10 - Stress and velocity distribution in an idealized glacier

Summary

In this chapter, the equations developed in Chapter 9 are used to solve for the stress and velocity distribution in an idealized “glacier” consisting of a slab of ice of infinite extent on a uniform slope. Solutions are first obtained for ice with a perfectly plastic rheology.Both the shear stress and the surface-normal stress increase linearly with depth. The shear stress equals the plastic yield stress at the bed. Longitudinal normal stresses vary non-linearly, and are compressive in the ablation area and extending in the accumulation area.The surface-normal velocity also varies linearly with depth. The surface-parallel velocity varies non-linearly, with a high gradient near the bed. The stress solutions and the solution for the surface-normal velocity are essentially the same in a non-linear material, except that the shear stress does not reach a limiting value at the bed.However, the surface-parallel velocity, while varying with depth in a similar way, is now dependent on the longitudinal strain rate, and the solution is much more complicated. Interestingly, however, it does not matter whether the longitudinal strain rate is compressive or extending.