Geoscience Reference
In-Depth Information
100 MN m
−
1
, and they tell how the ice deforms up to the yield stress. The original
bulk and shear moduli were given as K/h = 100 MN m
−
2
, G
10
-
≈
½ K in the AIDJEX model
by Coon et al. (1974). The corresponding Poisson
is ratio is 0.29. From physical basis the
ratio between compressive strength and bulk modulus of ice should be of the order of
10
−
3
, and therefore elastic strains remain below 10
−
3
(i.e., less than 10 m across 10 km
distances). Pritchard (1980) chose the ratio as 2 × 10
−
3
. The elastic moduli and brittle
strength are lower than in small-scale mechanics, since the amount of faults increases with
length scale. The strength of ice (
'
L
−
1/2
(Sanderson
σ
) scales with the length scale L as
σ ∝
1988).
In compressive deformation, if there are cracks ice
floes may override each other
resulting in rafting. Rafting may extend to long distances or end due to bending failure,
which starts piling up of ice
oe
edges are vertical in cracks, there is no overriding but the ice breaks in compression. In the
drift ice scale, the compressive elastic strength is
floes if rafting and breaking continue. However, if the
0.1 MN m
−
2
(Pritchard 1980).
Rafting or piling up of ice blocks may also take place on the windward shore. Then the
amount of shore ice accumulation depends on the thickness of ice and shoreline
morphology.
Drift ice models have mostly taken a viscous approach, largely due to computational
reasons. The linear viscous option is given analogously with the elastic model, with strain
replaced by strain-rate and the elastic moduli replaced by bulk and shear viscosities
σ
c
/
h ≈
ʶ
and
ʷ
, respectively:
ð I þ
2
ge
0
1
r
¼
r e; f; g
ð
Þ
¼
f
tr
2
P
;
F
r
1
; r
2
ð
Þ
\
0
ð
5
:
39
Þ
10
12
kg s
−
1
,
These viscosities have been kept large (
*
ʷ
*
½
ʶ
) to limit viscous
deformation and have a good approximation for the plastic
flow. Therefore, plastic yield
level is reached at the strain-rate of the order of 10
−
7
s
−
1
. Glacier
flow obeys a nonlinear
10
13
kg s
−
1
at the strain-rate
of 10
−
8
s
−
1
. An anisotropic extension was developed by Hibler and Schulson (2000) to
examine the dynamics of oriented lead and crack systems.
The original viscous-plastic drift ice model Hibler (1979) included an inconsistency of
having non-zero stress for an ice
viscous law (Paterson 1999), linearized viscosity would be
*
. This inconsistency
was later removed (Hibler 2001). Also in the case of low, long-term forcing, the viscous
case has an unrealistic feature for lake applications in leading to continuous creep. The
length of an ice beam would be changed by a factor of exp
field at rest, with
σ
=
½P
I
for
e
¼ 0
-
due to creep, and this
would account for 2.5 % in 1 month for a creep of 10
−
8
s
−
1
. The viscous strain-rates
should be much smaller than allowed in the model but it is not exactly known how much.
In sea ice
eðÞ
fields, however, the ice is mostly dynamically active that keeps the creep within
the noise.
Lake ice cover is loaded by the tangential air
ice stresses (e.g., Andreas
1998; McPhee 2008) and the surface pressure gradient, which is due to tilting of the water
ice and water
-
-
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