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Variational formulation of marine ice-sheet and subglacial-lake grounding-line dynamics

Published online by Cambridge University Press:  26 May 2021

Aaron G. Stubblefield Open the ORCID record for Aaron G. Stubblefield [Opens in a new window] ,
Marc Spiegelman  and
Timothy T. Creyts
Aaron G. Stubblefield*
Affiliation:
Lamont-Doherty Earth Observatory, Columbia University, Palisades, NY, USA
Marc Spiegelman
Affiliation:
Lamont-Doherty Earth Observatory, Columbia University, Palisades, NY, USA Department of Applied Physics and Applied Math, Columbia University, New York, NY, USA
Timothy T. Creyts
Affiliation:
Lamont-Doherty Earth Observatory, Columbia University, Palisades, NY, USA
*
†Email address for correspondence: aaron@ldeo.columbia.edu
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Abstract

Grounding lines exist where land-based glacial ice flows on to a body of water. Accurately modelling grounding-line migration at the ice–ocean interface is essential for estimating future ice-sheet mass change. On the interior of ice sheets, the shores of subglacial lakes are also grounding lines. Grounding-line positions are sensitive to water volume changes such as sea-level rise or subglacial-lake drainage. Here, we introduce numerical methods for simulating grounding-line dynamics in the marine ice sheet and subglacial-lake settings. Variational inequalities arise from contact conditions that relate normal stress, water pressure and velocity at the base. Existence and uniqueness of solutions to these problems are established using a minimisation argument. A penalty method is used to replace the variational inequalities with variational equations that are solved using a finite-element method. We illustrate the grounding-line response to tidal cycles in the marine ice-sheet problem and filling–draining cycles in the subglacial-lake problem. We introduce two computational benchmarks where the known lake volume change is used to measure the accuracy of the numerical method.

JFM classification

Geophysical and Geological Flows: Ice sheets Mathematical Foundations: Variational methods Mathematical Foundations: Computational methods
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 919 , 25 July 2021 , A23
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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