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Thermally driven migration of ice-stream shear margins

Published online by Cambridge University Press:  08 October 2012

Christian Schoof
Christian Schoof*
Affiliation:
Department of Earth and Ocean Sciences, University of British Columbia, 6339 Stores Road, Vancouver, BC, V6T 1Z4, Canada
*
†Email address for correspondence: cschoof@eos.ubc.ca
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Abstract

Ice-stream shear margins are the lateral boundaries of narrow, fast-flowing bands of ice within an ice sheet. We develop a theory for the migration of shear margins over time driven by viscous dissipation of heat within the ice, focusing on widening of the ice stream. The location of the margin is modelled as a transition from a cold to a temperate ice-sheet bed, and simultaneously as the transition from no slip to free slip at the same location. The temperature field in the ice is affected by intense shear heating as well as by the migration velocity of the margin (i.e. by the widening rate of the ice stream); if migration is too fast, there is little time for the ice to warm up and the margin remains cold, causing the bed to freeze. This suppresses widening. Conversely, if the migration speed is too slow, the ice in the margin warms up, causing the bed on the far side of the cold–temperate transition to reach the melting point, and migration to speed up. Using a Wiener–Hopf method, we show that for a given far-field shear stress, geothermal heat flux, and ice geometry, there is a single migration velocity that balances the two effects and permits widening at a steady rate. This velocity increases with the far-field lateral shear stress imposed by the ice stream, which controls shear heating in the margin. Our results also indicate that (i) a region of temperate ice must form in the margin, and that (ii) lateral advection of ice may play a significant role in controlling migration speeds.

JFM classification

Interfacial Flows (free surface): Contact lines Geophysical and Geological Flows: Ice sheets Phase change: Solidification/melting
Type
Papers
Information
Journal of Fluid Mechanics , Volume 712 , 10 December 2012 , pp. 552 - 578
Copyright
©2012 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. (Eds) 1972 Handbook of Mathematical Functions. Dover.Google Scholar
Alley, R. B. & Bindschadler, R. A. (Eds) 2001 The West Antarctic Ice Sheet: Behaviour and Environment. American Geophysical Union.Google Scholar
Aschwanden, A., Bueler, E., Khroulev, C. & Blatter, H. 2012 An enthalpy formulation for glaciers and ice sheets. J. Glaciol. 58 (209), 441–457.Google Scholar
Bamber, J. L., Vaughan, D. G. & Joughin, I. 2000 Widespread complex flow in the interior of the Antarctic ice sheet. Science 287 (5456), 1248–1250.Google Scholar
Barcilon, V. & MacAyeal, D. R. 1993 Steady flow of a viscous ice stream across a no-slip/free-slip transition at the bed. J. Glaciol. 39 (131), 167–185.Google Scholar
Bindschadler, R., Vornberger, P., Blankenship, D., Scambos, T. & Jacobel, R. 1996 Surface velocity and mass balance of Ice Streams D and E, West Antarctica. J. Glaciol. 42 (142).Google Scholar
Blankenship, D. D., Bentley, C. R., Rooney, S. T. & Alley, R. B. 1987 Till beneath Ice Stream B. 1. Properties derived from seismic travel times. J. Geophys. Res. 92 (B9), 8903–8911.Google Scholar
Bougamont, M., Price, S., Christoffersen, P. & Payne, A. J. 2011 Dynamic patterns of ice stream flow in a 3D higher-order ice sheet model with plastic bed and simplified hydrology. J. Geophys. Res. 116 (F04018) doi:10.1029/2011JF002025.Google Scholar
Budd, W. F., Keage, P. L. & Blundy, N. A. 1979 Empirical studies of ice sliding. J. Glaciol. 23 (89), 157–170.Google Scholar
Carslaw, H. S. & Jaeger, J. C. 1959 Conduction of Heat in Solids. Clarendon.Google Scholar
Cuffey, K. M. & Paterson, W. S. B. 2010 The Physics of Glaciers, 4th edn. Elsevier.Google Scholar
Debnath, L. & Mikusiński, J. 1999 Introduction to Hilbert Spaces with Applications. Academic.Google Scholar
Díaz, J. I., Muñoz, A. I. & Schiavi, E. 2007 Existence of weak solutions to a system of nonlinear partial differential equations modelling ice streams. Nonlin. Anal. Real World Appl. 8, 267–287.Google Scholar
Echelmeyer, K. A., Harrison, W. D., Larsen, C. & Mitchell, J. E. 1994 The role of margins in the dynamics of an active ice stream. J. Glaciol. 40 (136), 527–538.Google Scholar
Engelhardt, H. & Kamb, B. 1997 Basal hydraulic system of a West Antarctic ice stream: constraints from borehole observations. J. Glaciol. 43 (144), 207–230.Google Scholar
England, A. H. 1971 Complex Variable Methods in Elasticity. J. Wiley & Sons.Google Scholar
Fowler, A. C. 1987 Sliding with cavity formation. J. Glaciol. 33 (105), 255–267.Google Scholar
Fowler, A. C. 2001 Modelling the flow of glaciers and ice sheets. In Continuum Mechanics and Applications in Geophysics and the Environment (ed. Straughan, B., Greve, R., Ehrentraut, H. & Wang, Y.), pp. 276–304. Springer.Google Scholar
Fowler, A. C. & Johnson, C. 1996 Ice-sheet surging and ice-stream formation. Ann. Glaciol. 23, 68–73.Google Scholar
Harrison, W. D., Echelmeyer, K. A. & Larson, C. F. 1998 Measurement of temperature in a margin of Ice Stream B, Antarctica: implications for margin migration and lateral drag. J. Glaciol. 44 (148), 615–624.Google Scholar
Hinch, E. J. 1991 Perturbation Methods. Cambridge University Press.Google Scholar
Hulbe, C. & Fahnestock, M. 2007 Century-scale discharge stagnation and reactivation of the ross ice streams, west antarctica. J. Geophys. Res. 112 (F3), F0327.Google Scholar
Hulbe, C. & MacAyeal, D. R. 1999 A new thermodynamical numerical model of coupled ice sheet, ice stream, and ice shelf flow. J. Geophys. Res. 104 (B11), 25349–25366.Google Scholar
Hutter, K. & Olunloyo, V. O. S. 1980 On the distribution of stress and velocity in an ice strip, which is partly sliding over and partly adhering to its bed, by using a Newtonian viscous approximation. Proc. R. Soc. Lond. A. 373, 385–403.Google Scholar
Hutter, K., Yakowitz, S. & Szidarowsky, F. 1986 A numerical study of plane ice-sheet flow. J. Glaciol. 32 (111), 139–160.Google Scholar
Isaacson, E. & Keller, H. B. 1966 Analysis of Numerical Methods. J.Wiley & Sons.Google Scholar
Iverson, N. R., Hooyer, T. S. & Baker, R. W. 1998 Ring-shear studies of till deformation: Coulomb-plastic behaviour and distributed shear in glacier beds. J. Glaciol. 44 (148), 634–642.Google Scholar
Jacobel, R., Scambos, T. A., Raymond, C. F. & Gades, A. M. 1996 Changes in the configuration of ice stream flow from the West Antarctic ice sheet. J. Geophys. Res. 101, 5499–5504.Google Scholar
Jacobson, H. P. & Raymond, C. F. 1998 Thermal effects on the location of ice stream margins. J. Geophys. Res. 103 (B6), 12111–12122.Google Scholar
Joughin, I., Tulaczyk, S., Bindschadler, R. & Price, S. F. 2002 Changes in west antarctic ice stream velocities: observation and analysis. J. Geophys. Res. 107 (B11), 2289.Google Scholar
Kamb, B. 1991 Rheological nonlinearity and flow instability in the deforming bed mechanism of ice stream motion. J. Geophys. Res. 96 (B10), 16585–16595.Google Scholar
MacAyeal, D. R. 1989 Large-scale flow over a viscous basal sediment: theory and application to Ice Stream E, Antarctica. J. Geophys. Res. 94 (B4), 4017–4087.Google Scholar
Muskhelishvili, N. I. 1992 Singular Integral Equations. Dover, (unabridged republication of 2nd Edn published by P. Noordhoff, Groningen, 1953).Google Scholar
Noble, B. 1958 Methods Based on the Wiener–Hopf Technique for the Solution of Partial Differential Equations. Pergamon.Google Scholar
Perol, T. 2011 Why do west antarctica ice streams exist? Master’s thesis, École Normale Supérieure de Paris, Paris, France.Google Scholar
Raymond, C. 1996 Shear margins in glaciers and ice sheets. J. Glaciol. 42 (140), 90–102.Google Scholar
Sayag, R. & Tziperman, E. 2008 Spontaneous generation of pure ice streams via flow instability: role of longitudinal shear stresses and subglacial till. J. Geophys. Res. 113, B05411.Google Scholar
Schoof, C. 2004 On the mechanics of ice stream shear margins. J. Glaciol. 50 (169), 208–218.Google Scholar
Schoof, C. 2006 A variational approach to ice-stream flow. J. Fluid Mech. 556, 227–251.Google Scholar
Siegert, M. J., Welch, B., Vieli, A., Blankenship, D. D., Joughin, I., King, E. C., Vieli, G. J. M. C. L., Payne, A. J. & Jacobel, R. 2004 Ice flow direction change in interior west antarctica. Science 305 (5692), 1948–1951.Google Scholar
Truffer, M. & Echelmeyer, K. A. 2003 Of isbrae and ice streams. Ann. Glaciol. 36, 66–72.Google Scholar
Tulaczyk, S., Kamb, W. B. & Engelhardt, H. F. 2000a Basal mechanisms of ice stream b, west antarctica: 1. Till mechanics. J. Geophys. Res. 105 (B1), 463–481.Google Scholar
Tulaczyk, S., Kamb, W. B. & Engelhardt, H. F. 2000b Basal mechanisms of Ice Stream B, West Antarctica: 2. Undrained plastic bed model. J. Geophys. Res. 105 (B1), 483–494.Google Scholar
van der Veen, C. J. & Whillans, I. M. 1996 Model experiments on the evolution and stability of ice streams. Ann. Glaciol. 23, 129–137.Google Scholar