Non-temperate glacier flow over wavy sloping ground

The mean, steady-state particle velocity in gravity-driven glacial flow ove r sinusoidal, sloping ground is computed using a Lagrangian description of motion. A Newtonian viscous fluid approximation is used for the ice. The gl acier surface is free to move and is not subject to any stresses. At the bo ttom, the ice is frozen to the ground. The non-linear interaction between t he basic downslope Poiseuille flow and the bottom corrugations yields a mea n Lagrangian perturbation velocity that is always directed in the upslope d irection near the ground. The requirement of mass balance imposes a mean ne gative surface slope in the corrugated region and an associated downslope p erturbation 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 particular ly at the base. Analysis shows that the shear heating associated with short wave perturbations could, in the case of a marginally frozen ground, lead t o 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 res ulting high strain rates could lead to crevassing.