, the density front is steeper (Fig. , lower panels) and grows sharper (Fig. b) in 2D than in 3D.

The zonal-mean vertical eddy buoyancy flux w′b′‾x is an order of magnitude larger at depth (z=-28.75 m) than at the surface (see Fig. b, where as in summer the time-averaged w′b′‾x is shown). At both depths, this restratifying flux is at least an order of magnitude greater than in summer (compare the y axis scale of Fig. a and Fig. b). This restratification (positive flux) by eddies opposes the destratifying influence of cooling and ice formation. In Fig. c, a snapshot of the winter spatial variations w′b′ are shown at day 110, with salinity contours shown in black. The alignment of w′b′ and salinity demonstrates that buoyancy anomalies are salinity dominated. w′b′ reaches up to 10-7 m2s-3 in parts of the open ocean, where air-sea fluxes are also larger. These magnitudes of vertical eddy buoyancy fluxes are equivalent to vertical heat fluxes (Wm-2) in the submesoscale range .

As in the summer case, we investigate the heat budgets of the open ocean and ice-covered boxes. However, for the winter case, we set the bottom boundary of the boxes, Zb, at the approximate final MLD of 147 m. This is to ensure that all the SMLE dynamics are included within the heat budget.

The rapid onset of ice cover in the open ocean has a large influence on the time evolution of the winter heat budget (Fig. c). All winter heat budget terms other than the net surface heat flux, the MHT and the heat storage, are negligible and are not displayed in Fig. . In the open ocean, the initial net air-sea flux is -77 Wm-2. It stays at this value throughout the simulation at locations that remain ice-free (because it is controlled by the SST, which remains at freezing point). Where ice grows, the surface heat flux decreases to approximately -10 Wm-2. This explains the initial rapid reduction of the net surface heat flux averaged over the initially open ocean from over -50 Wm-2 to around -30 Wm-2 (Fig. c). After around 40 d, Qnet is dominated by the presence of sea ice and changes little over the remaining 70 d of the simulation. The ice growth significantly affects all components of Qnet: FLWnet (upwards) decreases from -120 to -82 Wm-2 (with a small effect due to decreasing SST), FSH decreases from -7 to -3 Wm-2 and FSWnet (downward) decreases by about one-half in 2D on average. As in the summer case, Qnet is the dominant term in the heat budget in the open ocean region although with weaker values (O(101) Wm-2).

The temperature tendency over the top few metres of the ML is actually close to zero, because of the balance between ice formation, heat lost at the surface, and heat entrained from below the initial MLD. As mentioned above, the depth-averaged lateral temperature gradient is weak (and reversed) compared to the summer case. As a result, the MHT acts to warm the open ocean, but it is smaller magnitude in winter than in summer.

In the ice-covered ocean region (Fig. d), the ice thickens over time in winter. Heat is conducted from the ocean through the ice and is lost to the atmosphere. Rates of ocean cooling (heat storage term) are lower than in the open ocean (by around 20 Wm-2) due to a complete and thicker ice cover. The heat storage term is dominated by the net surface heat flux Qnet and MHT in 3D (both cooling the ice-covered box), and only by Qnet in 2D. Again, the volume-averaged heat storage term also encompasses heat mixed upwards and lost at the surface, through the process of deepening the ML.

The MHT at the initial ice edge (Yb=38 km) is small in 2D, less than 1 Wm-2, but up to 17 Wm-2 in 3D. This difference mainly reflects the difference in the magnitudes of the total streamfunction ψiso between 2D and 3D (Fig. ).

As in the summer simulation, the Eulerian streamfunction is negligible (Fig. a, left) and the winter total overturning is dominated by the eddy dynamics in 3D. The eddy-induced overturning is now anticlockwise (reflecting the reversal of the lateral density gradient between summer and winter). Eddies act to drive fresher, warmer water upward in the ice-covered region and cooler, saltier waters downward in the open ocean region.

In 2D, where SMLEs are absent, only temporal changes contribute to the eddy-induced overturning. Whilst in summer this transient contribution is negligible, in winter it is important when averaged over the entire simulation (but, again, by construction, it is zero when calculated instantaneously). ψeddy in 2D is clockwise with a narrow meridional extent. It is worth noting that, if this transient component exists in 3D, it would lead to an underestimation of the 3D eddy-induced overturning shown in Fig. a (right). Nevertheless, as in the summer simulation, the total overturning ψiso in 2D (no eddies) is an order of magnitude weaker than in 3D.

The southward eddy-driven MHT acts to partially compensate the heat loss to the atmosphere that drives ML deepening in the open ocean, hence reducing MLD deepening there (see Fig. d). The eddy-driven cooling of the ice-covered ocean has a significant impact on the heat budget, reinforcing the heat loss through ice. The ML average heat storage in the ice-covered region decreases further, by about 30 % on average over time, in 3D compared to 2D (Fig. d).

The overall effect of the eddies on sea ice growth is however small. Eddies increase the total ice volume (over the whole domain) by only 3 % by day 110. This is due to compensating effects. As more heat is transported laterally into the open ocean from under the ice in 3D than in 2D, less heat is obtained from below the ML in 3D, because eddies restratify and the ML does not deepen as much.

Figure  shows the time evolution of the difference in MLD between the 2D and 3D simulations (blue shading indicates deeper MLDs in 2D). The meridional expansion of the region with deeper 2D MLDs reflects eddies travelling further away from the initial ice edge over time. Eddies reduce the deepening of the ML by 80 % when averaged over the open ocean region and 52 % when averaged over the ice-covered region by day 110. The difference between regions is because cooling and ML deepening are more rapid in the 2D open ocean region than in the ice-covered one. In both regions, the final 3D MLD is only 5 m deeper than the initial one, implying that eddies nearly balance the destratifying impact of atmospheric cooling and ice formation in both regions.

Nearer to the ice edge, the balance between these lateral and vertical heat exchange terms is very fine, but further south the difference is more stark and the differences between the 2D and 3D sea ice volume are larger. In the ice-covered region, rates of surface heat loss and also basal heating are a smaller factor in the heat budget, so lateral eddy heat transport is more important for heat storage and ice formation rates. This means there is also slightly higher ice growth and rates of heat loss in 3D compared to 2D in the winter ice-covered region. Overall, due to compensating eddy-induced MHT and VHT (though VHT in not displayed in Fig. , since the box captures full depth of SMLE dynamics), the rates of sea ice growth are not significantly impacted by the presence of eddies in the winter experiment.

Under summer conditions, the Antarctic-like initial stratification results in only small differences in eddy impacts compared with the Arctic case. For example, eddies decrease the final ice volume by 11 % with Antarctic-like initial stratification, compared to 10 % in the Arctic case. The MHT to the ice-covered region is only 4 % larger for the Antarctic-like 3D simulation on average than for the Arctic case (Figs. b and a). The time-averaged open ocean heat storage, ice-covered ocean heat storage, and 3D ψiso exhibited negligible differences for the two differing initial background stratitications too. Therefore, eddies also have a significant impact on ice-covered region heat budget with this change in initial background stratification (Fig. a).

This low sensitivity of the eddy impacts to initial stratification in the summer conditions is due to the tendency of the summer atmospheric forcings to enhance the upper ocean stratification and reduce the MLD abruptly. There is little interaction between the ML and the subsurface ocean in the summer simulations. Therefore, the differences in stratification deeper than the initial MLD do not alter the eddy dynamics and impacts.

Unlike in the summer case, the sensitivity to background stratification is significant in winter. This is simply because the ML deepens under winter forcing. The rate of vertical mixing and the heat from the subsurface ocean that is mixed upward depend on the strength of the stratification, which is weaker in the Antarctic-like initial profiles than in the Arctic case. As a result, the rate of ML deepening with Antarctic profiles is significantly larger than with Arctic profiles (compare Fig. d with Fig. d). This also applies to the 2D case: rates of MLD deepening for the Antarctic-like stratification are over three times faster than in the Arctic (0.54 versus 0.16 md-1). However, the 2D-3D differences are similar with the two background stratifications, about 10–15 m. For reference, the final open ocean MLDs are approximately 160 m in 2D and 149 m in 3D for the Antarctic stratification compared to 118 m in 2D and 103 m in 3D for Arctic stratification. Using the 2D-3D difference in MLD as a proxy for the strength of eddy restratification, the effect is smaller in the ice-covered region than in the open ocean region with both stratification profiles. Note, however, that eddies stop and reverse the MLD deepening in the Arctic winter simulation, but can only slow down the ML deepening with the weaker Antarctic stratification.

The greater vertical mixing of heat upwards from the subsurface ocean that occurs with the Antarctic stratification results in a slower ice formation, and in 2–3 times weaker lateral density gradients compared to the Arctic case (Figs. b and b). The 2D lateral density gradient reaches ∼-0.005/-0.014 kgm-3km-1 in the Antarctic/Arctic cases, respectively while the 3D gradients peak at ∼-0.002 and ∼-0.004 kgm-3km-1 for the Antarctic/Arctic stratification, respectively. This effect can also be seen on the storage term in Fig. b, which is of greater magnitude with the Antarctic-like stratification than in the Arctic case. That said, it is worth to note that eddies have a small impact on sea ice cover in the winter simulations for both Antarctic-like and Arctic-like stratifications. By day 110, the 2D-3D difference in sea ice formation is -3 % for the Arctic case, whilst it is +3 % with the Antarctic-like stratification. Therefore, although there is faster MLD deepening and slower rates of ice formation overall (in both 3D and 2D) with the Antarctic-like stratification compared to the Arctic case, the eddy impact on sea ice formation (2D-3D difference) in winter is not altered by this change to the background stratification and remains small.

The eddy-induced overturning streamfunction with the initial Antarctic stratification is overall deeper (in line with a deeper MLD) but only slightly weaker than in the Arctic case (Fig. c). This is consistent with scalings from , which predict a strengthening of the eddy-induced streamfunction with the MLD and the lateral density gradient. The weaker lateral density gradient and larger MLD in the Antarctic case might partially cancel out leaving an eddy-induced streamfunction of similar strength to that of the Arctic case. A more quantitative comparison of our results with the parameterization of is left to a future study.