Jökull - 01.12.1969, Page 62

of ice formation and negative for ice melting.
This gives
Ice formation — Ice melting
= Q-Ax-Ay-At (20)
Combining (18), (19), and (20) gives the ice
concentration equation
~ + V • (cvi) = Q (21)
3t
l'his equation together with the equation of
motion (16) determines the movement ancl con-
centration of the ice. The two equations are
coupled since some of the coefficients of the
equation of motion are dependent upon the
concentration and the concentration in turn
depends upon the velocity field. The two equa-
tions must therefore be solved together. Solu-
tions of the equations are cliscussed briefly in
the next section.
SOLUTIONS OF THE ICE EQUATIONS
For solutions of the ice equations reference
will be made to ihe sea area east of Green-
land frorn the strait between Spitzbergen and
Greenland southwarcl to Iceland. This area is
shown in Fig. 4 along witli a coordinate system
whicli might be used for solution of the equa-
tions.
In order to initiate a solution, the initial
conditions, i.e. the velocity field and concentra-
tion of the ice within the area under con-
sideration, must be known. Furthermore, cer-
tain boundary conditions must be satisfied,
which could be the following:
1. x = 0. This is the strait between Spitz-
bergen and Greenland. It is known that
the ice field is very dense on the Green-
land side whereas the sea is practically ice
free near Spitzbergen. The boundary condi-
tion could then be:
0 í| y 3yi: c = 1.0
yi < y < y2 : C = (y2 — y)/(y2 - ýi)
yjí yí L :c = 0
where L denotes the wiclth of the strait.
The quantities yi and y2 will obviously
change with the seasons.
JÖKULL 19. ÁR
2. y = Y0. This boundary is generally in re-
latively warm water, ancl it is unlikely that
ice can enter the area across this line.
The conditions here are therefore that ice
is moved out of the area across the line
but no ice into the area.
3. At the coasts of Iceland, Greenland, Jan
Mayen, and Spitzbergen the ice velocity
can only be directed away from the shore
or along the shore, or otherwise it must
be zero.
4. x = X0. Conditions at this boundary are
the same as described under (2) above, i.e.
ice can only leave the area across this
line.
Assuming all factors in the equation of mo-
tion (16) known, solution of the two equations
(16) and (21) is relatively straightforward. The
solution is obtained by the method of finite
differences. Tlie area of interest is divided into
a rectangular network and all derivatives in
the equations approximated by finite difler-
ence expressions. This method is well suited
for solution by a digital computer. The mesh
size of the network and thereby the accuracy
of the solution is governed by the size or stor-
age capacity of the computer.
SUMMARY AND CONCLUSIONS
This paper has dealt witli the forces acting
on drifting sea ice with special reference to
sea ice drift in the area east of Greenland and
north of Iceland where conditions differ from
those prevailing in the Arctic. The equations
of motion for the ice as well as an equation
describing the ice concentration are derived.
The derivation of these equations takes into
account the following.
1. F'orces due to surface winds
2. Forces due to currents
3. Coriolis force
4. Internal ice stresses
5. Formation of new ice
6. Melting of ice
Any analysis of the type cliscussed here can
at best only yield results as reliable or accurate
as the data used in the analysis. Extensive in-
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