Growing Sea Ice Research Articles

Unidirectional solidification with a mushy layer. The influence of weak convection

Motivated by industrial and geophysical solidification problems such as segregation in metallic castings and expulsion of brine from growing sea ice, we present and solve a model for steady convection in a mushy layer of a binary mixture. A non-linear problem of one-dimensional convection is studied. The model under consideration describes the main properties of the convective heat and mass transport. The concentration field in the liquid, solid and mushy phases, as well as the rate of solidification and mushy layer thickness are found analytically as functions of all thermophysical parameters. The role of convective transfer is detailed in the analysis. The domain of applicability of exact analytical solutions is found.

A non-destructive method for measuring the salinity and solid fraction of growing sea ice in situ

AbstractWe describe an instrument developed to make in situ measurements of salinity and solid- fraction profiles in growing sea ice. The vertical resolution of the measurements is up to a few millimeters, with a temporal resolution of up to fractions of a second. The technique is based on impedance measurements between platinum wires around which sea ice grows. Data obtained using this instrument in laboratory experiments are in good agreement with theoretical predictions. In a field test in the Arctic, the bulk salinity of growing sea ice has been measured in situ throughout the whole depth of the ice layer. The data are compared with bulk salinities obtained from ice cores, and confirm the general understanding that the bulk salinity in ice-core studies is significantly underestimated in the lower parts of the cores. The approach can also be used in other glaciological applications and for general studies of two-phase, two-component porous media.

Steady-state chimneys in a mushy layer

Motivated by industrial and geophysical solidification problems such as segregation in metallic castings and brine expulsion from growing sea ice, we present and solve a model for steady convection in a two-dimensional mushy layer of a binary mixture. At sufficiently large amplitudes of convection, steady states are found in which plumes emanate from vertical chimneys (channels of zero solid fraction) in the mushy layer. The mush–liquid interface, including the chimney wall, is a free boundary whose shape and location we determine using local equilibrium conditions. We map out the changing structure of the system as the Rayleigh number varies, and compute various measures of the amplitude of convection including the flux of solute out of the mushy layer, through chimneys. We find that there are no steady states if the Rayleigh number is less than a global critical value, which is less than the linear critical value for convection to occur. At larger values of the Rayleigh number we find, in agreement with experiments, that the width of chimneys and the height of the mushy layer both decrease relative to the thermal-diffusion length, which is the scale height of the mushy layer in the absence of convection. We find evidence to suggest that the spacing between neighbouring chimneys at high Rayleigh numbers is smaller than the critical wavelengths of both the linear and global stability modes.

Solidification of leads: Theory, experiment, and field observations

Thin sea ice plays a central role in the surface heat and mass balance of the Arctic Ocean. In order to develop understanding of these balances we describe and analyze highly resolved temperature data taken through the air/sea/ice interface during the transition from an ice‐free to an ice‐covered Arctic Ocean surface. The data were taken to observe the thermodynamic evolution of a lead, a process that has previously only been accessible to measurement techniques confined to the lead edge. Our detailed analysis of the field data is guided by recent theoretical and experimental advances in understanding the phase dynamics of directionally solidified alloys. Because of the dearth of direct observations we also present time series of the relevant heat fluxes inferred from our data and demonstrate the controlling influence that the internal phase evolution has on these quantities. We have previously examined the stability of the brine trapped in a growing sea ice matrix both theoretically and experimentally and now find that haline convection, driven from within the growing layer, is consistent with this previous work and with the nature of direct turbulence measurements. The importance of this process is that although ice growth is continuous, the local brine flux commences abruptly, only after some time, in contrast to what had previously been supposed. Hence the ice growth process itself is a source of intermittency in oceanic boundary layer turbulence. Furthermore, we find that in this particular situation the sea ice growth is not simply a square root function of time, in contrast to the model typically used in numerical simulations. By far the most practical methods of studying lead convection are numerical simulations and laboratory models, and a strong conclusion of this study is the importance of the proper treatment of the boundary conditions describing the buoyancy flux.

Linkages between salinity and brine channel distribution in young sea ice

A high‐resolution study of bulk salinity was undertaken on laboratory‐grown sea ice to determine the extent of spatial variability of salinity and whether this was associated with brine channel structures. Ice samples at two different stages of development were compared with respect to physical state, brine distribution, and brine channel structures. Cold, growing sea ice is shown to have steep bulk salinity gradients and a highly variable brine distribution that is closely linked to the location and morphology of brine channels. Areas of high bulk salinity are found to correspond directly to the positions of the brine channels, and these areas are surrounded by ice that shows significant brine depletion. It is observed that redistribution of the brine occurs as the ice cover goes through warming and melting phases. The redistribution is attributed to an increase in porosity and pore connectivity permitting migration of brine through the ice. The distribution of brine in “warm” ice is shown to be more homogeneous and independent of brine channel structures. A number of mechanisms exploiting the enhanced mobility of brine in warm sea ice are used to explain the changes in the salinity profiles and brine distribution.

Natural convection during solidification of an alloy from above with application to the evolution of sea ice

We describe a series of laboratory experiments in which aqueous salt solutions were cooled and solidified from above. These solutions serve as model systems of metallic castings, magma chambers and sea ice. As the solutions freeze they form a matrix of ice crystals and interstitial brine, called a mushy layer. The brine initially remains confined to the mushy layer. Convection of brine from the interior of the mushy layer begins abruptly once the depth of the layer exceeds a critical value. The principal path for brine expelled from the mushy layer is through ‘brine channels’, vertical channels of essentially zero solid fraction, which are commonly observed in sea ice and metallic castings. By varying the initial and boundary conditions in the experiments, we have been able to determine the parameters controlling the critical depth of the mushy layer. The results are consistent with the hypothesis that brine expulsion is initially determined by a critical Rayleigh number for the mushy layer. The convection of salty fluid out of the mushy layer allows additional solidification within it, which increases the solid fraction. We present the first measurements of the temporal evolution of the solid fraction within a laboratory simulation of growing sea ice. We show how the additional growth of ice within the layer affects its rate of growth.

The phase evolution of Young Sea Ice

Sea ice forms as a porous matrix consisting of pure ice crystals in equilibrium with brine. We present an experimental and theoretical study that reveals that the brine expelled by growing sea ice initially remains trapped within the crystalline interstices but that drainage into the underlying water is ultimately triggered abruptly due to the onset of buoyancy‐driven convection. The onset is quantified by a critical porous‐medium Rayleigh number, and we present an empirical marginal stability diagram that defines the transition.

Phytoplankton biomass, P-I relationships and primary production in the Weddell Sea, Antarctica, during the austral autumn

An investigation into the changing phytoplankton biomass and total water column production during autumn sea ice formation in the eastern Weddell Sea, Antarctica showed reduced biomass concentrations and extremely low daily primary production. Mean chlorophyll-a concentration for the entire study period was extremely low, 0.15±0.01 mg.m−3 with a maximum of 0.35 mg.m−3 found along the first transect to the east of the grid. Areas of low biomass were identified as those either associated with heavy grazing or with deep mixing and corresponding low light levels. In most cases phytoplankton in the < 20-μm size classes dominated. Integrated biomass to 100 m ranged from 7.1 to 28.0 mg.m−2 and correlated positively with surface chlorophyll-a concentrations. Mean PBmax (photosynthetic capacity) and αB (initial slope of the photosynthesis-irradiance curve) were 1.25±0.19 mgC. mgChl a−1.h−1 and 0.042+-0.009 mgC.mgChla−1.h−1.(μmol.m−2s−1)−1 respectively. The mean index of photoadaptation,Ik, was 32.2±4.0 μmol.m−2.s−1 and photoinhibition was found in all cases. Primary production was integrated to the critical depth (Zcr) at each production station and ranged from 15.6 to 41.5 mgC.m−2.d−1. It appears that, other than grazing intensity, the relationship between the critical depth and the mixing depth (Zmix) is an important factor as, ultimately, light availability due both to the late season and growing sea ice cover severely limits production during the austral autumn.

A laboratory study of frost flower growth on the surface of young sea ice

Frost flowers are fragile ice crystals containing salt which grow to a height of 10–30 mm on the surface of young sea ice. Such flowers are observed all over the Arctic. The importance of the flowers and their accompanying slush layer is that they provide a rapid way to change the surface albedo and increase the surface roughness of young sea ice. This paper describes a laboratory technique for growing frost flowers and the physical processes which accompany the growth. The study was carried out in a saltwater tank located in a cold room. To grow frost flowers, we alternately cool the surface of the growing sea ice with a fan, then supply it with water vapor from a vaporizer. For these conditions and a room temperature of −22°C, the frost flowers begin to grow when the ice thickness reaches 5–8 mm. The flowers form at random locations on the ice and grow vertically to a height of 10–15 mm while spreading laterally from their original sites. Beneath the flowers, the surface is initially dry; then as the flowers spread laterally, a high‐salinity slush layer forms beneath them. This layer, which forms only under the flowers, grows to a thickness of 5 mm in 48 hours and has a characteristic lateral scale of 100–200 mm. The salinity of the slush layer is about 80 psu, compared with a frost flower salinity of 100 psu. Within 24 hours of their appearance, the flowers grow to cover 75–90% of the surface. A surface water budget for the flowers and slush layer shows that most of the water in the flowers and slush layer comes from the ice interior, not from the vaporizer. This implies that an external vapor source may be important in determining the initial growth of the flowers but not in their subsequent development.

Double diffusive and direct instabilities below growing sea ice

A detailed study is presented of the instability of an initially motionless, ice-free and homogeneous layer of salt water which is sufficiently cooled from above such that ice formation occurs. Basic state boundary layer profiles of temperature and salinity are computed by solving the corresponding Stefan problem numerically. At sufficiently large Rayleigh numbers, these profiles become unstable to both direct and double diffusive instabilities. Of fundamental interest is the occurrence of a new type of oscillatory instability which is present when both temperature and salinity fields are destabilizing. Fastest growing modes are presented for the ice-water system. It is found that the wavelength of the dominant mode of convection increases with increasing ice thickness.

The formation of a haline shelf front in wintertime in an ice-covered arctic sea

During some winters, the water overlying Mackenzie shelf in the southeastern Beaufort Sea becomes quite saline (33–35) and at freezing temperature throughout. Although this water is found at the surface, its density is that of waters within the halocline of the arctic basin, and ventilation of the halocline occurs. The formation of sea ice is a necessary, but not a sufficient condition for the production of this water. Observations from the winter of 1980–1981 are presented which illustrate that a two-stage preconditioning of shelf waters is also required: first, surface waters of low salinity must be driven from the shelf by strong westerly winds; then, more saline water must upwell onto the shelf in response to prolonged easterly winds. A haline front forms on the outer shelf separating cold, saline shelf waters from slightly warmer, less saline slope waters. The characteristics of this front are controlled by the input of negative buoyancy from ice growth over the shelf, and by turbulent entrainment and mixing driven by under-ice convection. A simple model to predict the position, dimension and buoyancy contrast of this front is presented. The cross-isobath circulation is examined and found to be relatively ineffective at flushing dense waters from the shelf over a winter. Thus shelf waters accumulate almost all the salt expelled from growing sea ice over the same time. The magnitude of the contribution by this shelf to renewal of waters in the arctic halocline is estimated to average 0.04 × 10 6m 3s −1 over a period of years. Although small relative to the overall rate of renewal (1 × 10 6m 3s −1), this contribution is in proportion to the fraction of the arctic shelf area which this region represents.

Experimental examination of growing and newly submerged sea ice including acoustic probing of the skeletal layer

Results of an in-situ experiment to examine acoustic parameters and scattering properties of growing and newly submerged arctic sea ice are presented. The primary emphasis is on the acoustic properties of highly porous sea ice. High-resolution (to about 1 cm) vertical profiles of the longitudinal wave speed in growing and submerged sea ice are derived from the experimental data. The results indicate a skeletal layer about 3 cm thick at the bottom of the growing ice. The time dependence of vertical sound-speed profiles in a submerged ice block reveals a long time scale process of up to 80 h and a short process of a few hours. The former process is the warming of the block; the latter is thought to be due to the disturbance of hydrostatic equilibrium as the ice is submerged. Concurrently with the wave-speed measurements, scattering from the undersurface of the ice was measured at several frequencies. A comparison with predictions based on the sound-speed data demonstrates the ability to predict normal incidence ice reflectivity from sound-speed profiles as well as the viability of using scattering data in inversions to obtain sound-speed profiles. Absorption of a longitudinal wave propagating vertically in ice was also measured. The peak absorption rate found in the skeletal layer was between 2 and 5 dB/cm at 92 kHz. The temperature dependence of absorption seen in the submerged ice suggests that the McCammon–McDaniel equation (∼T−2/3) is useful away from the skeletal layer. The measurements of ice temperature as a function of time and depth allow a calculation of the thermal diffusivity of the upper region of growing sea ice (0.0080 cm2/s) and an ‘‘effective’’ thermal diffusivity of the submerged ice block (about 0.0015 cm2/s ). Measurements of salinity profiles in the ice, along with the temperature profiles, are used to calculate porosity, which is then used in models of the longitudinal wave speed as a function of porosity. A comparison between models and experiment is employed that suggests a possible mechanism for the increased speed seen experimentally in the bottom portion of the ice after submergence.

Laboratory and field measurements of acoustic scattering from sea ice

The morphology of sea ice growing thermodynamically in calm seas is complicated. The ice is characterized by temperature and salinity gradients that are driven by the prevailing oceanic and atmospheric conditions, the gradients, in turn, affecting physical properties such as permeability, porosity, liquid brine content, and the structure of the ice-water interface. That interface, in particular, exhibits a range of dynamic characteristics from submillimeter, pure ice dendrites that grow down into the liquid to smoother cellular structures that are believed to develop when either thermodynamic growth is slowed or when the salinity of the liquid is much reduced. The objective of the work presented here is to measure and understand the role changing ice morphology has on the acoustic properties of sea ice. To that end, measurements over the frequency band from 120 to 800 kHz have been made of the scattering properties of sea ice when insonified by a narrow beam at normal incidence. Observations made in an outdoor tank at CRREL and from the research vessel Polarstern, which operated in the Fram Straits during May 1988, reveal that the reflection coefficient can vary by at least a factor of 5 depending on the composition and structure of the ice near the ice/water boundary. The dendritic interface typical of growing sea ice plays a particularly important role resulting in improved acoustic coupling into the ice. As seasonal evolution changes the interface from dendritic to either cellular or ablating, the reflection coefficient rises to about 0.25. [Work supported by ONR and the Alfred Wegener Institute.]

Surface-Based Passive Microwave Observations of Sea Ice in the Bering and Greenland Seas

Measurements of brightness temperatures of sea ice were carried out during both the MIZEX field experiments in 1983, the first in Februrary in the Bering Sea and the second in June/July in the northern Greenland Sea. In the Bering Sea thin growing sea ice types from black ice to 400-mm-thick snow-covered floes were investigated. Brightness temperatures increased with ice thickness up to 100 mm from values of 100 K for open water to as high as 250 K (e= 0.97) for thick ice, and a moderate dependence on snow thickness was found. In the Greenland Sea thick first-year and multiyear ice types were studied. Brightness temperatures were quite variable depending on the daily melt-freeze cycle superimposed on the seasonal warming, ranging from near blackbody values for melting conditions to multiyear-like spectra when the surface layers refroze. The melt season was sufficiently advanced, however, that first-year and multiyear ice could not be differentiated radiometrically.

Fluxes associated with brine motion in growing sea ice

Laboratory and field studies have demonstrated that fluid motion occurs at two locations in growing sea ice: in a network of brine channels and within the skeletal layer at the ice-water interface. Brine channel fluxes estimated using brine channel areal density from natural sea ice and channel velocities from laboratory studies are compared with recent measurements reported in the literature. Fluxes into the porous skeletal layer of sea ice may be estimated using rates of nutrient uptake by ice algae and adjacent seawater nutrient concentrations. Both approaches indicate fluxes of the order of 10-6 cc cm-2 s-1 (l m-2 h-1), which are about equal to fluxes reported in bioirrigated sediments. Fluxes of this magnitude indicate a very short residence time for the liquid phase in the skeletal layer, suggesting that this fluid motion may be important in maintaining the ice algae community. © 1984 Springer-Verlag.

Measurements of salinity and volume of brine excluded from growing sea ice

The volume of brine excluded from growing sea ice and its salinity were measured using a brine sampler. The measurements were made, in both laboratory and field, under various growth conditions of the sea ice. The salinity of the brine becomes higher, and the volume flux decreases as the sea ice growth rate decreases. Consequently, the salt flux of the brine decreases with decreasing growth rate. In the case of sea ice growth at a constant rate, as the sea ice becomes thicker, the salinity of the brine excluded increases while its volume flux decreases. However, the salt flux is nearly independent of the ice thickness increase, at least up to a thickness of 15 cm. For sea ice growth rates between 1.7×10−5 and 1.4×10−4 cm s−1, and for a seawater salinity of 33.0‰, the brine salinity ranged from 42.3‰ to 92.7‰, the volume flux ranged from 6.3×10−6 to 3.4×10−5 cc cm−2 s−1, and the salt flux ranged from 6.4× 0−7 to 1.5×10−6 g cm−2 s−1.

Numerical study of the water movement driven by brine rejection from nearshore Arctic ice

A numerical model of brine‐induced circulation is used to study circulation in the lagoons and shelf waters of the Beaufort Sea. The model solves the equations of motion, continuity, and salt transport. The salt flux is set as a function of the salinity difference between growing sea ice and seawater and the rate of ice growth. Several experimental runs show that under‐ice haline circulation is controlled by salt flux and bottom configuration. An idealized model of a shallow arctic lagoon gives currents of 1 cm s−1 for brine‐induced circulation under landfast ice. This agrees very well with observations.

Ice stalactites: comparison of a laminar flow theory with experiment

Recent field observations in the polar oceans show that the hollow tubes of ice called ice stalactites form around streamers of cold brine rejected by the growing sea ice. In a laboratory study of this process, we inject cold, dense brine a t a constant salinity, temperature and volume flux into an insulated tank of sea water held at its freezing point, then photograph the resultant stalactite growth. Because the inner wall temperature of the stalactite remains on the salinity-determined freezing curve, as the stalactite grows and the temperature deficit of the brine goes into the growth of ice, the inner wall melts to dilute and cool the adjacent brine back to its freezing point. This melting means that both the inner and outer stalactite radii increase with time. The radius of the stalactite tip, which is constant for each experiment, is shown to be controlled by the onset of a convective instability. If the tip becomes too large, overturning occurs and the sea-water intrusion freezes, reducing the radius of the tip so that the flow leaving the tip is marginally stable. Inside the stalactite, since the inner radius increases with time, both theory and experiment show the interior flow to be convectively unstable. The present study also derives a solution from the constant-heat-flux Graetz solution for the growth in both length and side-wall area of the stalactite. The experiments show that away from the stalactite base and the very beginning of the experiment this solution, with convection accounted for by an adjustable coefficient, describes the experimental growth. Finally, analysis of the experiments shows that as much as 50% of the ice represented by the cold brine does not go into the stalactite, rather the ice goes directly into the ocean as loose crystals.

Sea ice and supercooled water

The existence of supercooled water below growing sea ice has been postulated in the past to explain anomalous temperature and salinity values in the water column. In addition supercooling has been invoked to explain ice-crystal production in the water that is tens of meters below the ice sheet and on the sea bed near the shore. From a study of the literature and the laboratory experiments we conclude that the postulate is unnecessary and that supercooling of the water mass, if it exists at all, is transitory.

The water structure under a growing sea ice sheet

Data illustrating seasonal changes in temperature and salinity profile beneath an annual sea ice cover are presented. The water column heat loss is about 15% of the latent heat extracted for ice growth. Time series temperatures (measured over one month with a thermistor chain depending from the ice sheet) indicate penetrative convective plumes as a probable mechanism for profile changes and are tentatively related to laboratory studies.