The Smith–Morland flow law revisited

Description

Abstract

The standard Nye–Glen flow law for ice deformation contains a physically questionable infinite-viscosity singularity at zero stress. We revisit the polynomial Smith–Morland flow law as a singularity-free alternative. After rescaling the law into a non-dimensional framework, we find that the original parameters produce ice that is significantly too soft. Using an idealized EISMINT Phase 2 steady-state test, we recalibrate the law to match the ice volume of the standard Nye–Glen law, resulting in a slowdown factor (inverse flow enhancement factor) of 5.776. Validation via a steady-state Greenland ice-sheet simulation shows that the modified law produces realistic geometries and velocities. Notably, the Smith–Morland law's linear term leads to relatively faster flow in low-stress regions and favours thermomechanical fingering instabilities in the ice-sheet interior. The results demonstrate that the modified Smith–Morland law is a viable, physically consistent alternative for large-scale ice-flow modelling.