(From Kovacs, 1971)
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Sea ice ice is one of the worlds's more complex
materials. It is a conglomerate of fresh water crystals interlaced
with inclusions of brine, air and salt which have formed between the
crystals and crystal plates (Weeks and Ackley,
1986). In general, it is nonhomogeneous and anistotropic.
Since component parts of sea ice are never in equilibrium the
physical properties of sea ice are not constant. However, the
manifistations of nonhomogeneity and anisotropy depend on the scale
of the region of interest. On small scale (dimensions of of
individual floes) the ice cover is homogeneous and highly
anisotropic. On large scale (several hundred kilometers) the ice
cover is nonhomogeneous and behaves practically as isotropic
medium.
Sea ice near shore is in one sense an extension of land
as it remains quasi-immobile during the winter. Offshore ice is
in perpetual motion, slowly twisting, turning, breaking into smaller
pieces, compacting and rarefying. This motion is an extremely complex
resultant of a combination of factors. These include wind stress,
water stress, coriolis force, tidal force, atmospheric pressure
gradients, internal ice stress and resistance, boundary layer
conditions and sea surface tilt. It has, however, been long
recognized that ice drift is dependent primarily upon wind stress and
secondly upon water stress (Thorndike and Colony,
1982).
The nature of sea ice deformation depends on its
characteristic scale. Large-scale deformations with characteristic
linear dimentions of the order of 100 km and more are determined
mainly by external forces (internal forces are mostly balanced).
Medium-scale deformations (10-20 km) are associated with the block
structure of ice fields and determined by external as well as
internal forces. Small-scale deformations (average diameter of single
ice floe) are caused by interaction of individual ice floes (internal
forces) and can be described in terms of a few basic
deformation processes. During the passage of anomalous
atmospheric-pressure fields, the internal forces in the sea ice field
present one of the most hazardous conditions for constructions and
ships in the sea-ice field.
Large scale deformation processes play the fundamental
role in determining the distribution of ice thickness, which in
itself controls heat and moisture fluxes between the ocean and
atmosphere (Maykut, 1982). On a large scale,
despite of discontinuities (cracks and fractures), the ice cover can
be treated as continuous medium. That allows to apply well-developed
rheological models to relate large scale deformations and internal
forces. A realistic sea ice rheology must
include the following general properties of sea ice cover (Hakkinen,
1987):
a) on large scale ice cannot support tension - openning
occurs with nearly no stress;
b) with high compactness ice will resist more
compression and shearing than with low compactness;
c) thick ice resists deformation more than thin ice;
c) the higher the compression is, the more ice will
resist it (strain hardening).
Two different approaches were used to derive large-scale
rheological properties (strength, viscositiy coefficients) of sea ice
cover based on mechanics of basic
deformation processes. The first one is based on linking the
amount of energy consumed in basic compressive processes (rafting
and ridging) to the large scale strength of
the pack ice (Rothrock, 1975). Another approach
appeals to self-similarity theory to determine scale-invariant
parameters of deformation field (Erlingsson,
1988).
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Buckling
Rafting
Ridging
Fracturing
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Simple
rafting
Finger
rafting
Pressure
ridging
Shear ridging
______|______
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Symmetric
Asymmetric
Back to sea ice deformation
features and processes
__________________________|____________________________
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Plastic
Viscous-plastic
Collisional
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Rigid-plastic
Elastic-plastic
Cavitating
fluid
Back to sea ice deformation
features and processes
Buckling referes to the
elastic folding deformation of sea ice. Since an amplitude of the
folds decreases as ice is becoming thicker, buckling is particularly
noticable in thin ice (thickness less than 10 cm). Buckling
determines the large-scale elastic behavior of sea ice. When internal
stresses exceed a critical value ice fails and buckling and hummocking
takes place.
(From Kovacs,
1971)
Back to basic deformation
processes
Rafting refers to the
pressure process whereby one floe overrides (simple
rafting) or forms interlocking thrusts with another (finger
rafting). Rafting is often associated with thin ice up to 15 cm
thick, but also occuring in ice in excess of 1 m thick. Bending
strains associated with the rafting of thick ice sheets invariably
result in fracturing of the rafted lobes. Often the fractured ice
mounds up in front of the advancing lobe. The weight of the ice in
this case is not balanced by the forces of buoyancy and causes
flexural stresses in the ice cover.
On a large scale, rafting can be treated statistically
by a thickness redistribution process whereby thin ice is transferred
to thick ice categories (Thorndike et al.,
1975).
Back to basic deformation
processes
(From Sanderson,
1988)
(From Kovacs,
1971)
Back to basic deformation
processes
(From Kovacs,
1971)
Back to basic deformation
processes
Symmetric finger
rafting:
(From Volkov
and Voronov, 1967)
Back to basic deformation
processes
(From Weeks
and Anderson, 1958)
Back to basic deformation
processes
Ridging refers to the
pressure process resulting to accumulation of ice blocks both above
and below pressurized ice floes. The term hummocking
is often used to describe ridging of the interior of the floe under
pressure. Ridging is common for the thick ice categories
(thicker than 1 m). The compressive forces causing ridge formation
are balanced by the buoyancy of the ice blocks and inertial and
elastic forces developing in the ice plate.
Theoretically, a ridge can be considered as a moving
contact break in which accumulation of ice mass and dissipation of
energy takes place. Ridges represent big and sometimes impassable
obstacles to navigation.
On a large scale, ridging can be treated statistically
by a redistribution process whereby thin ice is transferred to thick
ice categories
(Thorndike et al., 1975).
Back to basic deformation
processes
Pressure ridging is an accumulation of ice blocks which protrudes both above and below abutting ice flows. When two floes collide or squeeze together, great pressures can develop at points of contact. If the ice is unable to resist the stress, failure occurs. The result is an accumulation of blocks localized along a few points of contact or in a long ribbon. The latter is often related to the compression of thinner and, therefore, weaker ice formed in a lead system between two larger floes.
(From Sanderson,
1988)
(From Hajo Eicken's photo-archive)
(From Kovacs,
1971)
If the momentum of the
converging floes is not checked during initial impact and ridge
formation, deformation continues and a hummock field is formed.
Hummock fields most often consist of chaotic rubble of randomly
dispersed block structures and ridges. Sometimes hummoc fields can
take on rather uniform overall appearance.
(From Hajo Eicken's photo-archive)
(From Kovacs,
1971)
(From Kovacs,
1971)
If the sea is shallow the keels of ridges may ground. Floes moving in upon such anomalies will fail as they try to climb up or push the immobile mass aside. The result of that is the formation of great islands or ramparts of hummocked ice.
(From Kovacs,
1971)
Back to basic deformation
processes
Shear ridging
results from extensive shearing and grinding between two ice sheets.
The largest shear ridges generally occur between the moving pack and
the shore-fast ice. A shear ridge may be a local feature or may
consist of sinuous or rectilinear wall tens of miles long. The ice in
the shear zone undergoes extensive disaggregation and consisits of a
highly compact granular mass. Shear ridging itself do not play
significant role in the ice thickness redistribution process but it
has a strong impact on the ice drift and deformation near shore.
(From Sanderson,
1988)
(From Kovacs,
1971)
Back to basic deformation
processes
Fracturing refers to the process of forming cracks and, consequently, fractures (open cracks) in the ice cover. Surface defects of sea ice cover (e.g., thermal cracks) facilitate the formation of fractures. On a large scale, fracturing can be treated statistically as a process of forming thin ice through lead creation (Thorndike et al., 1975).
(From Kovacs,
1971)
Back to basic deformation processes
A material under stress is said to behave plastically if, at stresses below a critical level (yield stress), it reacts as a solid; while at stresses at or above the critical level, it flows (like a fluid) continuously without rupture to become permanently strained. Plastic rhelogy (Rothrock, 1975) had been preferred for the pack ice because observations show that the ice field can support varying strain rates under fairly uniform forcing.
If plastic material does not deform at all at stresses below yield stress, it is said to demonstrate rigid-plastic behavior. In this case elastic deformation of sea ice is considered to be negligibly small. The model works well for consolidated thick ice pack (Rothrock, 1975).
If plastic material deforms elastically (strain is directly proportional to stress) at stresses below yield stress, it is said to behave as an elastic-plastic. This rheology is most consistent with the local behavior of sea ice (Coon, 1974).
Viscous-plastic
rheology is based on quasi-linear dependence between stress and
strain rate (ice pack behaves as viscous fluid for small strain
rates, whereas for large strain rates it flows in a plastic
manner (Hibler, 1979). It has been demonstrated
that if time and/or length scales are chosen large enough, then the
averaging of nonlinear (plastic) stochastic fluctuations in sea ice
deformation rates yields viscouslike law
(Hibler, 1977). This approach essentially
facilitates numerical sheme as compared to elastic-plastic model.
Cavitating fluid rheology is a simplification of viscous-plastic rheology based on the assumption that the ice pack does not resist divergence and shear (Flato et al., 1991). It is less realistic than other reologies that include shear stress but computationally more efficient and allows smooth flow past an obstacle which makes the scheme attractive for coupling with ocean circulation model.
Collisional rheology takes into account collision-induced momentum transfer in a fragmented ice field (Shen et al., 1987). That gives rise to stresses depending on the square of the strain rate. The rheology appears to be good at modeling deformation in the marginal ice zone (near the ice edge).
Coon, M.D., G.A. Maykut, R.S. Pritchard, and D.A. Rothrock (1974). Modeling pack ice as an elastic-plastic material. AIDJEX Bull, vol. 24, pp. 1-105.
Erlingsson, B. (1988). Two-dimensional deformation patterns in sea ice. Journal of Glaciology, vol. 34, no. 118, pp. 301-308.
Flato , G.M, and W.D. Hibler III. (1991). Modeling pack ice as a cavitating fluid. Journal of Physical Oceanography, vol .22, pp.626-651.
Hakkinen, S. (1987). A constitutive law for sea ice and some applications. Mathematical modelling, vol. 9, no. 2, pp. 81-90.
Hibler III, W.D. (1977). A viscous sea ice law as stochastic average of plasticity. Journal of Geophysical Research, vol. 82, no. 27, pp. 3932-3938.
Hibler III, W.D. (1979). A dynamic thermodynamic sea ice model. Journal of Physical Oceanography, vol .9, pp. 815-846.
Kovacs, A. (1971). On pressured sea ice. In: Sea Ice: Proceedings of an International Conference, Rey Kjavik, Iceland, pp. 276-295.
Maykut, G.A. (1982). Large-scale heat exchange and ice production in the central Arctic. Journal of Geophysical Research, vol. 80, no. C8, pp. 7971-7984.
Rothrock, D.A. (1975). The energetics of the plastic deformation of pack ice by ridging. Journal of Geophysical Research, vol.80, no. 33, pp. 4514-4519.
Sanderson, T.J.O. (1988). Ice
mechanics - risks to offshore structures. Graham & Trotman,
London.
Shen , H.H, W.D. Hibler III, and M.
Lepparanta. (1987). The role of floe collisions in sea ice
rheology. Journal of Geophysical Research, vol. 92, no. C17, pp.
7085-7096.
Thorndike, A.S., D.A. Rothrock, G.A. Maykut, and R. Colony. (1975). The thickness distribution of sea ice. Journal of Geophysical Research, vol. 80, no, 33, pp. 4501-4513.
Thorndike, A.S., and R. Colony. (1982). Sea ice motion in response to geostrophic winds. Journal of Geophysical Research, vol. 87, no. C10, pp. 5845-5852.
Volkov, N.A., and P.S. Voronov. (1967). Investigation of Sea Ice Cryotechnique for Glaciogical and Geological Purposes. Problems of Arctic and Antarctic, vol. 27 (in Russian).
Weeks, N.A., and D.L. Anderson. (1958). Sea Ice Thrust Structures. Journal of Glaciology, vol. 3.
Weeks, W.F., and S.F. Ackley. (1986). The growth, structure and properties of sea ice. In: The Geophysics of Sea Ice, Martinus Nijhoff Publ., Dordrecht, pp. 9-165.
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