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A boundary layer model for ice stream margins

  • M. Haseloff (a1), C. Schoof (a1) and O. Gagliardini (a2) (a3) (a4)


The majority of Antarctic ice is discharged via long and narrow fast-flowing ice streams. At ice stream margins, the rapid transition from the vertical shearing flow in the ice ridges surrounding the stream to a rapidly sliding plug flow in the stream itself leads to high stress concentrations and a velocity field whose form is non-trivial to determine. In this paper, we develop a boundary layer theory for this narrow region separating a lubrication-type ice ridge flow and a membrane-type ice stream flow. This allows us to derive jump conditions for the outer models describing ridge and stream self-consistently. Much of our focus is, however, on determining the velocity and shear heating fields in the margin itself. Ice stream margins have been observed to change position over time, with potentially significant implications for ice stream discharge. Our boundary layer model allows us to extend previous work that has determined rates of margin migration from a balance between shear heating in the margin and the cooling effect of margin migration into the colder ice of the surrounding ice ridge. Solving for the transverse velocity field in the margin allows us to include the effect of advection due to lateral inflow of ice from the ridge on margin migration, and we demonstrate that this reduces the rate of margin migration, as previously speculated.


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Aschwanden, A., Bueler, E., Khroulev, C. & Blatter, H. 2012 An enthalpy formulation for glaciers and ice sheets. J. Glaciol. 58, 441457.
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, 167185.
Bueler, E. & Brown, J. 2009 The shallow shelf approximation as a sliding law in a thermomechanically coupled ice sheet model. J. Geophys. Res. 114, F03008.
Catania, G., Hulbe, C., Conway, H., Scambos, T. A. & Raymond, C. F. 2012 Variability in the mass flux of the Ross ice streams, West Antarctica, over the last millennium. J. Glaciol. 58, 741752.
Chugunov, V. A. & Wilchinsky, A. V. 1996 Modelling of a marine glacier and ice-sheet-ice-shelf transition zone based on asymptotic analysis. Ann. Glaciol. 23, 5967.
Conway, H., Catania, G., Raymond, C. F., Gades, A. M., Scambos, T. A. & Engelhardt, H. 2002 Switch of flow direction in an Antarctic ice stream. Nature 419, 465467.
Cornford, S. L., Martin, D. F., Graves, D. T., Ranken, D. F., Le Brocq, A. M., Gladstone, R. M., Payne, A. J., Ng, E. G. & Lipscomb, W. H. 2013 Adaptive mesh, finite volume modeling of marine ice sheets. J. Comput. Phys. 232, 529549.
Creyts, T. T. & Schoof, C. G. 2009 Drainage through subglacial water sheets. J. Geophys. Res. 114, F04008.
Cuffey, K. M., Conway, H., Hallet, B., Gades, A. M. & Raymond, C. F. 1999 Interfacial water in polar glaciers and glacier sliding at $-17\,^{\circ }\text{C}$ . Geophys. Res. Lett. 26 (6), 751754.
Echelmeyer, K. A. & Harrison, W. D. 1999 Ongoing margin migration of Ice Stream B, Antarctica. J. Glaciol. 45, 361369.
Engelhardt, H. & Kamb, B. 1997 Basal hydraulic system of a West Antarctic ice stream: constraints from borehole observations. J. Glaciol. 43, 207230.
Engelhardt, H. & Kamb, B. 1998 Basal sliding of Ice Stream B, West Antarctica. J. Glaciol. 44, 223230.
Fowler, A. C. 1986 Sub-temperate basal sliding. J. Glaciol. 32, 35.
Fowler, A. C. 1987 Sliding with cavity formation. J. Glaciol. 33, 255267.
Fowler, A. C. 2011 Mathematical Geoscience, Interdisciplinary Applied Mathematics, vol. 36. Springer Science & Business Media.
Fowler, A. C. 2013 The motion of ice stream margins. J. Fluid Mech. 714, 14.
Fowler, A. C. & Larson, D. A. 1978 On the flow of polythermal glaciers. I. Model and preliminary analysis. Proc. R. Soc. Lond. A 363 (1713), 217242.
Gagliardini, O., Cohen, D., Råback, P. & Zwinger, T. 2007 Finite-element modeling of subglacial cavities and related friction law. J. Geophys. Res. 112, F02027.
Gagliardini, O., Zwinger, T., Gillet-Chaulet, F., Durand, G., Favier, L., Fleurian, B., de Greve, R., Malinen, M., Martín, C., Råback, P., Ruokolainen, J., Saccettini, M., Schäfer, M., Seddik, H. & Thies, J. 2013 Capabilities and performance of Elmer/Ice, a new generation ice-sheet model. Geosci. Model Develop. 6, 12991318.
Gillet-Chaulet, F., Gagliardini, O., Seddik, H., Nodet, M., Durand, G., Ritz, C., Zwinger, T., Greve, R. & Vaughan, D. G. 2012 Greenland ice sheet contribution to sea-level rise from a new-generation ice-sheet model. Cryosphere 6, 15611576.
Haseloff, M.2015 Modelling the migration of ice stream margins. PhD thesis, The University of British Columbia. Retrieved from
Hulbe, C. L. & MacAyeal, D. R. 1999 A new numerical model of coupled inland ice sheet, ice stream, and ice shelf flow and its application to the West Antarctic Ice Sheet. J. Geophys. Res. 104, 2534925366.
Huppert, H. E. 1982 The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface. J. Fluid Mech. 121, 4358.
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 (1754), 385403.
Iken, A. & Bindschadler, R. A. 1986 Combined measurements of subglacial water pressure and surface velocity of Findelengletscher, Switzerland: conclusions about drainage system and sliding mechanism. J. Glaciol. 32, 101119.
Iverson, N. R., Baker, R. W., LeB Hooke, R., Hanson, B. & Jansson, P. 1999 Coupling between a glacier and a soft bed: I. A relation between effective pressure and local shear stress determined from till elasticity. J. Glaciol. 45, 3140.
Jacobson, H. P. & Raymond, C. F. 1998 Thermal effects on the location of ice stream margins. J. Geophys. Res. 103, 1211112122.
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.
Kamb, B. 2001 Basal zone of the West Antarctic ice streams and its role in lubrication of their rapid motion. In The West Antarctic Ice Sheet: Behaviour and Environment (ed. Alley, R. B. & Bindschadler, R. A.), Antarctic Research Series, vol. 77, pp. 157199. American Geophysical Union.
Kyrke-Smith, T. M., Katz, R. F. & Fowler, A. C. 2013 Stress balances of ice streams in a vertically integrated, higher-order formulation. J. Glaciol. 59, 449466.
Kyrke-Smith, T. M., Katz, R. F. & Fowler, A. C. 2014 Subglacial hydrology and the formation of ice streams. Proc. R. Soc. Lond. A 470 (2161), doi:10.1098/rspa.2013.0494.
MacAyeal, D. R. 1989 Large-scale ice flow over a viscous basal sediment – theory and application to ice stream B, Antarctica. J. Geophys. Res. 94, 40714087.
Moore, P. L., Iverson, N. R. & Cohen, D. 2010 Conditions for thrust faulting in a glacier. J. Geophys. Res. 115, F02005.
Morland, L. W. & Johnson, I. R. 1980 Steady motion of ice sheets. J. Glaciol. 25, 229246.
Muszynski, I. & Birchfield, G. E. 1987 A coupled marine ice-stream–ice-shelf model. J. Glaciol. 33, 315.
Nowicki, S. M. J. & Wingham, D. J. 2008 Conditions for a steady ice sheet-ice shelf junction. Earth Planet. Sci. Lett. 265 (1), 246255.
Paterson, W. S. B. 1994 The Physics of Glaciers. Elsevier.
Pattyn, F. 2003 A new three-dimensional higher-order thermomechanical ice sheet model: basic sensitivity, ice stream development, and ice flow across subglacial lakes. J. Geophys. Res. 108, 2382.
Payne, A. J. & Dongelmans, P. W. 1997 Self-organization in the thermomechanical flow of ice sheets. J. Geophys. Res. 102, 1221912234.
Perol, T., Rice, J. R., Platt, J. D. & Suckale, J. 2015 Subglacial hydrology and ice stream margin locations. J. Geophys. Res. 120, 13521368.
Raymond, C. 1996 Shear margins in glaciers and ice sheets. J. Glaciol. 42, 90102.
Rignot, E., Mouginot, J. & Scheuchl, B. 2011 Ice flow of the antarctic ice sheet. Science 333 (6048), 14271430.
Ritz, C., Rommelaere, V. & Dumas, C. 2001 Modeling the evolution of Antarctic ice sheet over the last 420 000 years: implications for altitude changes in the Vostok region. J. Geophys. Res. 106, 3194331964.
Sayag, R. & Tziperman, E. 2011 Interaction and variability of ice streams under a triple-valued sliding law and non-Newtonian rheology. J. Geophys. Res. 116, F01009.
Schoof, C. 2004 On the mechanics of ice-stream shear margins. J. Glaciol. 50, 208218.
Schoof, C. 2005 The effect of cavitation on glacier sliding. Proc. R. Soc. Lond. A 461 (2055), 609627.
Schoof, C. 2012 Thermally driven migration of ice-stream shear margins. J. Fluid Mech. 712, 552578.
Schoof, C. & Hewitt, I. 2013 Ice-sheet dynamics. Annu. Rev. Fluid Mech. 45, 217239.
Schoof, C. & Hindmarsh, R. C. A. 2010 Thin-film flows with wall slip: an asymptotic analysis of higher order glacier flow models. Q. J. Mech. Appl. Maths 63 (1), 73114.
Seroussi, H., Ben Dhia, H., Morlighem, M., Larour, E., Rignot, E. & Aubry, D. 2012 Coupling ice flow models of varying orders of complexity with the Tiling method. J. Glaciol. 58, 776786.
Suckale, J., Platt, J. D., Perol, T. & Rice, J. R. 2014 Deformation-induced melting in the margins of the West Antarctic ice streams. J. Geophys. Res. 119, 10041025.
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A boundary layer model for ice stream margins

  • M. Haseloff (a1), C. Schoof (a1) and O. Gagliardini (a2) (a3) (a4)


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