The Motion of Ice Sheets and Glaciers

Abstract

AbstractThe distribution of velocity along a vertical line in Greenland is calculated. Almost all the relative shear motion is concentrated at and very near to the bottom, and this result is thought to apply generally in Greenland and Antarctica. It is due to the relatively high temperature of the lowest layers and the strong dependence of creep rate on temperature. The outward velocity being thus almost constant with depth, it is assumed proportional to the mth power of the shear stress on the bed; the results previously obtained by the approximation of perfect plasticity then correspond to m→∞. Steady-state solutions for finite m are derived, and non-steady states are discussed by use of Weertman’s perturbation method. The steady-state height of an ice sheet is found to be very insensitive to the rate of accumulation. Surface waves in Antarctica are attributed to mountains buried beneath the ice, and it is shown how the height and form of a buried mountain ridge may be calculated from the associated surface disturbance.The application of a law of sliding to glaciers leads to an expression for the longitudinal strain-rate, hitherto an undetermined parameter.