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Report on Problems Relating to the Flow of Glaciers

M. F. Perutz

1947
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Journal of Glaciology
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Viscous Flow : Experiments and Theory The great naturalists of the nineteenth century discovered glacier flow and described its main features. They showed that the flow properties of glaciers resemble those of highly viscous fluids, and attributed the ductility of the apparently brittle substance ice to the effects of regelation or to the relative motion of individual ice crystals. Accurate measurements of glacier flow were begun in the Alps in the 1890's and continued for several decades. 1
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... face velocities were measured at many points on glacier tongues, bore-holes reaching down to the rock bed were drilled and their progression was carefully recorded. Finally, in the ic^o's, reliable and less tiresome methods of measuring glacier depths became possible with the introduction of seismic soundings. Many of the experiments and observations were accompanied by attempts at theoretical interpretation. One of the earliest of these was Finsterwalder's geometric streamline theory, 2 which correlated accumulation and ablation with glacier flow and explained the periodic advance and recession of glaciers. Finsterwalder's theory is mainly descriptive and free from all arbitrary assumptions; on the other hand, this makes the theory so general that it is difficult to derive from it any quantitative predictions. Hess actually employed it to obtain equations for the total mechanical energy of a glacier, involving integration over six dependent variables which cannot be evaluated without a host of dubious assumptions. The solutions of these equations led him to some exceedingly improbable conclusions concerning the stress distribution in glaciers. More important are Weinberg's and Somigliana's attempts to formulate a quantitative theory of glacier flow on a hydrodynamic basis. 3 ' 4 Somigliana treats the stationary flow of a viscous liquid in an evenly inclined cylindrical channel under the influence of gravity. His work is outstanding for the clear exposition of the underlying assumptions and important because it leads to a relation between the depth and surface velocity of a glacier. Lagally extended his theory and used it to derive the average viscosity of glacier ice from the change in flow velocity between the edges and the centre of a glacier surface 5 ; he obtained a value of /x = 1 X i o u g. cm. -1 sec. -1 . Taking the cross-section of the glacier bed to be a semi-ellipse whose major axis is very large compared to the minor one, and the velocity of flow on the rock bed to be negligibly small, he obtains the equation V pg sin <x where z is the depth of the glacier, /x the viscosity of ice, V 0 the surface velocity at the centre of the glacier, p the density of ice, g the acceleration of gravity and a the inclination of the

doi:10.3189/s0022143000007541
fatcat:ipmusf422ne6bklnswfetp2j7y