Stability of Glaciers and Ice Sheets Against Flow Perturbations

Abstract

AbstractA stability equation is derived for a model glacier of initially uniform thickness and of infinite extent transverse to the primary flow flowing without slip down an inclined plane. A stress-dependent power-law viscosity is wholly incorporated into the equations of motion. Stability of the glacier is tested against long-wavelength surface perturbations. Results for this initial formulation indicate that the glacier is stable against infinitesimal amplitude surface perturbations, although for certain variations of model parameters, the decay-rate of the disturbance becomes very slow, approaching neutral stability. Results are presented in terms of decay-rate magnitudes over a large range of perturbation wavelengths for many model glaciers in which bed slope, ice thickness, and ice rheology parameters are varied. For all models, the maximum decay-rate of the perturbation occurs at disturbance wavelengths of roughly three to six times the glacier thickness. Infinite-wavelength perturbations are found to be only neutrally stable. Long-wavelength perturbations propagate at a faster rate down-glacier than do the intermediate- or shorter-wavelength ones which tend to remain fixed on the glacier surface andride down-glacier with the primary flow as they decay.