Geoscience Reference
In-Depth Information
solution is the same as in the ice-only channel model. However, to reach the equilibrium
may take a long time.
5.5.5 Ice Thickness and Compactness Profiles
Let us start with an ice
field that ranges from x =0tox = L, with h = h
o
= constant and
A = 1. Let us further assume that
P
n
h
n
q(A), where q is the in
σ
=
uence of ice
-
compactness,
q
(0) = 0 and
q
(1) = 1. Wind stress is taken as a constant
˄
a
> 0. The solution
to the landfast ice problem shows that motion starts when
˄
a
L
>
σ
(
L
). Plastic rheology
allows a steady-state solution
field.
It is known that q is highly sensitive to compactness. Ice stress goes down one order of
magnitude when compactness drops from about 1 to 0.8
u ≡
0 with a
finite ice
0.9 and furthermore thereafter.
This means that a very sharp ice edge, less than 1 km wide, forms at on-ice forcing (see
Leppäranta and Hibler 1985). Beyond this edge zone, A
-
≈
1, and we have two conditions
to solve for the ice thickness pro
le. The thickness increases with distance from the ice
edge due to the increasing fetch, and the conservation of ice must be satis
ed:
dP
n
h
n
dx
¼
s
a
ð
5
:
51a
Þ
Z
L
x
o
hdx ¼ h
0
L
ð
5
:
51b
Þ
where x
o
is location of the ice edge. In the steady state, wind force must exactly balance
the ice strength at the channel end:
x
o
)=P
n
h
n
. For the linear form n = 1, the ice
thickness in the channel end, the location of the ice edge, and the friction number are:
˄
a
(L
-
!
r
1
4
þ
2X
0
1
2
s
a
L
P
1
h
h
ðÞ
¼hx
ðÞ
;
X
0
¼
ð
5
:
52
Þ
x
0
¼ L 1
X
0
h
ð
L
Þ
h
ð
x
0
Þ
0 or, in words, the landfast ice condition results from
the initial conditions. The excess of X
0
above 1 states how much deformation will take
place during the adjustment process. For
For X
0
→
1, h
L
→
h
0
and x
0
→
10
−
5
or,
in words, ice thickness increases by 1 m over 100 km. In the adjustment process, the
motion of ice starts to change at the boundaries. At the free boundary the ice edge zone
develops by outward opening (i.e., the compactness of ice decreases to satisfy the no-
stress condition). Then the edge zone remains static and the deformation zone spreads out
from the boundary, with compactness equal to 1 and thickness gradient approaching
10
4
Pa, dh/dx
˄
a
*
0.1 Pa and P
1
*
*
˄
a
/P
1
throughout the ice
field (see also Leppäranta and Hibler 1985).
Search WWH ::
Custom Search