Geoscience Reference
In-Depth Information
resulting in n = 3/2. The stability condition depends on ice thickness. The crushing and
buckling failure criteria become equal at h
20 cm; for thinner ice buckling is more likely
while for thicker ice it is crushing. In sea ice dynamics, potential energy created in
overriding of ice sheets is proportional to the square of the ice thickness (Coon et al.
1974). This is a minor term but, however, it has been found that frictional losses in
pressure ridge follow the square law (Hopkins 1994), and therefore the power n =2
represents small-scale sea ice dynamics.
When thin ice fractures, it is also possible that the fractured sheets are overridden into a
double ice layer. This phenomenon is called rafting. A speci
c, eye-striking case of
rafting is
finger rafting, where the interacting ice sheets fracture along lines perpendicular
to the direction of the fracture and form an interlocked structure with alternate overthrust
and underthrust
ngers.
A model for simple rafting was presented by Parmerter (1975). Two
floating ice sheets
h
of thickness
are forced together, and if the edges are not exactly vertical, overriding
takes place and develops into rafting. The ice sheets can be treated as plates on elastic
foundation except where a plate is submerged (or lifted up) with respect to the water
surface level. The solution depends on the parameter n ¼ q w q i
ð Þ=q w , which deter-
mines where the lower plate submerges, as well as on the elastic properties of ice. The
problem can be formulated using a dimensionless force
N
and stress
ʣ
:
F
q w g k 2 ; R ¼
r t h
q w g k 2
N ¼
ð
5
:
23
Þ
where
0.4 is reached when the
submerged plate buckles. This is about 40 % of the force required in normal case of
buckling of an ice sheet on water foundation. Bending of the ice sheets during rafting
creates tensile stresses. Simple rafting can take place when the stresses are beneath the
fracture levels, but otherwise, blocks break off from the ice sheet to form a rubble
σ t is the tensile strength of ice. The limiting value N
*
field or a
ridge. The largest stress is experienced by the submerged ice sheet is obtained from an
asymptotic limit
ʣ 0 = 0.46 (see Parmerter 1975). Then we can obtain an estimate for the
maximum thickness of rafting ice as
2 31 l 2
Þr t
R 0
ð
h max ¼
ð
5
:
24
Þ
q w gE
Inserting freshwater ice parameters, we have h max = 32 cm. Parmerter examined sea
ice, and due to the lower tensile strength his estimate was 17 cm which corresponded well
with observations. In the case of freshwater ice there is not much data about rafted ice to
con
rm to thicker limit.
If the ice breaks and starts to drift, the next question is that how large lead is formed.
Also the persistence and recurrence of leads is of interest. The location of leads is often at
the lee side of lake basins but also across lakes guided by the lake geometry. If leads open
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