Glacier Sliding Down an Inclined Wavy Bed With Friction

Abstract

The effects of frictional tangential traction combined with regelation on the basal sliding of a temperate glacier down an inclined wavy bed are examined. Two friction models are treated. First, a Coulomb law model having the assumptions that sliding occurs everywhere and that the tangential traction is proportional to the normal pressure. Secondly, a velocity power law in which the tangential traction is proportional to a power of the slip velocity. The ice motion is approximated by steady slow Newtonian flow and the bed undulation about a mean bed-line has a maximum slope ∊ ≪I. Flow solutions are constructed as perturbations (in powers off ∈) of the plane laminar flow corresponding to non-slip on the mean bed-line assuming that the ice remains everywhere in contact with the bed; that is, no cavitation takes place. If the normal traction is predicted to be tensile over part of the bed, implying that cavitation has occurred, then a new solution is needed in which the ice base over cavities is traction-free. Since the cavity sections and profile of the free ice base are then part of the overall solution, an intricate mixed boundary-value problem is set up for the flow and the present analysis is inadequate.For a sinusoidal bed the perfect-slip (zero tangential traction) solution predicts compressive normal traction everywhere on the bed provided that the mean bed-line inclination α (to the horizontal) is less than a critical value αewhich is of order ε. For greater values of α including a range of order ∊, the normal traction is tensile on some parts of the bed, and a solution with cavitation is needed. If the tensile sections are relatively small it is expected that the resulting cavitation will not change the overall solution significantly. However, the Coulomb friction solution has extensive zones of tensile traction for all values of α, so that extensive cavitation would occur. In contrast, the velocity-power friction solution has compressive traction everywhere on the bed for α ⩽αe=0(I) provided that the ice depth is not too large, and also for deep glaciers forα ⩽αe=O∊ Furthermore, the predicted basal sliding velocity varies much less with the length scale of the bed undulation than in the perfect-slip solution, and is smaller.