1. Introduction
The majority of grounded ice in Antarctica drains through its peripheral ice shelves, the floating extension of the ice sheet where the most profound changes in ice thickness have been observed (Pritchard et al. 2012; Rignot et al. 2013). Ice shelves vary in thickness from a few tens of meters to as much as 2000 m and provide an important interface between the continental ice sheets and the surrounding ocean. Changes in the shape and thickness of ice shelves can modulate the flow speed of their tributary glaciers (Dupont and Alley 2005; Rott et al. 2002). Thinning of ice shelves because of unsteady ocean melting can reduce lateral and basal traction at the terminus of outlet glaciers, reducing the restriction on the flow of the grounded ice upstream (Shepherd et al. 2004; Schoof 2007), thereby mediating the ice sheet’s contribution to sea level rise. Direct oceanographic measurements beneath ice shelves are limited by the difficulty in gaining access through the ice shelf itself. The access can be made by drilling an ice shelf with a pressurized hot water drill, and the procedure requires expensive logistics. A few measurements have been made beneath ice shelves that are subject to the intrusion of Circumpolar Deep Water (CDW), which retains its temperature a few degrees above the in situ freezing point: George VI Ice Shelf (Cooper et al. 1988) and Pine Island Glacier (Stanton et al. 2013).
The George VI Ice Shelf occupies George VI Sound, a narrow channel running north–south between the west coast of the Antarctic Peninsula and Alexander Island. In a state of equilibrium, an ice shelf loses mass through basal melting and ice front calving at the same rate as it gains mass through the accumulation of snow and the inflow of ice from tributary glaciers. Bishop and Walton (1981) determined that steady-state melt rate of the George VI Ice Shelf varies with position from 1 to 8 m yr−1, while Potter et al. (1984) estimated an equilibrium melt rate averaged over the entire ice shelf to be 2 m yr−1. Corr et al. (2002) used a phase-sensitive radar at one site on the southern part of the ice shelf to measure a melt rate of 2.8 m yr−1 over a 12-day period in December 2000. Jenkins and Jacobs (2008) derived a melt rate from oceanographic data using tracer conservation equations and assuming that the ocean currents were in geostrophic balance; they found melt rates ranging between 2.3 and 4.9 m yr−1 in March 1994. The modeling study of Holland et al. (2010) found a local maximum melt rate of ≈8 m yr−1 beneath the southern part of the shelf, with the melt rate decreasing to 1 m yr−1 toward the thinner ice farther north, which is in good agreement with the observations by Bishop and Walton (1981). These studies reveal that the George VI Ice Shelf is currently losing mass, which correlates well with sustained thinning of ice shelves reported in the western part of Antarctic Peninsula (e.g., Pritchard et al. 2012; Rignot et al. 2013). In the Antarctic Peninsula, mean atmospheric temperature has risen rapidly in the past 50 yr (Comiso 2000; Vaughan et al. 2001), and ice shelves in this region have retreated. For example, the Larsen Ice Shelf (Rott et al. 2002) and Wordie Ice Shelf (Doake and Vaughan 1991) have reacted to this warming by disintegrating. The present George VI Ice Shelf may thus represent an ice shelf that is in the process of disintegrating from the surface (Vaughan and Doake 1996) as well as from rapid basal melting by the intrusion of CDW (Bishop and Walton 1981; Talbot 1988).
The majority of measurements beneath ice shelves have been made in the ice shelf cavities flooded with a cold water mass (temperature near the surface freezing point), for example, the Filchner–Ronne (Nicholls et al. 1991; Nicholls and Jenkins 1993; Nicholls et al. 1997), Fimbul (Orheim et al. 1990; Hattermann et al. 2012), Larsen C (Nicholls et al. 2012), and Ross (Gilmour 1979; Jacobs et al. 1979; Arzeno et al. 2014; Robinson et al. 2014) ice shelves. Robin (1979) argues that thermohaline forcing, rooted in the depth dependence of the freezing point of seawater coupled with the exchange of heat and salt at the ice shelf–ocean interface, generates thermohaline convection within these colder subice shelf cavities. The resulting circulation leads to high melt rates near the grounding line, the point where the ice goes afloat, with freezing possible at lower ice shelf drafts (Hellmer and Olbers 1989; Jenkins 1991). The observations lend support to the idea that the circulation beneath the ice shelf is energized by a combination of the ascending plume of meltwater and tidal forcing, with the subice shelf cavity environments not isolated but sensitive to external climatic conditions.
The ice shelf melt rate from given oceanic conditions, such as temperature, salinity, and water speed, is typically estimated using a parameterization, a set of equation that approximate the fluxes of heat and salt from the ocean to the ice. The parameterization is used in various ocean models with different coordinate formulations, for example, z-coordinate (Losch 2008), σ-coordinate (Grosfeld et al. 1997; Beckmann et al. 1999; Dinniman et al. 2007), isopycnal-coordinate (Holland and Jenkins 2001; Little et al. 2008), and finite-element (Kimura et al. 2013) ocean models. The most commonly used parameterization is a “three-equation model,” which conserves the fluxes of heat and salt within the ice–ocean boundary layer and constrains the temperature of the ice–ocean boundary layer to be at the freezing point (e.g., Holland and Jenkins 1999). The three-equation model expresses oceanic transport of heat and salt as a function of the bulk differences in velocity, heat, and salt across the boundary layer based on results from laboratory experiments reported by Kader and Yaglom (1972). The two assumptions that underpin the existing parameterization are 1) a smooth ice base morphology and 2) a fully developed turbulent flow in the boundary layer.
One of the pronounced manifestations of diffusive convection is a thermohaline staircase, a stack of well-mixed layers separated by sharp interfaces. Diffusive convection in the ocean occurs when temperature and salinity increase with increasing depth in the presence of a gravitationally stable stratification. Diffusive convection is prevalent at high latitudes where the logistics of sampling is demanding. However, diffusive convection–favorable thermohaline staircases have been observed both in the Arctic Ocean (e.g., Neal et al. 1969; Neshyba et al. 1971; Padman and Dillon 1987; Polyakov et al. 2012) and in the Weddell Sea in Antarctica (e.g., Foster and Carmack 1976; Muench et al. 1990; Robertson et al. 1995). Diffusive convection leads to a set of growing oscillations at the interface between cool, fresh, and warm, salty water (e.g., Turner and Stommel 1964; Marmorino and Caldwell 1976; McDougall 1981; Linden and Shirtcliffe 1978; Fernando 1987). A diffusive convection–favorable staircase can be generated in a laboratory by heating a salinity-stratified fluid from below (e.g., Turner and Stommel 1964; Turner 1968; Marmorino and Caldwell 1976; Fernando 1987, 1989a). These experiments show that the destabilizing buoyancy flux provided by the heating generates convection at the bottom and results in successive convective layers separated by sharp interfaces.
We present observations of a thermohaline staircase beneath the George VI Ice Shelf. We apply a parameterization of heat and salt fluxes formulated from a laboratory experiment of heating a stable salinity gradient from below to predict the melt rate at an ice shelf base in the presence of a diffusive convection–favorable staircase. Our formulation to predict the melt rate assumes the absence of shear (a vertically varying horizontal current). While the melting of ice shelves can produce the vertical distribution of water masses that is susceptible to diffusive convection, none of the observations beneath ice shelves have so far detected such signals. Thus, the effect of diffusive convection on melting ice shelves has never before been considered. In the presence of a thermohaline staircase, the assumptions employed in the current framework are not valid to estimate the melt rate of the ice shelf. We present an overview of the diffusive convection–favorable staircase beneath the George VI Ice Shelf in section 2. Section 3 summarizes the three-equation model, the widely used method to predict ice shelf melt rate, based on the assumption of shear-driven turbulence, and presents our formulation, based on the assumption of diffusive convection. The limitations of the formulation and implications of diffusive convection beneath the ice shelf are discussed in section 4. Our conclusions are summarized in section 5.
2. Observations
The George VI Ice Shelf has two ice fronts, one in the north, in Marguerite Bay, and one in the south, in Ronne Entrance (Figs. 1a,b). The maximum ice thickness reaches around 500 m about 70 km from Ronne Entrance, where a ridge of thick ice extends across the sound (near 70°W). The vast majority of ice enters the ice shelf from Palmer Land and flows toward Alexander Island (Potter et al. 1984; Humbert 2007). As the ice travels toward the ice fronts, the majority of the continental ice mass from glacier discharge is removed by the high basal melt rate in this region and is replaced by local surface accumulation. In total, the surface accumulation makes up ~20% of its mass budget (Potter et al. 1984). Both Ronne Entrance and Marguerite Bay are known to be flooded by CDW. It is the intrusion of this water mass beneath the ice shelf that gives rise to rapid basal melting. In the austral summer of 2012, two access holes were drilled at the site (72°49.9′S and 70°50.6′W) a few days apart, allowing for two sets of CTD profiles. In each case, a FastCAT SBE49 CTD and power data interface module (PDIM) interface were lowered down the borehole on a steel frame, recording data at 16 Hz to a laptop PC. We obtained 12 profiles over a period of 10 h from the first access hole on 8–9 January 2012 and a further 20 profiles were obtained from the second hole on 12–13 January. In the upper 25 m of the water column, a low profiling speed of ~0.07 m s−1 was used to capture the details of a well-defined staircase. The CTD used pumped sensors that ensured adequate sampling. The depth of the ice base is identified by finding the depth that matches the in situ temperature and freezing temperature, calculated from the salinity and pressure measurements. Salinities are reported using the International Thermodynamic Equation of Seawater-2010 (TEOS-10) Absolute Salinity scale (IOC et al. 2010) with the correction factor δSA = 0, since there are no direct anomaly measurements beneath the ice shelf. At the drill site, the ice thickness and the depth of the ocean are approximately 340 and 900 m, giving a water column thickness beneath the ice base of 560 m.
(a) Map of the Amundsen/Bellingshausen sector of Antarctica showing the area enlarged in Fig. 1b. (b) Map of the George VI Ice Shelf and surrounding continental shelf. The color scale shows the thickness of the George VI Ice Shelf; contours indicate the bathymetry. The location of two adjacent boreholes (72°49.9′S and 70°50.6′W) is indicated by the black dot.
Citation: Journal of Physical Oceanography 45, 1; 10.1175/JPO-D-14-0106.1
Profiles of (a) potential temperature and (b) T − Tf, where Tf is the local freezing temperature. The zero depth indicates the base of the ice shelf.
Citation: Journal of Physical Oceanography 45, 1; 10.1175/JPO-D-14-0106.1
Profiles of (a) temperature, (b) salinity, and (c) Rρ, indicating the result of a layer detection technique based on conductivity gradient. The portions of the water column identified as layers or interfaces are colored red and blue, respectively.
Citation: Journal of Physical Oceanography 45, 1; 10.1175/JPO-D-14-0106.1
PDF of (a) Rρ and (b) ΔT. The PDFs are calculated by binning Rρ and ΔT every 0.2° and 0.02°C, respectively. (c) A scatterplot of ΔT and Rρ. Red dots indicate the first layer below the ice shelf.
Citation: Journal of Physical Oceanography 45, 1; 10.1175/JPO-D-14-0106.1
The thermohaline staircase structure observed here differs in an important respect from that reported by Jacobs et al. (1981) and Neal et al. (1969). Jacobs et al. (1981) observed a staircase structure beside the Erebus Glacier Tongue in Antarctica. Their staircase structure is generated by cooling from the side, analogous to the laboratory experiment of Huppert and Turner (1980). The layering structure beside the Erebus Glacier Tongue occupies the water column from the surface down to a depth of 400 m (Jacobs et al. 1981). The observed staircase had a statically stable configuration of relatively warm, fresh water overlying cold, salty water, which is not susceptible to diffusive convection but to differential diffusion. Stevens et al. (2014) argues that the layers observed beside the Erebus Glacier Tongue might have formed as a result of shear-driven instability, where the shear is caused by flow over nearby bottom topography. There are no similar topographic features near our drilling sites. Neal et al. (1969) observed diffusive convection–favorable staircases under a drifting ice island in the Arctic, but these staircases were found 220–340 m below the base of the sea ice. In contrast, the diffusive convection–favorable staircase beneath the George VI Ice Shelf is confined to the upper 20 m of the water column beneath the ice shelf, so, even if the bottom topography existed, it is unlikely to play a role in forming the staircase structure.
The thickness of the layers changes with time, resulting in their coalescing (Fig. 5). The layer thickness may change because of 1) the imbalance in the turbulent kinetic energy between two adjacent layers or 2) the advection of an unchanging layer past the borehole. A thermohaline staircase is known to undergo merging events whereby two adjacent layers coalesce. Radko (2007) proposes two distinct mechanisms: B- and H-merging scenarios. In the B-merging scenario, slightly stronger interfaces strengthen at the expense of weaker interfaces, which gradually erode away, with the position of stronger interfaces remaining stationary. In contrast, in the H-merging scenario slightly thicker layers thicken at the expense of thin layers, which shrink and eventually disappear. Changes in the thickness of layers allow interfaces to drift vertically and eventually to collide with the adjacent interface. Radko (2007) suggests that the dependence of heat and salt fluxes on ΔT and ΔS results in the B-merging scenario, whereas the dependence of fluxes on the height of layers can lead to the H-merging scenario. Examples of the B-merging scenarios in field data are presented by Zodiatis and Gasparini (1996) and Radko et al. (2014) who documented the temporal changes in a staircase in the Tyrrhenian Sea and central Canada basin. Numerical simulations of Radko et al. (2014) show that the B-merging scenario is preferred over the H-merging scenario. When the turbulent heat flux within a layer is dominated by convective elements rising from a thin boundary layer, the flow dynamics are governed by the instabilities within the layer, and the height of the layer becomes unimportant in determining the turbulent heat flux (Turner 1973). This classic argument suggests the preference of the B merger over the H merger in the oceanic thermohaline staircase, where the layers are sufficiently thick.
Evolution of potential temperature profile in the upper 10 m from the ice shelf between 0645 and 0749 UTC on 9 Jan. Each profile is separated by 0.5°C. The zero depth indicates the base of ice shelf. The red dots on the profiles indicate the layers, whereas the black lines indicate the interfaces. The numbers below the profiles indicates the time in hours with respect to the first profile, the temperature difference between the first and second homogeneous layers beneath the ice shelf (ΔT1), and Rρ of the first interface.
Citation: Journal of Physical Oceanography 45, 1; 10.1175/JPO-D-14-0106.1
In our data, a large temperature step of ~0.3°C persists for 15 min, but this step erodes into smaller steps after 30 min (Fig. 5). Below this step, the ~0.09°C interface tends to migrate up and down over the 50-min observation period. Vertical migration of an interface has been observed in a laboratory experiment when the interface is separated by two layers that are subjected to cabbeling (McDougall 1981). Alternatively, the interface migrates when a thermohaline staircase is generated by an external source of buoyancy (e.g., Turner 1968; Marmorino and Caldwell 1976; Fernando 1987). The external buoyancy source causes an imbalance in the turbulent intensities in the adjoining layers, and the interface migrates away from the source (Turner 1968; Marmorino and Caldwell 1976; Fernando 1987). In our case, the ice is a heat sink and acts as a buoyancy sink. One may expect that the first interface below the ice shelf would migrate downward; there are, however, no clear indications of downward migrations in the observations. Our thermohaline staircases appear to be transient, and we are unable to identify the dominant merging scenario from the CTD data.
Exchange of heat and salt between the ice shelf and source water (the water mass that is the source of heat and salt for melting) constrains the temperature and salinity gradients of the water mass beneath an ice shelf in T–S space. Assuming that the turbulent diffusivities of temperature and salinity are equal, any water masses generated by the melting of glacial ice should lie on the meltwater mixing line (Gade 1979). The meltwater mixing line is a straight line in T–S space with a gradient typically lying between 2.4° and 2.8°C kg g−1, passing through the source water properties (Greisman 1979; Gade 1979). Use of the meltwater mixing line has been successful in deducing source waters from the T–S properties measured beneath ice shelves (e.g., Gade 1979; Nicholls and Jenkins 1993; Hattermann et al. 2012; Nicholls et al. 2012), which lends support to the idea that the flows beneath these ice shelves are fully turbulent. Near the ice base the T–S gradient found in our field observations deviates considerably from the expected value of 2.4–2.8°C kg g−1 (Fig. 6). Our staircase has Rρ = 2, which corresponds to the T–S slope of 6.8, and the dotted line in Fig. 6 is parallel with the observed T–S characteristic. This suggests that 1) turbulent diffusivities of temperature and salinity are not the same and 2) a role for diffusive convection in modulating the T–S relationship beneath the George VI Ice Shelf.
T–S plot for the borehole data. The solid line indicates the meltwater mixing line with the source water of T = 1.18°C and S = 34.80 g kg−1. The temperature and salinity relationship, derived from the mean Rρ = 2, is represented by the dashed line.
Citation: Journal of Physical Oceanography 45, 1; 10.1175/JPO-D-14-0106.1
3. An estimate of ice shelf melt rate in the presence of a diffusive convection–favorable staircase
The boundary layer beneath ice shelves can be divided into three distinct but overlapping regions: 1) the viscous sublayer (millimeters to a few centimeters) just below the ice shelf, where molecular processes and surface roughness both influence the mixing; 2) the inertial sublayer (a few meters), where turbulent mixing is influenced by the proximity and overall roughness of the boundary; and 3) the outer layer (a few tens of meters), where effects of rotation and stratification dominate the mixing (McPhee 2008). The role of the viscous sublayer in regulating the heat and salt fluxes toward the ice base was first recognized by Mellor et al. (1986). Since then, a number of studies have included a different parameterization of the viscous sublayer and turbulent flow in the inertial and outer layers into the prediction of melt rate from given oceanic conditions below the ice, commonly referred to as a three-equation model (e.g., McPhee et al. 1987; Steele et al. 1989; Holland and Jenkins 1999). We begin by briefly summarizing the three-equation model. We then consider heat and salt flux balances between the viscous and inertial sublayers to estimate the melt rate of an ice shelf. We estimate the molecular heat and salt fluxes at the edge of the viscous sublayer by solving the one-dimensional diffusion equations. In our case, the inertial sublayer and outer layer consist of diffusive convection–favorable staircases. We represent the heat and salt fluxes of a diffusive convection–favorable staircase by applying the parameterization described by Fernando (1987).
a. Three-equation model
b. Diffusion of heat and salt within the viscous sublayer
Dependence of (a) λ and (b) Sb on T*.
Citation: Journal of Physical Oceanography 45, 1; 10.1175/JPO-D-14-0106.1
Evolution of (a) melt rate (b) ice shelf–ocean interface, hS, hR, and hT. These quantities are calculated by assuming T∞ = 0.45°C and S∞ = 34.46 g kg−1.
Citation: Journal of Physical Oceanography 45, 1; 10.1175/JPO-D-14-0106.1
c. Balance of heat and salt fluxes between the viscous and inertial sublayers
Schematic representation of the ice shelf–ocean interface and thermohaline staircase.
Citation: Journal of Physical Oceanography 45, 1; 10.1175/JPO-D-14-0106.1
d. Comparison of model results with observation
Melt rate derived from our formulation for different ΔT and N2. Dark dots indicate the observed ΔT and N2 from George VI Ice Shelf. Our measurements show a melt rate of 1.4 m yr−1 during the CTD casts.
Citation: Journal of Physical Oceanography 45, 1; 10.1175/JPO-D-14-0106.1
4. Discussion
Previous direct oceanographic measurements beneath ice shelves suggest that the flow in the outer layer is fully turbulent as a result of the large-scale circulation, modulated by tidal motion (e.g., Gilmour 1979; Jacobs et al. 1979; Nicholls et al. 1991; Nicholls and Jenkins 1993). When the far field is sufficiently energetic, a parameterization based on Kader and Yaglom (1972) is commonly used to represent the heat and salt fluxes within the viscous and inertial sublayers to estimate the melt rate (e.g., Holland and Jenkins 1999; McPhee 2008). This parameterization has been successful in predicting the melt rate of large ice shelves that have a relatively smooth ice base morphology and are surrounded by cold water (near-surface freezing point), such as the Filchner–Ronne Ice Shelf and Larsen C Ice Shelf (e.g., Nicholls and Jenkins 1993; Jenkins et al. 2010; Nicholls et al. 2012). The low melt rate regime decreases the likelihood of a rough base and of strong stratification, while the energetic tidal flows in the sector contribute to maintaining a high level of turbulence (e.g., Makinson and Nicholls 1999). Beneath these ice shelves, Nicholls and Jenkins (1993) conjectured that signatures of diffusive convection had been obliterated by the turbulence associated with the tidal motions and buoyancy-driven ascending plume.
Although the geometric configuration of the George VI Ice Shelf is unique, there are many ice shelves in the eastern Pacific sector of Antarctica that are subject to the intrusion of CDW, which induces high melt rates, complex basal topography, and the possibility of strong stratification. The weak tidal regime in these regions (e.g., Padman et al. 2002) reduces the likelihood of a fully turbulent flow, although with a sloping base, strong melting gives buoyancy-driven flows that might be quite energetic and turbulent. It is unclear if the assumptions made in the existing boundary layer parameterization are compatible with these ice shelves. We have applied the existing parameterization of diffusive convection to predict a melt rate of the George VI Ice Shelf, where the upper 20 m of the water column is occupied by a diffusive convection–favorable thermohaline staircase. In the staircase, the upward molecular diffusion of destabilizing thermal buoyancy flux across the relatively high-gradient interface exceeds stabilizing saline buoyancy flux, resulting in a downward density flux that drives convection in the well-mixed layers. The vertical fluxes in the well-mixed layers are maintained by the convection, while molecular diffusion dominates the transfer of heat and salt at the interfaces. The vertical fluxes of temperature and salinity produce an upgradient density flux rather than the downgradient density flux characteristic of “ordinary” turbulence. As a result, Ruddick and Gargett (2003) argue that diffusive convection is dramatically unlike ordinary turbulence and hence must be considered, and incorporated in models, separately. It is unlikely that diffusive convection can be fully incorporated into the existing ice shelf melt rate parameterizations. Our calculation suggests that diffusive convection can melt the ice up to 1.3 m yr−1 for the observed oceanic condition beneath the George VI Ice Shelf. However, we do not have measurements beneath other ice shelves to confirm if diffusive convection is a significant process more generally. The vertical distribution of water mass beneath the majority of Antarctic ice shelves is susceptible to diffusive convection (cool, freshwater overlying warm, salty water), but it is likely that the mechanical energy (e.g., tidal force and meltwater outflow) available to obliterate the manifestation of a thermohaline staircase is different. In the presence of weak mechanical energy regime, the thermohaline staircase can survive beneath ice shelves.
Statically stable, density-stratified shear layers are ubiquitous in the ocean. Shear flow beneath an ice shelf cavity can be generated by tides and ascending meltwater plumes. Unlike previously published formulations for estimating melt rate, our formulation ignores the effect of shear beneath an ice shelf and does not consider the possibility of ice formation as a result of in situ supercooling. The density near the freezing point is tightly coupled to salinity, and therefore the formation of ice and the consequential expulsion of salt is likely to result in an unstably stratified environment, leading to pure convection (McPhee 2008). In the presence of sufficiently strong shear, the thermohaline staircase may be obliterated, and the assumptions made in this formulation are no longer valid. Turbulence in the ocean is often governed by a competition between shear, which promotes instability, and statically stable stratification, which acts to stabilize the water column. It is not clear how shear, when combined with diffusive convection, will influence the melt rate. Padman (1994) speculates that shear may act to reduce the stability of the diffusive convection interface, thereby increasing the scalar fluxes, while the shear inhibits scalar fluxes in salt fingering, the other type of double-diffusive convection (Linden 1974; Ruddick 1985; Kunze 1994; Kimura et al. 2011). Laboratory experiments of diffusive convection in the presence of grid-generated turbulence show that the ratio of saline to thermal buoyancy flux can be maintained at a much higher ratio than in the absence of the shear, as a result of an increase in an “entrainment flux” by the mechanical mixing (Crapper 1976). The formulation presented here relies on the flux ratio that prevails in the absence of shear, and some modification will be likely needed to incorporate the effect of shear.
5. Conclusions
We observed thermohaline staircases beneath the George VI Ice Shelf. The staircase structure is confined to the upper 20 m of the water column, which is 500 m thick. A well-mixed layer occupies the upper few meters of the water column. The observation raises a doubt about the applicability of the widely used three-equation model to predict the melt rate. This motivated us to consider an alternative approach to estimating the melt rate, one that incorporates the effect of diffusive convection. Melting of the ice cools and freshens the ocean below, which both destabilizes and stabilizes the water column, depending on the depth below the ice base. At the ice shelf–ocean interface, the stabilization of buoyancy by the freshening overwhelms the destabilization of buoyancy by the cooling, maintaining the net stable stratification, but the molecular diffusivity of heat is two orders of magnitude larger than salt. As a result, sufficiently far from the ice base (~1 cm), the cooling of the ocean by the ice generates overturning eddies, thereby creating the staircase in a way that is an inverted analog to the situation of a salt-stratified water column being warmed from below. We have applied the parameterization of heat and salt fluxes formulated and calibrated in laboratory experiments by Fernando (1987). The destabilizing buoyancy flux from the melting of ice dictates the velocity scale of overturning eddies within the well-mixed layer. The eddies impinge on the interface and engulf the nonturbulent fluid into the well-mixed layer, thereby supplying heat to melt the ice. We estimate heat and salt fluxes by the above mechanism beneath the George VI Ice Shelf, and these fluxes are broadly consistent with the observed melt rate of the ice shelf. This is the first study to consider the effects of thermohaline staircases beneath a melting ice shelf. More experiments, observations, and numerical simulations are needed to fully understand the role of turbulence and thermohaline staircases on melting ice shelves.
Acknowledgments
Comments from two anonymous reviewers improved the manuscript. The work was supported by the U.K. Natural Environment Research Council under NE/H009205/1.
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