Creep-Velocity Bounds and Glacier-Flow Problems

Abstract

Abstract A general result due to Martin can be used to find upper and lower bounds on velocities in steady-creep problems. This method can be applied to glacier flow if ice can be assumed to satisfy a powerlaw stress–strain-rate relation. Bounds on the mean velocity over the glacier cross-section and on the mean velocity on the surface are determined for a particular example (a uniform parabolic channel, with powerlaw exponent 3) and they are shown to bound quite closely the exact solutions due to Nye. Bounds can be found rapidly by hand calculation. The method can be applied to real glacier cross-sections measured in the field.