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Pressure-dependent viscosity and interfacial instability in coupled ice–sediment flow

Published online by Cambridge University Press:  14 October 2021

Christian Schoof*
Affiliation:
Department of Earth and Ocean Sciences, University of British Columbia, 6339 Stores Road, Vancouver, BC, V6T 1Z4, Canada

Abstract

We study an interfacial instability in the coupled flow of ice and subglacial sediment, both modelled as viscous media. Unlike other interfacial instabilities in coupled viscous flows at zero Reynolds number, the mechanism considered here does not rely on buoyancy or the effect of an upper free surface, but on the pressure-dependence of the sediment viscosity. Specifically, the instability relies on sediment rheology being such that, when sediment flows in simple shear, sediment flux increases with compressive normal stress at the ice–sediment interface when the velocity of the interface is kept constant. When ice moves over a shallow bump in the interface, it generates a higher compressive stress on the bump's upstream side than in its lee. If in addition the effective sediment viscosity is low compared with that of ice, interfacial velocity remains approximately constant, and this then implies that more sediment flows into the bump than out of it, causing it to grow. Modelling ice as a Newtonian material, we show that this mechanism works for a wide range of sediment rheologies, including the highly nonlinear shear-thinning ones typically thought most appropriate for the description of ‘nearly plastic’ sediment. The instabilities predicted are essentially two-dimensional, with infinite transverse wavelength, and a nonlinear model shows that growth is unbounded until cavitation occurs in the lee of evolving bumps on the interface. The instability mechanism does not seem to predict the formation of common glacial landforms, but may explain the formation of water-filled cavities on deformable glacier beds.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2007

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