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Ice shelves as floating channel flows of viscous power-law fluids

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Banik_2016_JOMR_IceShelves_CC.pdf (1.840Mb)
Date
04/11/2016
Author
Banik, I.
Dauparas, J.
Keywords
Glaciers
Marine ice sheets
Ice shelves
Fluid dynamics
Viscous flows
Non-newtonian fluids
QC Physics
NDAS
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Abstract
We explain the force balance in flowing marine ice sheets and the ice shelves they often feed. Treating ice as a viscous shear-thinning power law fluid, we develop an asymptotic (late-time) theory in two cases: the presence or absence of contact with sidewalls. Most real-world situations fall somewhere between the two extreme cases considered. The solution when sidewalls are absent is a fairly simple generalization of that found by Robison (JFM, 648, 363). In this case, we obtain the equilibrium grounding line thickness using a simple computer model and have an analytic approximation. For shelves in contact with sidewalls, we obtain an asymptotic theory valid for long shelves. We determine when this is. Our theory is based on the velocity profile across the channel being a generalized version of Poiseuille flow, which works when lateral shear dominates the force balance. We conducted experiments using a laboratory model for ice. This was a suspension of xanthan in water, at a concentration of 0.5% by mass. The model has n ≈ 3.8, similar to that of ice. Our theories agreed extremely well with our experiments for all relevant parameters (front position, thickness profile, lateral velocity profile, longitudinal velocity gradient and grounding line thickness). We also saw detailed features similar to natural systems. Thus, we believe we have understood the dominant force balance in both types of ice shelf. Combining our understanding of the forces in the system with a basic model for basal melting and iceberg formation, we uncovered some instabilities of the natural system. Laterally confined ice shelves can rapidly disintegrate but ice tongues cannot. However, ice tongues can be shortened until they no longer exist, at which point the sheet becomes unstable and ultimately the grounding line should retreat above sea level. While the ice tongue still exists, the flow of ice into it should not be speeded up and the grounding line should also not retreat, assuming that only conditions in the ocean change. However, laterally confined ice shelves experience significant buttressing. If removed, this leads to a rapid speed-up of the sheet and a new equilibrium grounding line thickness. We believe that something like this occurred in the Larsen B ice shelf.
Citation
Banik , I & Dauparas , J 2016 , ' Ice shelves as floating channel flows of viscous power-law fluids ' , Journal of Oceanography and Marine Research , vol. 4 , no. 2 , 150 . https://doi.org/10.4172/2572-3103.1000150
Publication
Journal of Oceanography and Marine Research
Status
Peer reviewed
DOI
https://doi.org/10.4172/2572-3103.1000150
ISSN
2332-2632
Type
Journal article
Rights
© 2016 Banik I, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Description
IB is supported by a Science and Technology Facilities Council studentship.
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  • University of St Andrews Research
URL
https://arxiv.org/abs/1310.7998
https://www.esciencecentral.org/peer-reviewed/ice-shelves-as-floating-channel-flows-of-viscous-powerlaw-fluids-83254.html
URI
http://hdl.handle.net/10023/10134

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