The role of membrane-like stresses in determining the stability and sensitivity of the Antarctic ice sheets: back pressure and grounding line motion

Hindmarsh, Richard C.A. ORCID: 2006 The role of membrane-like stresses in determining the stability and sensitivity of the Antarctic ice sheets: back pressure and grounding line motion. Philosophical Transactions of the Royal Society of London, A, 364 (1844). 1733-1767.

Full text not available from this repository. (Request a copy)


Membrane stresses act along thin bodies which are relatively well lubricated on both surfaces. They operate in ice sheets because the bottom is either sliding, or is much less viscous than the top owing to stress and heat softening of the basal ice. Ice streams flow over very well lubricated beds, and are restrained at their sides. The ideal of the perfectly slippery bed is considered in this paper, and the propagation of mechanical effects along an ice stream considered by applying spatially varying horizontal body forces. Propagation distances depend sensitively on the rheological index, and can be very large for ice-type rheologies. A new analytical solution for ice-shelf profiles and grounded tractionless stream profiles is presented, which show blow up of the profile in a finite distance upstream at locations where the flux is non-zero. This is a feature of an earlier analytical solution for a floating shelf. The length scale of decay of membrane stresses from the grounding line is investigated through scale analysis. In ice sheets, such effects decay over distances of several tens of kilometres, creating a vertical boundary layer between sheet flow and shelf flow, where membrane stresses adjust. Bounded, physically reasonable steady surface profiles only exist conditionally in this boundary layer. Where bounded steady profiles exist, adjacent profile equilibria for the whole ice sheet corresponding to different grounded areas occur (neutral equilibrium). If no solution in the boundary layer can exist, the ice-sheet profile must change. The conditions for existence can be written in terms of whether the basal rate factor (sliding or internal deformation) is too large to permit a steady solution. The critical value depends extremely sensitively on ice velocity and the back stress applied at the grounding line. High ice velocity and high stress both favour the existence of solutions and stability. Changes in these parameters can cause the steady solution existence criterion to be traversed, and the ice-sheet dynamics to change. A finite difference model which represents both neutral equilibrium and the dynamical transition is presented, and preliminary investigations into its numerical sensitivity are carried out. Evidence for the existence of a long wavelength instability is presented through the solution of a numerical eigenproblem, which will hamper predictability.

Item Type: Publication - Article
Digital Object Identifier (DOI):
Programmes: BAS Programmes > Global Science in the Antarctic Context (2005-2009) > Glacial Retreat in Antarctica and Deglaciation of the Earth System
ISSN: 1364-503X
Additional Information. Not used in RCUK Gateway to Research.: Full text not available from this repository
Additional Keywords: Ice sheets ; Flow ; Stability; Holocene
NORA Subject Terms: Glaciology
Date made live: 31 Aug 2007 10:35 +0 (UTC)

Actions (login required)

View Item View Item

Document Downloads

Downloads for past 30 days

Downloads per month over past year

More statistics for this item...