Jökull - 01.12.1955, Qupperneq 3

II
JÖKLARANNSÓKNAFÉLAGS ÍSLANDS
5. ÁR REYKJAVlK 1955
On the Flow of Ice-Sheets and Glaciers
by
GUNNAR BODVARDSSON1)
ABSTRACT: Differential equations for the
form of a flowing thin ice-sheet are derived by
the boundary condition that the shear stress on
the bed is proportional to the product of the
thickness and the gliding velocity. The general
mathernatical character of the equations, stability
of solutions and the response of ice-sheets to
climatic variations are discussed.
INTRODUCTION
The difficulties encountered in the mathe-
matical treatment of the flow of ice-sheets and
glaciers can be listed as follow:
(I) The general non-linear character of the
basic equations of free-surface flow. Some
simplification can be obtained by the assump-
tion of a static distribution of pressure within
the ice, and by the assumption of flow-lines
parallel to the bed.
(II) The complex rheological character of
ice and its low strength. It is known that ice
does not flow as a Newtonian fluid but shows
1) State Electricity Authority, Reykjavík,
Iceland.
a rather complex relation of sliear stress to the
rate of strain. (Glen, 1952). This implies a
further non-linearity of the basic equations of
flow. The low strength furthermore implies
that planes of discontinuity are encountered
which leads to a great complication. Approxi-
mations by the treatment of ice as a New-
tonian fluid with constant viscosity have been
made (Somigliana, 1921).
(III) The unknown relation of the shear
stress on Ihe bed to the gliding velocity. This
uncertainty in the boundary conditions at the
bed is probably at present the most serious
difficulty encountered in the numerical treat-
ment of the flow problems. Constant shear
stress has been used by some authors (Nye, 1952).
(IV) Complex three-dimensionl contours of
the bed and variations in space and time of the
rate of accumululation and ablation. In the
treatment of the flow of actual ice-sheets it is
consequently necessary to collect a great deal
of clata on the contours of the bed and
on the conditions in the accumulation and the
ablation regions.
The purpose of thc present paper is the dis-
1