A variationally derived, depth-integrated approximation to a higher-order glaciological flow model

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Abstract

An approximation to the first-order momentum balance with consistent boundary conditions is derived using variational methods. Longitudinal and lateral stresses are treated as depth-independent, but vertical velocity gradients are accounted for both in the nonlinear viscosity and in the treatment of basal stress, allowing for flow over a frozen bed. A numerical scheme is presented that is significantly less computationally expensive than that of a fully three-dimensional (3-D) solver. The numerical solver is subjected to the ISMIP-HOM experiments and experiments involving nonlinear sliding laws, and results are compared with those of 3-D models. The agreement with first-order surface
velocities is favorable down to length scales of 10 km for flow over a flat bed with periodic basal traction, and ∼40 km for flow over periodic basal topography.
Original languageEnglish
Pages (from-to)157-170
Number of pages14
JournalJournal of Glaciology
Volume57
Issue number201
DOIs
Publication statusPublished - 1 Feb 2011

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