Geology Reference
In-Depth Information
On the other hand, the thermal diffusion field near the
interface can be described by the same diffusion equation:
will then grow even more rapidly. The unstable planar
interface evolves into nonplanar dendritic interface (also
called cellular or platelet). The growth becomes stable
within certain limits as presented in
Woodruff
[1973].
Considering sea ice like a simple binary alloy,
Wettlaufer
et al.
[1997] presented a model for a two‐component melt
during solidification. This takes place in what is defined
as the “mush layer.” They applied the model to the brine
flow in sea ice and the flow of the ocean beneath it,
which resulted in the formation of a corrugated sea ice-
ocean interface. The results predicted strong corrugated
interface in young sea ice under conditions of rapid oce-
anic flow.
The bottom layer of a growing sea ice sheet that fea-
tures the cellular ice‐water interface is called “skeletal
layer.” It is extremely important to understand the struc-
ture of this layer because this is where history is made as
far as the microstructural features of the crystallographic
lattice of the bulk ice. The best method for making real‐
life observations of the cellular interface morphology
of sea ice is to obtain cores from ice sheets undergoing
a steady state of growth. The ice coring should be per-
formed on very cold days, preferably at air temperatures
less than −20 °C and calm conditions without any wind
blowing snow particles on the recovered specimen. It
would also be desirable to be a cloudy day or evening
with no solar radiation to avoid any solar radiation to
affect the delegate dendritic layer.
A photograph showing the bottom of a 100 mm
diameter, 1.78 m long FY sea ice core is presented in
Figure 2.20. It shows the nonplaner structure of the
bottom of the skeletal layer. The core was extracted in
D
dT
dx
2
V
dT
dx
0
(2.27)
t
2
where
D
t
is the thermal diffusivity of seawater. Solving
this equation with the boundary condition
T
=
T
b
at
x
= 0
yields the solution
TT
DG
dV
xV
D
(2.28)
tt
1exp
b
t
where
G
t
is the temperature gradient of the seawater near
the interface. Since a solution is required only in the
region where solute concentration varies markedly, then
the above solution can be simplified to [
Woodruff,
1973]
TTGx
b
(2.29)
t
It means that in the region of interest the temperature
gradients can be assumed to be linear. As mentioned
above, and shown in Figure 2.19, a constitutionally super-
cooled layer is formed when the temperature gradient at
the ice interface is less than the gradient of the freezing
temperature. This condition can be developed mathemat-
ically by differentiating equations (2.26) and (2.28) and
evaluating the resulting expressions at
x
= 0.
mVC
D
1
K
K
G
0
(2.30)
t
Even with the assumptions implied in the above deriva-
tion, this condition has been verified experimentally and
has been used in the materials science literature [
Tiller,
1991;
Flemings,
1974]. The above equation shows that
compositional supercooling can be avoided under either
one or both of the following two conditions: (1) the
freezing progresses very slowly, i.e., the speed (
V
) is small
enough, or (2) the distribution coefficient
K
is extremely
small, which means that the solute in ice is negligible com-
pared to the solute in the underlying water as in the case
of freshwater ice growth. However, compositional super-
cooling occurs even for lake water of salinities less than
0.1‰ as correctly pointed out by
Weeks and Ackley
[1982].
2.3.2. Dendritic Interface of Sea Ice
Figure 2.20
Photograph exhibiting dendritic (platelet) structure
at the bottom of a freshly sampled 1.78 m long, 100 mm diame-
ter, core of first‐year S3‐type sea ice in Eclipse Sound, Baffin
Island in March 1978. The insert is magnification of the area
shown in the box (photographed by N. K. Sinha, unpublished).
The presence of a supercooled layer leads to instability
of the planar ice interface. Any perturbation is likely to
bring the growing crystal into the supercooled zone and
