Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-28T22:05:56.041Z Has data issue: false hasContentIssue false
  • English
  • Français

A boundary layer model for ice stream margins

Published online by Cambridge University Press:  18 September 2015

M. Haseloff ,
C. Schoof  and
O. Gagliardini
M. Haseloff*
Affiliation:
Department of Earth, Ocean and Atmospheric Sciences, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
C. Schoof
Affiliation:
Department of Earth, Ocean and Atmospheric Sciences, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
O. Gagliardini
Affiliation:
CNRS, LGGE, UMR5183, 38041 Grenoble, France Université de Grenoble Alpes, LGGE, UMR5183, 38041 Grenoble, France Institut Universitaire de France, Paris, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

JFM classification

Boundary Layers: Boundary Layers Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Ice sheets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 781 , 25 October 2015 , pp. 353 - 387
Check for updates
Copyright
© 2015 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aschwanden, A., Bueler, E., Khroulev, C. & Blatter, H. 2012 An enthalpy formulation for glaciers and ice sheets. J. Glaciol. 58, 441–457.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, 167–185.CrossRefGoogle Scholar
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.Google Scholar
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, 741–752.Google Scholar
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, 59–67.Google Scholar
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, 465–467.Google Scholar
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, 529–549.Google Scholar
Creyts, T. T. & Schoof, C. G. 2009 Drainage through subglacial water sheets. J. Geophys. Res. 114, F04008.Google Scholar
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), 751–754.CrossRefGoogle Scholar
Echelmeyer, K. A. & Harrison, W. D. 1999 Ongoing margin migration of Ice Stream B, Antarctica. J. Glaciol. 45, 361–369.Google Scholar
Engelhardt, H. & Kamb, B. 1997 Basal hydraulic system of a West Antarctic ice stream: constraints from borehole observations. J. Glaciol. 43, 207–230.Google Scholar
Engelhardt, H. & Kamb, B. 1998 Basal sliding of Ice Stream B, West Antarctica. J. Glaciol. 44, 223–230.Google Scholar
Fowler, A. C. 1986 Sub-temperate basal sliding. J. Glaciol. 32, 3–5.Google Scholar
Fowler, A. C. 1987 Sliding with cavity formation. J. Glaciol. 33, 255–267.CrossRefGoogle Scholar
Fowler, A. C. 2011 Mathematical Geoscience, Interdisciplinary Applied Mathematics, vol. 36. Springer Science & Business Media.Google Scholar
Fowler, A. C. 2013 The motion of ice stream margins. J. Fluid Mech. 714, 1–4.Google Scholar
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), 217–242.Google Scholar
Gagliardini, O., Cohen, D., Råback, P. & Zwinger, T. 2007 Finite-element modeling of subglacial cavities and related friction law. J. Geophys. Res. 112, F02027.Google Scholar
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, 1299–1318.Google Scholar
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, 1561–1576.Google Scholar
Haseloff, M.2015 Modelling the migration of ice stream margins. PhD thesis, The University of British Columbia. Retrieved from http://hdl.handle.net/2429/54268.Google Scholar
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, 25349–25366.Google Scholar
Huppert, H. E. 1982 The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface. J. Fluid Mech. 121, 43–58.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 (1754), 385–403.Google Scholar
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, 101–119.Google Scholar
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, 31–40.Google Scholar
Jacobson, H. P. & Raymond, C. F. 1998 Thermal effects on the location of ice stream margins. J. Geophys. Res. 103, 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. 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. 157–199. American Geophysical Union.Google Scholar
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, 449–466.Google Scholar
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.Google Scholar
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, 4071–4087.Google Scholar
Moore, P. L., Iverson, N. R. & Cohen, D. 2010 Conditions for thrust faulting in a glacier. J. Geophys. Res. 115, F02005.Google Scholar
Morland, L. W. & Johnson, I. R. 1980 Steady motion of ice sheets. J. Glaciol. 25, 229–246.Google Scholar
Muszynski, I. & Birchfield, G. E. 1987 A coupled marine ice-stream–ice-shelf model. J. Glaciol. 33, 3–15.Google Scholar
Nowicki, S. M. J. & Wingham, D. J. 2008 Conditions for a steady ice sheet-ice shelf junction. Earth Planet. Sci. Lett. 265 (1), 246–255.Google Scholar
Paterson, W. S. B. 1994 The Physics of Glaciers. Elsevier.Google Scholar
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.Google Scholar
Payne, A. J. & Dongelmans, P. W. 1997 Self-organization in the thermomechanical flow of ice sheets. J. Geophys. Res. 102, 12219–12234.Google Scholar
Perol, T., Rice, J. R., Platt, J. D. & Suckale, J. 2015 Subglacial hydrology and ice stream margin locations. J. Geophys. Res. 120, 1352–1368.Google Scholar
Raymond, C. 1996 Shear margins in glaciers and ice sheets. J. Glaciol. 42, 90–102.Google Scholar
Rignot, E., Mouginot, J. & Scheuchl, B. 2011 Ice flow of the antarctic ice sheet. Science 333 (6048), 1427–1430.Google Scholar
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, 31943–31964.Google Scholar
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.Google Scholar
Schoof, C. 2004 On the mechanics of ice-stream shear margins. J. Glaciol. 50, 208–218.Google Scholar
Schoof, C. 2005 The effect of cavitation on glacier sliding. Proc. R. Soc. Lond. A 461 (2055), 609–627.Google Scholar
Schoof, C. 2012 Thermally driven migration of ice-stream shear margins. J. Fluid Mech. 712, 552–578.Google Scholar
Schoof, C. & Hewitt, I. 2013 Ice-sheet dynamics. Annu. Rev. Fluid Mech. 45, 217–239.Google Scholar
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), 73–114.Google Scholar
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, 776–786.Google Scholar
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, 1004–1025.Google Scholar