Non-temperate glacier flow over wavy sloping ground

The mean, steady-state particle velocity in gravity-driven glacial flow over sinusoidal, sloping ground is computed using a Lagrangian description of motion. A Newtonian viscous fluid approximation is used for the ice. The glacier surface is free to move and is not subject to any stresses. At the bottom, the ice is frozen to the ground. The non-linear interaction between the basic downslope Poiseuille flow and the bottom corrugations yields a mean Lagrangian perturbation velocity that is always directed in the upslope direction near the ground. The requirement of mass balance imposes a mean negative surface slope in the corrugated region and an associated downslope perturbation flow in the upper part of the glacier. The no-slip condition at the wavy bottom induces a strong velocity shear in the ice, and particularly at the base. Analysis shows that the shear heating associated with shortwave perturbations could, in the case of a marginally frozen ground, lead to melting and subsequent sliding at wave crests along the bottom, while the ice stays frozen at the troughs. It is suggested that for glaciers the resulting high strain rates could lead to crevassing.