Measurement of the velocity distribution along a vertical line through a glacier

Abstract

Various theories of glacier flow have been used to predict widely different changes of velocity with depth. The paper describes a direct measurement of the vertical velocity distribution in a glacier in the Bernese Oberland. Using an electric heating element, a vertical hole 137 m long was melted from the glacier surface to the rock-bed. The hole was lined with a 3 in. steel tube which froze into the glacier and became tilted and bent according to the velocities prevailing at different depths. Using electrically recording pendulum instruments, the inclination of the tube at different depths was measured at the start of the experiment and again after one and two years. The rate of surface flow was found to be 35 m per year. Of this amount, roughly half seemed to be due to flow within the ice and the other half due to sliding of the glacier over its bed. The velocity decreased regularly from the glacier surface downwards, and there was no indication of a yield stress below which ice was completely rigid. If the assumption is made that the deformation of the ice in the glacier is due to simple shear stress, a tentative relationship between this stress and the rate of shear strain can be derived from the results. This shows that flow is not Newtonian, but approximates to a relation where $\dot{\gamma}$ = 10$^{-8}\tau ^{1^{\cdot}5}$ ($\dot{\gamma}$ = rate of shear strain per second, $\tau $ = shear stress in bars), over a range of $\tau $ between 0$\cdot $1 and 0$\cdot $75 bars. Comparison with laboratory compression tests by Glen (1952) indicates that the exponent of $\tau $ increases at shear stresses above 1 bar.