Boundary layer models for calving marine outlet glaciers
Abstract
Abstract. We consider the flow of marine-terminating outlet glaciers that are laterally confined in a channel of prescribed width. In that case, the drag exerted by the channel side walls on a floating ice shelf can reduce extensional stress at the grounding line. If ice flux through the grounding line increases with both ice thickness and extensional stress, then a longer shelf can reduce ice flux by decreasing extensional stress. Consequently, calving has an effect on flux through the grounding line by regulating the length of the shelf. In the absence of a shelf, it plays a similar role by controlling the above-flotation height of the calving cliff. Using two calving laws, one due to Nick et al. (2010) based on a model for crevasse propagation due to hydrofracture and the other simply asserting that calving occurs where the glacier ice becomes afloat, we pose and analyse a flowline model for a marine-terminating glacier by two methods: direct numerical solution and matched asymptotic expansions. The latter leads to a boundary layer formulation that predicts flux through the grounding line as a function of depth to bedrock, channel width, basal drag coefficient, and a calving parameter. By contrast with unbuttressed marine icemore »
- Authors:
- Publication Date:
- Research Org.:
- Univ. of Texas, Austin, TX (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- OSTI Identifier:
- 1397981
- Alternate Identifier(s):
- OSTI ID: 1507095
- Grant/Contract Number:
- SC0010518
- Resource Type:
- Published Article
- Journal Name:
- The Cryosphere (Online)
- Additional Journal Information:
- Journal Name: The Cryosphere (Online) Journal Volume: 11 Journal Issue: 5; Journal ID: ISSN 1994-0424
- Publisher:
- Copernicus Publications, EGU
- Country of Publication:
- Germany
- Language:
- English
- Subject:
- 54 ENVIRONMENTAL SCIENCES
Citation Formats
Schoof, Christian, Davis, Andrew D., and Popa, Tiberiu V. Boundary layer models for calving marine outlet glaciers. Germany: N. p., 2017.
Web. doi:10.5194/tc-11-2283-2017.
Schoof, Christian, Davis, Andrew D., & Popa, Tiberiu V. Boundary layer models for calving marine outlet glaciers. Germany. https://doi.org/10.5194/tc-11-2283-2017
Schoof, Christian, Davis, Andrew D., and Popa, Tiberiu V. Sun .
"Boundary layer models for calving marine outlet glaciers". Germany. https://doi.org/10.5194/tc-11-2283-2017.
@article{osti_1397981,
title = {Boundary layer models for calving marine outlet glaciers},
author = {Schoof, Christian and Davis, Andrew D. and Popa, Tiberiu V.},
abstractNote = {Abstract. We consider the flow of marine-terminating outlet glaciers that are laterally confined in a channel of prescribed width. In that case, the drag exerted by the channel side walls on a floating ice shelf can reduce extensional stress at the grounding line. If ice flux through the grounding line increases with both ice thickness and extensional stress, then a longer shelf can reduce ice flux by decreasing extensional stress. Consequently, calving has an effect on flux through the grounding line by regulating the length of the shelf. In the absence of a shelf, it plays a similar role by controlling the above-flotation height of the calving cliff. Using two calving laws, one due to Nick et al. (2010) based on a model for crevasse propagation due to hydrofracture and the other simply asserting that calving occurs where the glacier ice becomes afloat, we pose and analyse a flowline model for a marine-terminating glacier by two methods: direct numerical solution and matched asymptotic expansions. The latter leads to a boundary layer formulation that predicts flux through the grounding line as a function of depth to bedrock, channel width, basal drag coefficient, and a calving parameter. By contrast with unbuttressed marine ice sheets, we find that flux can decrease with increasing depth to bedrock at the grounding line, reversing the usual stability criterion for steady grounding line location. Stable steady states can then have grounding lines located on retrograde slopes. We show how this anomalous behaviour relates to the strength of lateral versus basal drag on the grounded portion of the glacier and to the specifics of the calving law used.},
doi = {10.5194/tc-11-2283-2017},
journal = {The Cryosphere (Online)},
number = 5,
volume = 11,
place = {Germany},
year = {Sun Jan 01 00:00:00 EST 2017},
month = {Sun Jan 01 00:00:00 EST 2017}
}
https://doi.org/10.5194/tc-11-2283-2017
Web of Science
Works referenced in this record:
A physically based calving model applied to marine outlet glaciers and implications for the glacier dynamics
journal, January 2010
- Nick, F. M.; Van Der Veen, C. J.; Vieli, A.
- Journal of Glaciology, Vol. 56, Issue 199
Assessment of the importance of ice-shelf buttressing to ice-sheet flow: BUTTRESSING SENSITIVITY
journal, February 2005
- Dupont, T. K.; Alley, R. B.
- Geophysical Research Letters, Vol. 32, Issue 4
Upper and lower limits on the stability of calving glaciers from the yield strength envelope of ice
journal, November 2011
- Bassis, J. N.; Walker, C. C.
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 468, Issue 2140
An observationally validated theory of viscous flow dynamics at the ice-shelf calving front
journal, January 2012
- Hindmarsh, Richard C. A.
- Journal of Glaciology, Vol. 58, Issue 208
Marine ice sheet dynamics. Part 2. A Stokes flow contact problem
journal, May 2011
- Schoof, Christian
- Journal of Fluid Mechanics, Vol. 679
Stability of the Junction of an Ice Sheet and an Ice Shelf
journal, January 1974
- Weertman, J.
- Journal of Glaciology, Vol. 13, Issue 67
Potential Antarctic Ice Sheet retreat driven by hydrofracturing and ice cliff failure
journal, February 2015
- Pollard, David; DeConto, Robert M.; Alley, Richard B.
- Earth and Planetary Science Letters, Vol. 412
Ice sheet grounding line dynamics: Steady states, stability, and hysteresis
journal, January 2007
- Schoof, Christian
- Journal of Geophysical Research, Vol. 112, Issue F3
Rapid grounding line migration induced by internal ice stream variability
journal, November 2014
- Robel, A. A.; Schoof, C.; Tziperman, E.
- Journal of Geophysical Research: Earth Surface, Vol. 119, Issue 11
Iceberg calving of Thwaites Glacier, West Antarctica: full-Stokes modeling combined with linear elastic fracture mechanics
journal, January 2017
- Yu, Hongju; Rignot, Eric; Morlighem, Mathieu
- The Cryosphere, Vol. 11, Issue 3
Dynamics of laterally confined marine ice sheets
journal, February 2016
- Kowal, Katarzyna N.; Pegler, Samuel S.; Worster, M. Grae
- Journal of Fluid Mechanics, Vol. 790
Results of the Marine Ice Sheet Model Intercomparison Project, MISMIP
journal, January 2012
- Pattyn, F.; Schoof, C.; Perichon, L.
- The Cryosphere, Vol. 6, Issue 3
Marine ice-sheet profiles and stability under Coulomb basal conditions
journal, January 2015
- Tsai, Victor C.; Stewart, Andrew L.; Thompson, Andrew F.
- Journal of Glaciology, Vol. 61, Issue 226
The dynamics of confined extensional flows
journal, August 2016
- Pegler, Samuel S.
- Journal of Fluid Mechanics, Vol. 804
Sea level as a stabilizing factor for marine-ice-sheet grounding lines
journal, November 2010
- Gomez, Natalya; Mitrovica, Jerry X.; Huybers, Peter
- Nature Geoscience, Vol. 3, Issue 12
Bounds on the calving cliff height of marine terminating glaciers
journal, February 2017
- Ma, Yue; Tripathy, Cory S.; Bassis, Jeremy N.
- Geophysical Research Letters, Vol. 44, Issue 3
Fracture mechanics approach to penetration of surface crevasses on glaciers
journal, February 1998
- van der Veen, C. J.
- Cold Regions Science and Technology, Vol. 27, Issue 1
Assessment of ice flow dynamics in the zone close to the calving front of Antarctic ice shelves
journal, January 2015
- Wearing, Martin G.; Hindmarsh, Richard C. A.; Worster, M. Grae
- Journal of Glaciology, Vol. 61, Issue 230
Grounding line movement and ice shelf buttressing in marine ice sheets
journal, January 2009
- Goldberg, D.; Holland, D. M.; Schoof, C.
- Journal of Geophysical Research, Vol. 114, Issue F4
A Theoretical Treatment of the Sliding of Glaciers in the Absence of Cavitation
journal, January 1981
- Fowler, A. C.
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 298, Issue 1445
Marine ice-sheet dynamics. Part 1. The case of rapid sliding
journal, February 2007
- Schoof, Christian
- Journal of Fluid Mechanics, Vol. 573
Glacier calving: a numerical model of forces in the calving-speed/water-depth relation
journal, January 2000
- Hanson, Brian; Hooke, Roger LeB.
- Journal of Glaciology, Vol. 46, Issue 153
On the Sliding of Glaciers
journal, January 1957
- Weertman, J.
- Journal of Glaciology, Vol. 3, Issue 21
The stability of grounding lines on retrograde slopes
journal, January 2012
- Gudmundsson, G. H.; Krug, J.; Durand, G.
- The Cryosphere, Vol. 6, Issue 6
An updated-Lagrangian damage mechanics formulation for modeling the creeping flow and fracture of ice sheets
journal, January 2017
- Jiménez, Stephen; Duddu, Ravindra; Bassis, Jeremy
- Computer Methods in Applied Mechanics and Engineering, Vol. 313
Persistence and variability of ice-stream grounding lines on retrograde bed slopes
journal, January 2016
- Robel, Alexander A.; Schoof, Christian; Tziperman, Eli
- The Cryosphere, Vol. 10, Issue 4
Modeling hydraulic fracture of glaciers using continuum damage mechanics
journal, May 2016
- Mobasher, Mostafa E.; Duddu, Ravindra; Bassis, Jeremy N.
- Journal of Glaciology, Vol. 62, Issue 234
Future sea-level rise from Greenland’s main outlet glaciers in a warming climate
journal, May 2013
- Nick, Faezeh M.; Vieli, Andreas; Andersen, Morten Langer
- Nature, Vol. 497, Issue 7448
Dynamics of a viscous layer flowing radially over an inviscid ocean
journal, March 2012
- Pegler, Samuel S.; Worster, M. Grae
- Journal of Fluid Mechanics, Vol. 696
Marine ice sheet stability
journal, March 2012
- Schoof, Christian
- Journal of Fluid Mechanics, Vol. 698
Empirical Studies of Ice Sliding
journal, January 1979
- Budd, W. F.; Keage, P. L.; Blundy, N. A.
- Journal of Glaciology, Vol. 23, Issue 89
A Model for Holocene Retreat of the West Antarctic Ice Sheet
journal, September 1978
- Thomas, Robert H.; Bentley, Charles R.
- Quaternary Research, Vol. 10, Issue 2
Lateral controls on grounding-line dynamics
journal, April 2013
- Pegler, Samuel S.; Kowal, Katarzyna N.; Hasenclever, Leonard Q.
- Journal of Fluid Mechanics, Vol. 722
Diverse calving patterns linked to glacier geometry
journal, July 2013
- Bassis, J. N.; Jacobs, S.
- Nature Geoscience, Vol. 6, Issue 10
Fracture mechanics approach to penetration of bottom crevasses on glaciers
journal, June 1998
- van der Veen, C. J.
- Cold Regions Science and Technology, Vol. 27, Issue 3
On the Flow of Polythermal Glaciers. I. Model and Preliminary Analysis
journal, November 1978
- Fowler, A. C.; Larson, D. A.
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 363, Issue 1713
Shear margins in glaciers and ice sheets
journal, January 1996
- Raymond, Charles
- Journal of Glaciology, Vol. 42, Issue 140
Combining damage and fracture mechanics to model calving
journal, January 2014
- Krug, J.; Weiss, J.; Gagliardini, O.
- The Cryosphere, Vol. 8, Issue 6
Ice-stream stability on a reverse bed slope
journal, October 2012
- Jamieson, Stewart S. R.; Vieli, Andreas; Livingstone, Stephen J.
- Nature Geoscience, Vol. 5, Issue 11