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Consolidated pancake ice forms when pancake ice packs, rafts and freezes together with interstitial frazil ice. Its heterogeneous granular structure can retain stacked layers and acquire later columnar basal growth.

// Target: geophysics.bigb

The Odden ice tongue is an intermittent extension of young sea ice into the Greenland Sea. Repeated formation and export of frazil ice and pancake ice can produce brine rejection without a steadily thickening local ice cover, increasing the salinity of the water left behind.

In seawater, freezing produces nearly salt-free solid and leaves salt in the interstitial liquid. The growing cover is therefore a mushy layer, with sea-ice crystal fabric determined by both crystal growth and the mechanical history. Crystallographic c-axes are perpendicular to the plates' basal planes; grain elongation and c-axis orientation must not be confused.

For first-year sea ice growing by congelation, heat loss first brings the surface water to its salinity-dependent freezing point. Small frazil ice crystals may form and collect into a thin continuous sheet, or a quiet surface can freeze directly; the resulting nilas provides the initial cover. Once the water surface is protected from strong agitation, heat transported by heat conduction upward through the sheet permits freezing onto its underside. Competitive growth favors grains with fast basal-plane growth directed downward, so grains with approximately horizontal c-axes crowd out less favorably oriented grains. The mature congelation ice consists predominantly of long vertical columns beneath a finer initial surface layer. Within and between these grains, the advancing cellular interface traps brine-bearing spaces. The growth sequence and crystallographic selection explain why the resulting texture is columnar rather than a random aggregate of floating crystals.

For pancake ice, wind and surface gravity waves prevent an uninterrupted ice sheet. Supercooled surface water produces suspended frazil ice; crystals accumulate into grease ice and then small coherent cakes. Wave-induced convergence, collisions and repeated accumulation of frazil increase cake size and thickness. Collisions and overwash deposit slush around the margins, building the characteristic raised rims. The crystal aggregate is predominantly granular, with much less systematic orientation than in congelation ice. A calmer interval can add a columnar basal layer, so a pancake need not be purely granular throughout. Observed pancake structures include frazil layers, basal congelation growth and rafted cakes.

In Antarctic consolidated pancake ice, the active edge initially follows this frazil-pancake route. As concentration rises and waves are attenuated, pancakes jam, raft and become frozen together, with interstitial frazil filling the gaps. The consolidated sheet retains overlapping cake outlines, stacked granular layers and an irregular underside, rather than acquiring the simple fabric of a single quiet-water-grown sheet. Later basal freezing can add congelation ice, but the granular fraction often remains large. Snow loading or overwash can flood the top; freezing this slush adds granular snow ice, a separate contribution from seawater-derived frazil. These mechanisms produce the heterogeneous sea-ice crystal fabric documented in cores from the Antarctic marginal ice zone. Quiet basal growth produces columnar ice; wave-driven aggregation and consolidation produce predominantly granular, layered ice.

The main efficient net desalination mechanisms require transport through the ice boundary. In gravity drainage of sea-ice brine, cold saline liquid is denser than the water below, so a connected permeable pore network permits downward flow and compensating entry of less saline seawater. Dense brine can collect into channels and convective drainage pathways. For a layer of depth $H$, a Darcy law estimate of drainage speed is $u_D\sim K\Delta \rho g/\mu$, giving a drainage time $H/u_D$ and showing directly why permeability of a porous medium and buoyancy matter. Warm, brine-rich ice drains much more readily than cold ice whose pores have become poorly connected. This is important during growth and can intensify as warming reconnects channels; an isolated sealed brine pocket cannot drain merely because its liquid is dense. The connectivity constraint is supported by sea-ice permeability measurements.

In meltwater flushing of sea ice, water supplied by surface snow melt or melt ponds has a hydraulic head above sea level and percolates down connected pores and cracks, displacing brine. It can remove salt rapidly in warm summer ice. Its limits are the supply and head of meltwater and pore connectivity; lateral runoff may reduce the amount available for vertical flushing. Gravity-driven drainage can act without surface melting, whereas flushing cannot.

Brine expulsion occurs when additional freezing and solid expansion pressurize an inclusion and force liquid into nearby passages. This is often internal redistribution: expelling brine from one inclusion does not desalinate the entire floe unless that liquid reaches the ocean. Migration of brine inclusions involves melting on a warmer wall and refreezing on the colder wall; molecular salt diffusion through liquid connections is also possible. These slow processes are far less effective at exporting bulk salt than connected advective drainage. Diffusion through the ice lattice itself is extremely slow. Likewise, excluding salt from each growing crystal is not by itself proof of salt loss from a whole ice-brine mixture. Desalination experiments and transport calculations distinguish net salt export from internal redistribution. Gravity drainage dominates desalination of permeable growing ice; meltwater flushing can dominate summer desalination; expulsion, inclusion migration and diffusion are comparatively ineffective without a boundary-crossing flow.

Assume small-amplitude motion, a thin uniform elastic plate, no prestress, and inviscid, irrotational deep water. Write the upward displacement as $\eta (x,t)$, the ice mass per unit area as $m={\rho }_{i}h$, and its flexural rigidity aswhere $E$ is Young's modulus and $\nu$ is Poisson's ratio. The plate equation is $m{\eta }_{tt}+D{\eta }_{xxxx}=p$, where $p$ is the perturbation of upward water pressure.

Let the water velocity potential be $\varphi =A{e}^{kz}{e}^{i(kx-\omega t)}$ below the mean surface $z=0$, with $k>0$. This solves the Laplace equation and decays at depth. For $\eta ={\eta }_0{e}^{i(kx-\omega t)}$, the kinematic boundary condition ${\eta }_t={\varphi }_z$ gives $A=-i\omega {\eta }_0/k$. The linear Bernoulli equation givesEliminating $p$ proves the dispersion relation of a floating elastic plate:Thus the desired wavenumber is the positive root ofFor positive $D$ and $\omega$, this root is unique: the polynomial is negative at zero and positive eventually; if its derivative starts negative, that derivative crosses zero only once, at a negative-valued minimum before the positive root. If a finite water depth $d$ is required, the corresponding relation is ${\omega }^2=(gk+D{k}^5/{\rho }_w)\tanh (kd)/[1+({\rho }_{i}h/{\rho }_w)k\tanh (kd)]$.

Put $\beta =D/{\rho }_w$ and $\alpha ={\rho }_{i}h/{\rho }_w$. Differentiation gives the group velocityFor long periods, the surface gravity wave limit gives $c_g\sim gT/(4\pi )$. At sufficiently short periods, plate inertia and bending dominate, $\omega \sim \sqrt{D/m}{k}^2$ and $c_g\sim 2\sqrt{D/m}k$. Consequently the curve has a group-velocity minimum of a flexural-gravity wave between branches that rise toward both long and short periods, within the formal deep-water plate model. Very short waves eventually fall outside the thin-plate approximation.

The plot is an original model illustration with $h=1\mathrm{m}$, $E=5\mathrm{GPa}$, $\nu =0.3$, ${\rho }_i=917\mathrm{kg}{\mathrm{m}}^{-3}$, ${\rho }_w=1025\mathrm{kg}{\mathrm{m}}^{-3}$, and $g=9.81\mathrm{m}{\mathrm{s}}^{-2}$. Its two minima occur at different periods.

A wave packet near the group-speed minimum carries energy away relatively slowly, so sustained forcing can concentrate energy in that period band. However, wind generation cannot be decided from $c_g$ alone. A steadily translating pressure pattern resonates through its phase velocity $c_p=\omega /k$; it must reach the minimum phase speed of a flexural-gravity wave. Actual wind-wave growth also requires suitable pressure coupling and enough energy input to overcome damping. A coherent cover suppresses ordinary free-surface wave generation, while incoming ocean swell can still excite bending and break the cover.

For disconnected pancake ice or frazil ice, remove the assumption of coherent elastic bending and retain the effective mass loading as a first conservative approximation. Setting $D=0$ gives ${\omega }^2=gk/[1+({\rho }_{i}h/{\rho }_w)k]$. To describe damping as well, replace the elastic layer by a viscous suspension and match velocity and stress to the water beneath: the resulting viscous layer model of frazil-pancake ice has complex $k$, whose real part gives dispersion and imaginary part gives attenuation. Keller's 1998 two-layer model implements this replacement. Effective viscosity and connectedness must reflect the particular cover; zero rigidity alone does not model attenuation.

A polynya is a persistent or recurrent area of open water or relatively thin ice within an otherwise ice-covered region. Persistence of the opening does not mean absence of ice formation: a latent-heat polynya can continuously make ice and export it. In contrast, a sensible-heat polynya remains open because ocean heat inhibits freezing. Both processes may occur at the same site.

At an Antarctic coast, cold air descending from the elevated continent produces strong katabatic winds. Their offshore component drives sea ice away from a fixed coastline, fast-ice edge or grounded-iceberg barrier. Open water exposed to the cold atmosphere loses heat rapidly; frazil ice forms, aggregates into pancake ice or consolidated new ice, and is exported offshore. The opening continues as long as export balances production. Headlands, the shelter provided by fast ice and the direction of the prevailing winds determine the location and size. Terra Nova Bay is a characteristic coastal example. Such latent-heat polynyas are ice factories rather than permanently warm holes in the ice pack.

At an ice shelf front the fixed boundary is floating shelf ice instead of land. Offshore winds blowing across the shelf can similarly remove newly formed sea ice, so an ice-front polynya need not have a different thermodynamic mechanism from a coastal one; the Ross Ice Shelf front provides an important wind-driven example. Shelf-front geometry, ice tongues, grounded icebergs and changes in calving alter the shelter and the supply of drifting pack ice. Some ice-front openings also receive significant sensible heat from currents, tidal mixing or upwelling, and heat carried out of an ice-shelf cavity can affect freezing. A sensible-heat polynya requires a sufficiently warm ocean supply, whereas the latent-heat mechanism requires continuing removal of the ice that does form. Consequently a strict identification of all coastal openings with one mechanism and all ice-shelf openings with the other would be incorrect.

The oceanic roles are substantial. Rapid heat loss and freezing produce brine rejection, raising shelf-water salinity and mass density. The resulting convection and circulation can carry dense shelf water into ice-shelf cavities; melting beneath an ice shelf modifies it into colder, fresher ice-shelf water. Dense shelf and cavity-modified waters can subsequently descend the continental slope, mix with adjacent waters and contribute to Antarctic bottom water. The outcome depends on bathymetry and the density after mixing: not all rejected brine reaches the abyss.

These localized regions can therefore have a disproportionate effect on deep-ocean ventilation, oxygen supply, carbon transport and the large-scale ocean circulation. They are also intense sites of ocean-to-atmosphere heat and moisture transfer. Seasonal sunlight arriving in open water supports high biological production where nutrients are available, with consequences for marine food webs and carbon cycling. Antarctic polynyas connect wind-driven ice export, concentrated ice production and dense-water formation; ice-shelf fronts add a floating boundary and possible cavity-related heat and freshwater exchanges.

It is important to distinguish loss of forward-going surface-gravity-wave energy from conversion of mechanical energy into heat. Scattering attenuation by ice floes redirects energy; it can attenuate a coherent transmitted wave without dissipating the total energy.

For fixed floe geometry, increasing frequency usually increases attenuation over the relevant swell range: shorter wavelengths respond more strongly to the contrast between water and the elastic plate, and to repeated floe edges. Long surface gravity waves have weak curvature and often penetrate much farther. This is a trend over a specified frequency range, not a theorem excluding resonances.

The diameter dependence is governed by $d/\lambda$. An ice floe much smaller than the wavelength moves nearly with the water and scatters weakly. Scattering becomes appreciable when floe size is comparable with the wavelength, and interference between its two edges can give maxima and minima. At fixed ice concentration, larger ice floes also mean fewer edges per unit propagation distance, roughly proportional to $p/d$. Consequently the attenuation coefficient need not increase monotonically with diameter: the single-floe reflection and the number of encounters must both be considered. Thickness increases areal inertia as ${\rho }_{i}h$ and bending stiffness as $h^3$, generally increasing wave mismatch and reflection, although detailed frequency-dependent resonances again prevent a universal monotonic law.

When $d\ll \lambda$, particularly for frazil ice and pancake ice, weak individual scattering leaves other processes dominant. Relative crystal and water motion causes viscous dissipation; an aggregate layer can behave as a viscous or viscoelastic material, and pancake ice collisions, rubbing and overwash remove energy. Their importance depends on concentration and wave amplitude.

For a uniform continuous sheet with horizontal dimensions much greater than the wavelength, there are no repeated floe edges in its interior. A perfectly elastic sheet over inviscid water supports undamped flexural-gravity waves, so internal scattering is not an explanation of decay there. Real attenuation can instead arise from internal ice anelasticity or viscoelasticity, a dissipative sub-ice viscous boundary layer, turbulence, cracks and brine-related processes. Small-floe mixtures and continuous sheets require dissipation models beyond the isolated-floe scattering picture.

Represent disconnected frazil ice and pancake ice as an upper layer with effective density, thickness and viscosity, rather than a continuous elastic plate. Linear Navier-Stokes equations in that layer are coupled to underlying water through velocity and stress conditions. A complex wavenumber describes both dispersion and wave attenuation in sea ice. A simpler conservative limit keeps ice mass loading but removes the elastic bending term; it does not predict viscous attenuation. The suspension model's effective viscosity is a fitted property, and a compact pancake cover need not behave like dilute frazil.