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  • View in gallery

    Initial vertical profile of (a) temperature and (b) salinity.

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    Concentration of the lead-originated salt for (a),(b) day 1, (c),(d) day 5, and (e),(f) day 10 in CTRL: (left) slice at 30-m depth with velocity vector and (right) y-mean profile with density (σθ) contour.

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    As in Fig. 2 but for (a),(b) day 10, (c),(d) day 30, and (e),(f) day 50 in CTRL.

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    As in Fig. 2 (right column) but for (a) NORAND and (b) NOROT at day 10.

  • View in gallery

    Time series of horizontal distribution of the lead-originated salt in each region for (a) CTRL, (b) NORAND, and (c) NOROT.

  • View in gallery

    Time series of vertical distribution of the lead-originated salt for (a) CTRL, (b) NORAND, and (c) NOROT.

  • View in gallery

    As in Fig. 2 but for (a),(b) H15 and (c),(d) H60 at day 30.

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    As in Fig. 2 but for (a),(b) DS01 and (c),(d) DS16 at day 30.

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    As in Fig. 6 but for (a) H15, (b) H60, (c) DS01, and (d) DS16.

  • View in gallery

    As in Fig. 2 (left column) but for (a) TA10, (b) TA40, (c) W02, (d) W04, (e) TS01, and (f) TS10 at day 30.

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    As in Fig. 5 but for (a) TA10, (b) TA40, (c) W02, (d) W04, (e) TS01, and (f) TS10.

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    As in Fig. 6 but for (a) TA10, (b) TA40, (c) W02, (d) W04, (e) TS01, and (f) TS10.

  • View in gallery

    Schematic views of the structure of dense water mass and the direction of along-lead jets (a) before and (b) after closing of the lead.

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    Schematic of eddy generation at the base of the mixed layer under the lead.

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    Plot of radius of eddies in all experiments except NORAND and NOROT. Error bar indicates resolution of the model.

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Brine-Driven Eddies under Sea Ice Leads and Their Impact on the Arctic Ocean Mixed Layer

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  • 1 Center for Climate System Research, University of Tokyo, Chiba, Japan
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Abstract

Eddy generation induced by a line-shaped salt flux under a sea ice lead and associated salt transport are investigated using a three-dimensional numerical model. The model is designed to represent a typical condition for the wintertime Arctic Ocean mixed layer, where new ice formation within leads is known to be one of the primary sources of dense water. The result shows that along-lead baroclinic jets generate anticyclonic eddies at the base of the mixed layer, and almost all the lead-originated salt is contained inside these eddies. These eddies survive for over a month after closing of the lead and transport the lead-originated salt laterally. Consequently, the lead-origin salt settles only on the top of the halocline and is not used for increasing salinity of the mixed layer. Sensitivity experiments suggest that the horizontal scale of generated eddies depends only on the surface forcing and is proportional to the cube root of the total amount of salt input. This scaling of eddy size is consistent with a theoretical argument based on a linear instability theory. Parameterizing these processes would improve representation of the Arctic Ocean mixed layer in ocean general circulation models.

Corresponding author address: Yoshimasa Matsumura, Center for Climate System Research, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8568, Japan. Email: ymatsu@ccsr.u-tokyo.ac.jp

Abstract

Eddy generation induced by a line-shaped salt flux under a sea ice lead and associated salt transport are investigated using a three-dimensional numerical model. The model is designed to represent a typical condition for the wintertime Arctic Ocean mixed layer, where new ice formation within leads is known to be one of the primary sources of dense water. The result shows that along-lead baroclinic jets generate anticyclonic eddies at the base of the mixed layer, and almost all the lead-originated salt is contained inside these eddies. These eddies survive for over a month after closing of the lead and transport the lead-originated salt laterally. Consequently, the lead-origin salt settles only on the top of the halocline and is not used for increasing salinity of the mixed layer. Sensitivity experiments suggest that the horizontal scale of generated eddies depends only on the surface forcing and is proportional to the cube root of the total amount of salt input. This scaling of eddy size is consistent with a theoretical argument based on a linear instability theory. Parameterizing these processes would improve representation of the Arctic Ocean mixed layer in ocean general circulation models.

Corresponding author address: Yoshimasa Matsumura, Center for Climate System Research, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8568, Japan. Email: ymatsu@ccsr.u-tokyo.ac.jp

1. Introduction

The sea surface mixed layer works as an interface of air–sea interaction, so it plays a very important role in the global climate, particularly in polar regions where a great amount of buoyancy is lost from the ocean and dense water is formed. The polar ocean is covered by sea ice, and input and output of salt due to its freezing and melting is one of the primary factors of sea surface mixed layer formation there. However, ocean general circulation models (OGCMs) suffer from difficulties in representing the profile of salinity and temperature in polar regions (Steiner et al. 2004). One major reason for such difficulties is that small-scale processes in the mixed layer are not resolved explicitly but are just empirically parameterized. To develop more appropriate parameterizations, we should quantitatively investigate small-scale processes in the mixed layer.

Since the wintertime Arctic Ocean is covered by thick sea ice that acts as a thermal insulator, air–sea heat transfer and new ice formation mostly occur in open water regions such as leads/polynyas. Leads are long narrow openings in large ice floes with a width of several meters to several kilometers, and duration time ranging from a few hours to several days in winter (Smith et al. 1990). Previous studies point out that leads play a very important role in air–sea interaction. Maykut (1982) estimates that freezing in leads accounts for half of the total amount of new ice formation in the wintertime Arctic Ocean, even though the total area of leads only accounts for a few percent of the whole ice-covered area. This estimate suggests that the source of salt flux caused by brine rejection in the wintertime Arctic Ocean is highly localized and is organized in a long narrow line shape. Such localized salt flux could have a great impact on the structure of the Arctic Ocean mixed layer. Previous laboratory experiments (Bush and Woods 1999, 2000 suggest that such a line-shaped salt flux under a lead generates eddies. Those eddies survive even after closing of the lead and work as carriers of the lead-originated salt. Therefore, while opening and closing of a single lead is a localized and short-term event, it could influence the Arctic Ocean mixed layer for a longer period and over a wider area. For quantitative investigation of such processes in the wintertime Arctic Ocean, numerical experiments using high-resolution models are required because direct observation is difficult due to severe weather and thick ice cover.

There have been several studies that investigate processes under a freezing lead using numerical models. Kozo (1983) investigates the convection induced by local brine rejection due to freezing of a lead using a two-dimensional hydrostatic model. He simply applies a constant surface salt flux over 120-m width, resulting in a cellular structure with convergence at the surface and divergence at the base. Since the duration of the integration is only 3 h, effects of rotation are not realized. Smith and Morison (1993) perform similar experiments with a wider lead using a higher-resolution model. At first, plumes with strong downward velocity develop under both edges of the lead, and relatively weak compensating upwelling is found at the center. After a few hours the salinity under the lead is homogenized by convection, and a cellular secondary circulation with convergence at the surface and divergence at the base is formed. Since the integration time is 24 h, rotational effects appear and along-lead geostrophic jets develop. The direction of these jets is opposite between the surface and the base, but such baroclinicity does not lead to instability because the model is two-dimensional. While the studies mentioned above treat a lead as a source of constant salt flux, Kantha (1995) uses an ice–ocean coupled model and focuses on the variation of the salt flux due to sea ice growth. He points out the importance of thermodynamics of ice for the correct estimation of salt flux, especially when sea ice cover and position of leads are moving, because the temperature under leads is not always at the freezing point. Smith and Morison (1998) investigate nonhydrostatic effects of convection under leads using a two-dimensional nonhydrostatic model. Their result suggests that nonhydrostatic effects are dominant when the convection reaches below 100-m depth. In the presence of the halocline, convection is confined to a shallow mixed layer and nonhydrostatic effects are not as important.

Skyllingstad and Denbo (2001) investigate the small-scale structure of convection under leads using a high-resolution large-eddy simulation model coupled with sea ice. Their results suggest that the vertical mixing due to convective plumes under leads strongly depends on the velocity of the sea ice motion. Since their integration time is no more than 12 h, rotational effects and secondary circulation formed by the pressure gradient between local saline water beneath the lead and ambient freshwater do not appear.

A three-dimensional long-term integration that focuses on the secondary processes after closing of a lead was performed by Smith et al. (2002). In their result, anticyclonic eddies that contain high-salinity water are generated in a few days, as predicted by laboratory experiments of Bush and Woods (1999). However, the experimental domain in Smith et al. includes only the region above the halocline, so the penetration of convective plumes into the halocline is not represented. Therefore, it has not been clarified how the lead-originated salt is distributed and affects the structure of the halocline in the Arctic Ocean mixed layer.

The purposes of the present study are to investigate eddy generation processes induced by localized salt flux due to freezing of a lead and to make a quantitative estimate of the impact of the lead-originated salt on the Arctic Ocean mixed layer through long-term integrations. We also discuss parameter sensitivity of eddy properties, particularly their scale.

2. Model description and experimental design

The ocean model used in this study is a three-dimensional nonhydrostatic model for an incompressible fluid, similar to one described by Marshall et al. (1997a, b). The rigid-lid and Boussinesq approximations are used. Smagorinsky-type shear-dependent viscosity is adopted with a biharmonic operator (Griffies and Hallberg 2000), and harmonic diffusion is applied. Since the focus of this study is on the small-scale salt transport processes, we use a high-accuracy tracer advection scheme “COSMIC-QUICKEST” (Leonard 1979, 1991; Leonard et al. 1996). The horizontal size of the model domain is 25.6 km × 25.6 km with periodic boundaries. The latitude is set at 80°N, and an f-plane approximation is used. The depth of the domain is 80 m (except for sensitivity experiments, described later, whose mixed layer depth is varied), and the bottom boundary is free slip. The resolution is 200 m horizontally and 2.5 m vertically. Integration is initiated by a stationary state and continues for 50 days in each experiment. Physical constants and model parameters used in the model are listed in Table 1.

The initial salinity and temperature are horizontally uniform and have a vertical profile characteristic of the wintertime Arctic Ocean, where a cold halocline separates the fresh mixed layer near the surface and the high salinity dense water below (Cavalieri and Martin 1994; Rudels et al. 1996). We idealize this vertical profile by fixing temperature at the freezing point and approximating the salinity change by a hyperbolic-tangent curve. In the control experiment the inflection point of the hyperbolic-tangent curve is at 40-m depth, and the salinity is 32.0 psu in the surface mixed layer and 32.5 psu below the halocline (Fig. 1). We define the mixed layer depth H as the thickness of the water column where salinity is almost uniform (32.0 < S < 32.01 psu). The sea surface is covered by thick sea ice except that there is a lead at the center of the domain. The thickness of the ice cover outside the lead is 2 m. Initially there is thin ice of random thickness within the lead, whose maximum thickness is 2.5 cm, to seed baroclinic instability.

The x axis of the model coordinate is oriented perpendicular to the lead, and the y axis is along the lead. The direction of increasing z is upward. The coordinate origin is set at the center of the lead.

The surface temperature is restored to an apparent air temperature (Haney 1971). Since the water temperature is fixed at the freezing point in the model, the heat loss within the lead directly results in freezing. Note that we treat the thick ice cover as an ideal insulator, so freezing and corresponding salt supply occurs only within the lead. The thermodynamic growth rate of young ice within the lead and corresponding salt flux are calculated by zero-layer thermodynamics (Semtner 1976). Closing of leads in the Arctic Ocean is induced by thermodynamic growth of new ice cover within the lead or convergent motion of ice floes. Since we do not treat ice dynamics explicitly, we close the lead artificially after several days to represent the dynamic closing, and there is no salt flux afterward.

In the control experiment (referred to as CTRL) we choose the lead width W = 800 m, the mixed layer depth H = 30 m, the salinity difference between the upper mixed layer and the lower dense water ΔS = 0.5 psu, the apparent air temperature Ta = −20°C, and the duration time of the lead ts = 3 days. The values for these parameters in all sensitivity experiments are listed in Table 2.

To investigate the transport process of the salt supplied by the freezing lead, we use a virtual tracer, which is initially set to zero for all of the domain, and whose surface flux is the same as the salt flux induced by brine rejection. Our analysis of the distribution of the lead-originated salt is based on the concentration of this virtual tracer.

Note that we idealize the Arctic Ocean mixed layer and omit some important processes, such as wind-driven drift of sea ice pack and heat transport induced by upwelling of deeper warm water beneath the thermocline. These processes could significantly affect the transport processes and distribution of the lead-originated salt. However, in the present study we only treat a condition where sea ice cover does not move and there is no upward heat flux from the deeper ocean. This idealization is suitable when winds are not so strong or ice cover is sufficiently thick and compact, and the cold halocline blocks upwelling of deeper warm water.

3. Results

a. The reference experiment

Figures 2 and 3 show the results of the CTRL experiment. After 24-h integration, brine-driven convection under the lead reaches 40-m depth (Fig. 2b). The concentration of the lead-originated salt increases by about 0.04 psu under the lead, and fronts are formed between the high salinity dense water under the lead and the ambient freshwater. These fronts accompany along-lead jets as a result of geostrophic adjustment (Fig. 2a). At the surface, these jets flow in the direction of increasing y on the positive-x side and toward decreasing y on the negative-x side, so the interior high density region has positive relative vorticity. On the other hand, the direction of the jets is opposite at the base of the mixed layer, so the interior region has negative relative vorticity. By day 3, the concentration under the lead exceeds 0.05 psu, and each front slants outward at the base of the mixed layer (Fig. 2d). Figure 2c shows that baroclinic instability is developing at each front with a wavelength of 3 km. By day 5, the meandering of the along-lead jets induced by baroclinic instability divides the dense water mass into seven separate masses (Fig. 2e). By day 10, some of these separate masses merge and five discrete eddies are generated (Fig. 3a). The horizontal size of these eddies is about 3–5 km, and all eddies have negative vorticity. Almost all salt supplied under the lead is contained inside these eddies. The peak of the salt concentration is found at the 30-m depth, which means that the cores of the eddies are located at the base of the mixed layer (Fig. 3d). After day 30, smaller-scale secondary eddies are also found, which are generated as a result of the interaction of the original eddies (Fig. 3c). The eddies survive even at day 50, and some of them move horizontally by about 5 km (Fig. 3e). Since these eddies contain the lead-originated salt, such lateral motion of eddies transports the lead-originated salt.

For comparison, we show the results of experiments without initial random perturbation of ice thickness (referred to as NORAND) and without rotation (referred to as NOROT). In NORAND, baroclinic instability cannot develop because of the absence of the seed of instability, and no eddy is generated. Consequently, there is no salt transport by eddies, and the salt supplied under the lead stays just under the lead in a geostrophically adjusted steady state (Fig. 4a). On the other hand, the geostrophic adjustment does not occur in NOROT, so the lead-originated salt spreads above the halocline (Fig. 4b) by cellular overturning.

To investigate the lateral salt transport, we divide the domain horizontally into five regions by the distance from the lead. The width of the each region is 2 km except the farthest regions that have 4.8-km width. Note that the regions on the positive-x and negative-x sides at the same distance are counted as the same region. Figure 5 is the time series of the amount of the lead-originated salt contained in each region (normalized by the total amount of salt input). In CTRL, while all the lead-originated salt is contained in the nearest region during the first few days, more than 20% of the lead-originated salt is transported into the next region, which is 2 km away from the lead, by day 10. This is due to slanting of the fronts during the geostrophic adjustment. After day 10, eddy-induced salt transport begins to work, and the lead-originated salt is transported by more than 6 km away from the lead. After day 50, the nearest region loses more than 50% of the total salt, while the 2–4-km region has 25% and each of the 4–6- and 6–8-km regions has about 15%. The fact that little salt is transported to the farthest region, which is 8 km away from the lead, indicates that the lateral motion of the eddies is limited within 8 km in CTRL. NORAND has no eddy-induced salt transport, and all of the lead-originated salt stays only in the nearest region. In NOROT, a cellular overturning circulation develops, unrestricted by geostrophic adjustment, and the lead-originated salt is rapidly distributed over all regions uniformly by this overturning circulation.

Figure 6 is the same as Fig. 5, but the domain is divided vertically into five layers. The thickness of each layer is 10 m except the bottom layer, which has 40-m thickness. In CTRL, almost all the lead-originated salt is contained in the layers 20–30 and 30–40 m thick after day 5. At day 50, 55% and 40% of the lead-originated salt is contained in the 30–40- and 20–30-m layers, respectively. Since the top of the halocline is at 30 m, this vertical profile suggests that the lead-originated salt is distributed mostly around the base of the mixed layer. Contrary to CTRL, the lead-originated salt is distributed over a wider depth range in NORAND and NOROT. In NORAND, 20% of the lead-originated salt is contained in the 10–20-m layer, and 35% is contained in each of the 20–30- and 30–40-m layers. In NOROT, 50%, 33%, and 14% of the lead-origin salt is contained in the 20–30-, 30–40-, and 10–20-m layers, respectively. In NORAND, the high salinity water column under the lead is not broken by baroclinic instability and keeps a geostrophic steady state, so the lead-originated salt can stay at upper levels even after the closing of the lead. In NOROT, cellular overturning circulation mixes the lead-originated salt over a wider vertical range.

Comparison of the results of these three experiments suggests that the eddies transport the lead-originated salt to a wider area for a longer period, even after the closing of the lead, in the presence of rotation. Therefore, distribution of the lead-originated salt may be strongly affected by the properties of the generated eddies, such as their size, location, and core salinity. Next we investigate parameter sensitivity of eddy properties and distribution of the lead-originated salt.

b. Sensitivity to the initial state

First we show the result of the experiments where the mixed layer depth is set to 15 and 60 m (referred to as H15 and H60, respectively). The domain depth of the model is 40 and 160 m, and the vertical resolution is 1.25 and 5.0 m in H15 and H60, respectively. Figure 7 shows the results at day 30. The lead-originated salt concentration at the core of eddies is 0.10 psu in H15 and as low as 0.03 psu in H60. Although there is a large difference in the core concentration among these experiments, the horizontal size of the eddies is similar. However, the vertical scale of the eddies changes as the mixed layer depth changes. Shorter eddies with higher salinity cores are generated in H15, and taller eddies with lower salinity cores are generated in H60. (Note that the vertical scale is different between Figs. 7b and 7d.)

Next we show the results of the experiments after changing the strength of the halocline. In DS01 the difference of salinity between the upper mixed layer and the dense water under the halocline, ΔS, is set to 0.125 psu, which corresponds to a density difference of 0.1 kg m−3; in DS16, ΔS = 2.0 psu (1.6 kg m−3). The concentration of the lead-originated salt and the scale of eddies do not seem to be affected by the strength of the halocline, but the depth of the eddy core is different (Fig. 8). While convection reaches deeper than 40 m and the eddies are formed at the middle of the halocline in DS01, the eddies are formed above the halocline and the salt stays around 30-m depth in DS16 because penetrative convection is prevented by strong stratification.

The same analysis as in Fig. 5 shows a tendency similar to CTRL for all of these four cases after changing the halocline strength (figure not shown), so the lateral salt transport by eddies does not seem to be affected by the initial mixed layer depth or the strength of the halocline. Contrary to the similarity in horizontal distribution, the vertical distribution of the lead-originated salt is different for the four cases (Fig. 9). While more than 50% of the lead-originated salt is contained at 20–30 m in DS01, more than 60% is contained at 30–40 m in DS16. When the halocline is weak, the vertical convection under the lead easily penetrates into the halocline and eddies are formed at a deeper level. Otherwise, the convection is restricted by strong stratification and eddies are formed at a shallower level.

c. Sensitivity to the forcing parameters

We also investigate sensitivity to the surface salt flux by changing the forcing parameters, that is, the apparent air temperature Ta, the width of the lead W, and the duration time of the lead ts; TA10 and TA40 are the same as CTRL, but Ta is −10° and −40°C, respectively. Low apparent air temperature leads to high ice growth rate, which results in a larger surface salt flux. In TA10, where the salt flux is weaker than CTRL, generated eddies are smaller and the concentration of the lead-originated salt at their core is smaller than in CTRL (Fig. 10a). In TA40, where the salt flux is stronger than CTRL, the eddies are bigger and the core concentration is greater than in CTRL (Fig. 10b). The depth of the peak of the salt concentration is also different because the eddies sink to the depth where the density of ambient water matches the core density (figure not shown).

W02 and W04 are the same as CTRL, but W is 200 and 400 m, respectively. The results (Figs. 10c,d) show that a narrower lead induces smaller eddies with smaller core concentration, and a wider lead induces bigger eddies with higher core concentration. These results are similar to the results of the experiments with changing the apparent air temperature in terms of dependence on total salt input; that is, both lower air temperature and a wider lead cause greater total salt input, and both result in bigger eddies with higher core salt concentration.

TS01 and TS10 are the same as CTRL, but ts is 1 and 10 days, respectively. The longer duration time of the lead causes greater total salt input. Note that the total salt input and ts are not linearly related because the growth rate decreases as ice grows. Figures 10e,f also show similar results; that is, the eddy scale and the concentration inside the eddies increase as the total salt input increases.

Figure 11 is the time series of horizontal distribution of the lead-originated salt. Note that the scale of the vertical axis is normalized by the total salt input for each experiment. Generally speaking, eddy transport works more efficiently in the experiments where larger eddies with higher salinity cores are generated. Figure 12 is the time series of the vertical distribution of the lead-originated salt. Stronger salt flux or a wider area of flux increases the ratio of the lead-originated salt contained at 30–40-m depth and decreases at both 10–20- and 20–30-m depth, which means that eddies are generated at a deeper level. On the other hand, the ratio contained at 10–20-m depth increases when the lead duration increases. This is because the salt supply continues even after the generation of eddies, and some of the lead-originated salt is mixed at a shallower level by continuous convection without being captured inside eddies.

4. Discussion

The parameter sensitivity experiments described in the previous section suggest that the horizontal scale of generated eddies is controlled by the total amount of salt input but is independent of the initial mixed layer properties. In this section, we discuss the mechanism of the eddy generation and the scaling for eddy size, based on a linear instability theory.

Before instability develops, quantities are uniform along the lead, so the problem can be treated as two-dimensional. When buoyancy is lost at the surface of nonstratified rotating fluid, dense water created near the surface drives vertical convection and sinks until rotation takes effect (Jones and Marshall 1993). Maxworthy and Narimousa (1994) estimate the depth of such free convection as
i1520-0485-38-1-146-e1
where B0 is the buoyancy flux and f is the Coriolis parameter. In the present study B0 is of the order of 10−7 m2 s−3 and f is about 10−4 s−1, so the critical depth zc is about 4000 m, which is much greater than the mixed layer depth. Therefore the brine-driven convection under the lead in the present study can reach the halocline without being affected by rotation. Salinity of the water column under the lead is well homogenized throughout the mixed layer by such convection, and a high salinity water mass with sharp fronts is formed under the lead. Such a localized dense water mass tends to induce cellular overturning, but it is interrupted by geostrophic adjustment in a few days. During geostrophic adjustment, along-lead geostrophic jets develop at both fronts. Since the cellular overturning is convergent at the surface and divergent at the base of the mixed layer, the directions of these geostrophic jets are opposite between the surface and the base, and they satisfy the thermal wind balance
i1520-0485-38-1-146-e2
where the buoyancy b is defined as
i1520-0485-38-1-146-e3
During geostrophic adjustment, the cellular overturning circulation tilts the fronts, and the displacement of the fronts is scaled by the local internal deformation radius
i1520-0485-38-1-146-e4
where Δb is the buoyancy difference between inside and outside of the fronts (Dewar and Killworth 1990; Send and Marshall 1995). Note that Rd is defined by local density anomaly induced by the freezing lead, not derived from the mean stratification.
The total buoyancy change of the dense water mass (the trapezoidal region in Fig. 13a) and the total buoyancy loss due to salt input at the surface should be balanced:
i1520-0485-38-1-146-e5
Using a scaling argument, we can omit the lowest-order term. If RdW, (5) yields
i1520-0485-38-1-146-e6
On the other hand, if Rd, ≫ W, (5) yields
i1520-0485-38-1-146-e7
When RdW, both (6) and (7) are satisfied except for the factor of 2−1/2 in (6) and 2−1/3 in (7). In CTRL, B0 ∼ 1.2 × 10−7 m2 s−3, ts ∼ 3.0 × 105 s, and f ∼ 1.4 × 10−4 s−1, and (6) yields Rd ∼ 1.2 × 103, but this value of Rd violates the assumption that Rd < W, so the former case is not appropriate. On the other hand, (7) yields Rd ∼ 1.1 × 103 m, which is consistent with the assumption that Rd > W. All experiments in the present study satisfy the condition Rd > W, so we adopt (7) as the scaling of the internal deformation radius Rd.
After a few days, baroclinic instability develops at both fronts. Linear instability theory (Eady 1949; Pedlosky 1979) indicates that the wavelength of the fastest growing mode is
i1520-0485-38-1-146-e8
and its growth rate is
i1520-0485-38-1-146-e9
where Ri is the Richardson number
i1520-0485-38-1-146-e10
and V is velocity of the along-lead jets. Since the horizontal scale of the front displacement is Rd = ΔbH/f and the vertical scale is H, the Richardson number is scaled as
i1520-0485-38-1-146-e11
Therefore, the maximum growth rate is 0.3f, and the time scale of the development of instability is estimated as 1–2 days, in good agreement with the results of our experiments.
After closing of the lead, dense saline water forms a domelike structure (Fig. 13b). Based on the previous discussion, the distance between both fronts at the base of the mixed layer is W + 2Rd, which is less than the wavelength of the fastest growing mode λc ∼ 3.9Rd. Supposing that the amplitude of the perturbation increases up to its own wavelength, the meandering of the along-lead jets induced by baroclinic instability developed at both fronts divides the underlead dense water regions into separated masses (Fig. 14). Since the dense water region has negative vorticity at the base, each separated dense water mass has anticyclonic circulation and is geostrophically balanced. The basal area of each mass is scaled as
i1520-0485-38-1-146-e12
and it follows that the radius of eddies is scaled as
i1520-0485-38-1-146-e13

Note that baroclinic instability generates pairs of positive and negative vorticity columns. The negative ones are generated in the dense water region inside the fronts and form anticyclonic eddies with high salinity cores. Therefore, these anticyclonic eddies are in geostrophic balance. On the other hand, positive vorticity columns are generated outside of the fronts, and there is no mechanism for maintaining the positive vorticity. Consequently, only anticyclonic eddies survive.

Figure 15 is a plot of the radius of eddies generated in all experiments. The vertical axis is the radius, which is the average distance between the core of eddies and their velocity maxima at 10 days after closing the lead. The horizontal axis is the scaled internal deformation radius as in (7). The radius looks approximately proportional to Rd, and least squares fitting yields
i1520-0485-38-1-146-e14
This result is consistent with the scaling analysis (13), and it also agrees with the laboratory experiments of Bush and Woods (1999) in which the eddy radius is scaled as
i1520-0485-38-1-146-e15
However, (14) does not agree with Smith et al. (2002) in which the eddy radius is scaled as
i1520-0485-38-1-146-e16
or
i1520-0485-38-1-146-e17
when the condition ts ∼ 1/f is used.

The reason for this disagreement is that the lead in Smith et al. (2002) is wider (720–5600 m), so (6) should be adopted for scaling the deformation radius. In the present paper, the lead width is no greater than 800 m and all cases satisfy W < Rd, so (7) is adopted.

The term WB0ts in (14) stands for the product of the buoyancy flux, the width where the flux is applied, and the duration time of the flux, so it represents the total buoyancy loss per unit length of the lead. Since the number of generated eddies should be proportional to the lead length and f is constant, (13) suggests that the radius of generated eddies is proportional to the cube root of the total buoyancy loss.

5. Summary and conclusions

We have performed numerical experiments to investigate the effects of brine rejection under leads above the Arctic Ocean mixed layer. A three-dimensional nonhydrostatic ocean model coupled with a thermodynamic sea ice model is used. The initial condition and the surface forcing are set to a characteristic situation of the wintertime Arctic Ocean.

Brine-driven vertical convection caused by freezing of a lead forms density fronts in the mixed layer between saline dense water under the lead and ambient relatively freshwater. At such fronts, baroclinic instability develops in a few days and separates the dense water mass into discrete anticyclonic eddies with a scale of 3 to 5 km at the base of the mixed layer. These eddies, containing saline water, survive for over 50 days and move horizontally in the mixed layer. Consequently, the salt that is supplied locally under the lead is transported by the eddies to a wider area.

The results of parameter sensitivity experiments suggest that the scale of the generated eddies is proportional to the cube root of the total buoyancy loss. This conclusion agrees with scaling analysis using a linear instability theory and the results of laboratory experiments (Bush and Woods 1999) but does not agree with the results of the previous numerical experiments by Smith et al. (2002). The reason for this disagreement is the difference in the choice of lead width W. While W is less than the internal deformation radius in the present study, that used in Smith et al. (2002) is greater.

Our model result and previous studies (Smith et al. 2002; Bush and Woods 2000) show that a line-shaped salt flux under leads create baroclinic eddies. Subsurface anticyclonic eddies with cold and high salinity cores have been observed in the Arctic Ocean (Manley and Hunkins 1985; Muench et al. 2000), but their origin is not yet clear. Those observed eddies are very similar to the eddies in our model in terms of their anticyclonicity, core T/S, and depth of kinetic energy peak. However, the horizontal scale of these observed eddies is typically 10–20 km, which is much larger than the eddies in the present study. One possibility is that several smaller eddies generated under leads merge into a larger one. Note that those eddies are observed from stations on moving ice floes, so small-scale eddies might not be detected. Another possible origin of the observed subsurface eddies is the baroclinic structure of coastal currents, discussed by Chao and Shaw (2003).

Distribution of the lead-originated salt is notable. Almost all salt supplied under the lead is captured inside the generated eddies, which exist just above the halocline. Therefore, the lead-originated salt settles only at the base of the mixed layer and is not used to increase salinity of the upper mixed layer. In many OGCMs, the salt supplied as a result of freezing leads is uniformly distributed over the mixed layer by convective adjustment or other boundary layer parameterizations, so it increases the salinity uniformly over the mixed layer. This process decreases the density gap between freshwater in the mixed layer and salty water beneath the halocline, so the vertical structure of the halocline tends to be broken. However, the result of the present study suggests an opposite scenario; that is, the salt supplied under leads settles only at the base of the mixed layer and reinforces the salinity gap at the halocline. Parameterizing these effects may improve representation of the Arctic Ocean mixed layer in OGCMs.

In the present study, we idealize the Arctic Ocean and omit some important factors, such as wind-driven drift of the sea ice pack, thermodynamic growth of thick sea ice cover, and heat transport induced by upwelling of deeper warm water. In particular, drift of the sea ice pack can significantly affect the vertical distribution of lead-originated salt because movement of the salt flux prevents formation of sharp fronts and baroclinic eddies. To develop a new parameterization of the Arctic Ocean mixed layer, those factors should be investigated. We have actually performed moving ice pack experiments, and their results suggest that the lead-originated salt is distributed to shallower levels in the mixed layer as the sea ice velocity increases. Those results will be discussed elsewhere.

Acknowledgments

We acknowledge Prof. Masahiro Endoh and Dr. Yoshiki Komuro for helpful comments and fruitful discussions. Thanks are extended to Dr. Akira Oka and Dr. Hiroaki Tatebe for helpful suggestions.

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Fig. 1.
Fig. 1.

Initial vertical profile of (a) temperature and (b) salinity.

Citation: Journal of Physical Oceanography 38, 1; 10.1175/2007JPO3620.1

Fig. 2.
Fig. 2.

Concentration of the lead-originated salt for (a),(b) day 1, (c),(d) day 5, and (e),(f) day 10 in CTRL: (left) slice at 30-m depth with velocity vector and (right) y-mean profile with density (σθ) contour.

Citation: Journal of Physical Oceanography 38, 1; 10.1175/2007JPO3620.1

Fig. 3.
Fig. 3.

As in Fig. 2 but for (a),(b) day 10, (c),(d) day 30, and (e),(f) day 50 in CTRL.

Citation: Journal of Physical Oceanography 38, 1; 10.1175/2007JPO3620.1

Fig. 4.
Fig. 4.

As in Fig. 2 (right column) but for (a) NORAND and (b) NOROT at day 10.

Citation: Journal of Physical Oceanography 38, 1; 10.1175/2007JPO3620.1

Fig. 5.
Fig. 5.

Time series of horizontal distribution of the lead-originated salt in each region for (a) CTRL, (b) NORAND, and (c) NOROT.

Citation: Journal of Physical Oceanography 38, 1; 10.1175/2007JPO3620.1

Fig. 6.
Fig. 6.

Time series of vertical distribution of the lead-originated salt for (a) CTRL, (b) NORAND, and (c) NOROT.

Citation: Journal of Physical Oceanography 38, 1; 10.1175/2007JPO3620.1

Fig. 7.
Fig. 7.

As in Fig. 2 but for (a),(b) H15 and (c),(d) H60 at day 30.

Citation: Journal of Physical Oceanography 38, 1; 10.1175/2007JPO3620.1

Fig. 8.
Fig. 8.

As in Fig. 2 but for (a),(b) DS01 and (c),(d) DS16 at day 30.

Citation: Journal of Physical Oceanography 38, 1; 10.1175/2007JPO3620.1

Fig. 9.
Fig. 9.

As in Fig. 6 but for (a) H15, (b) H60, (c) DS01, and (d) DS16.

Citation: Journal of Physical Oceanography 38, 1; 10.1175/2007JPO3620.1

Fig. 10.
Fig. 10.

As in Fig. 2 (left column) but for (a) TA10, (b) TA40, (c) W02, (d) W04, (e) TS01, and (f) TS10 at day 30.

Citation: Journal of Physical Oceanography 38, 1; 10.1175/2007JPO3620.1

Fig. 11.
Fig. 11.

As in Fig. 5 but for (a) TA10, (b) TA40, (c) W02, (d) W04, (e) TS01, and (f) TS10.

Citation: Journal of Physical Oceanography 38, 1; 10.1175/2007JPO3620.1

Fig. 12.
Fig. 12.

As in Fig. 6 but for (a) TA10, (b) TA40, (c) W02, (d) W04, (e) TS01, and (f) TS10.

Citation: Journal of Physical Oceanography 38, 1; 10.1175/2007JPO3620.1

Fig. 13.
Fig. 13.

Schematic views of the structure of dense water mass and the direction of along-lead jets (a) before and (b) after closing of the lead.

Citation: Journal of Physical Oceanography 38, 1; 10.1175/2007JPO3620.1

Fig. 14.
Fig. 14.

Schematic of eddy generation at the base of the mixed layer under the lead.

Citation: Journal of Physical Oceanography 38, 1; 10.1175/2007JPO3620.1

Fig. 15.
Fig. 15.

Plot of radius of eddies in all experiments except NORAND and NOROT. Error bar indicates resolution of the model.

Citation: Journal of Physical Oceanography 38, 1; 10.1175/2007JPO3620.1

Table 1.

List of physical constants used in the model.

Table 1.
Table 2.

List of parameter settings in each experiment. Blank entries stand for the same value as in CTRL.

Table 2.
Save