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Marine ice sheet stability

Published online by Cambridge University Press:  15 March 2012

Christian Schoof
Christian Schoof*
Affiliation:
Department of Earth and Ocean Sciences, University of British Columbia, 6339 Stores Road, Vancouver, BC, V6T 1Z4, Canada
*
†Email address for correspondence: [email protected]
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Abstract

We examine the stability of two-dimensional marine ice sheets in steady state. The dynamics of marine ice sheets is described by a viscous thin-film model with two Stefan-type boundary conditions at the moving boundary or ‘grounding line’ that marks the transition from grounded to floating ice. One of these boundary conditions constrains ice thickness to be at a local critical value for flotation, which depends on depth to bedrock at the grounding line. The other condition sets ice flux as a function of ice thickness at the grounding line. Depending on the shape of the bedrock, multiple equilibria may be possible. Using a linear stability analysis, we confirm a long-standing heuristic argument that asserts that the stability of these equilibria is determined by a simple mass balance consideration. If an advance in the grounding line away from its steady-state position leads to a net mass gain, the steady state is unstable, and stable otherwise. This also confirms that grounding lines can only be stable in positions where bedrock slopes downwards sufficiently steeply.

JFM classification

Interfacial Flows (free surface): Contact lines Geophysical and Geological Flows: Ice sheets Low-Reynolds-number flows: Lubrication theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 698 , 10 May 2012 , pp. 62 - 72
Copyright
Copyright © Cambridge University Press 2012

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