Steady flow of a viscous ice stream across a no-slip/free-slip transition at the bed

Abstract

AbstractAn exact, analytic description of the steady, downhill flow of a viscous ice stream across a no-slip to free-slip transition in basal boundary condition suggests ways in which such transitions might be detected by observations of ice-stream surface properties. We find that the best expression of this transition is in the free-surface profile, which dips over the point of transition and becomes horizontal far downstream. The streamwise velocity at the surface shows a gradual change across the transition, and this is in disagreement with previous studies which suggest a marked change. Basal shear stress and basal pressure exhibit singularities at the point of transition. As concluded in previous study, the former singularity is a likely point of strong basal erosion. The latter singularity is problematical, however, because it violates the assumptions which make the exact solution possible. It is not clear how this problem can be overcome without appealing to thermodynamics, non-Newtonian material properties, cavitation or wake separation.