Skip to main content
×
×
Home

Application of a continuum-mechanical model for the flow of anisotropic polar ice to the EDML core, Antarctica

  • Hakime Seddik (a1), Ralf Greve (a1), Luca Placidi (a2), Ilka Hamann (a3) and Olivier Gagliardini (a4)...
Abstract

We present an application of the newly developed CAFFE model (Continuum-mechanical, Anisotropic Flow model based on an anisotropic Flow Enhancement factor) to the EPICA ice core at Kohnen Station, Dronning Maud Land, Antarctica (referred to as the EDML core). A one-dimensional flow model for the site is devised, which includes the anisotropic flow law and the fabric evolution equation of the CAFFE model. Three different solution methods are employed: (1) computing the ice flow based on the flow law of the CAFFE model and the measured fabrics; (2) solving the CAFFE fabric evolution equation under the simplifying assumption of transverse isotropy; and (3) solving the unrestricted CAFFE fabric evolution equation. Method (1) demonstrates clearly the importance of the anisotropic fabric in the ice column for the flow velocity. The anisotropic enhancement factor produced with method (2) agrees reasonably well with that of method (1), even though the measured fabric shows a girdle structure (which breaks the transverse isotropy) in large parts of the ice core. For method (3), we find that the measured fabric is reproduced well by the model down to ∼2100 m depth. Systematic deviations at greater depths are attributed to the disregard of migration recrystallization in the model.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Application of a continuum-mechanical model for the flow of anisotropic polar ice to the EDML core, Antarctica
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Application of a continuum-mechanical model for the flow of anisotropic polar ice to the EDML core, Antarctica
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Application of a continuum-mechanical model for the flow of anisotropic polar ice to the EDML core, Antarctica
      Available formats
      ×
Copyright
References
Hide All
Azuma, N. 1994. A flow law for anisotropic ice and its application to ice sheets. Earth Planet. Sci. Lett., 128(3–4), 601614.
Azuma, N. 1995. A flow law for anisotropic polycrystalline ice under uniaxial compressive deformation. Cold Reg. Sci. Technol., 23(2), 137147.
Castelnau, O., Thorsteinsson, T., Kipfstuhl, J., Duval, P. and Canova, G.R.. 1996. Modelling fabric development along the GRIP ice core, central Greenland. Ann. Glaciol., 23, 194201.
Castelnau, O. and 7 others. 1998. Anisotropic behavior of GRIP ices and flow in central Greenland. Earth Planet. Sci. Lett., 154(1–4), 307322.
Dafalias, Y.F. 2001. Orientation distribution function in non-affine rotations. J. Mech. Phys. Solids, 49(11), 24932516.
Dansgaard, W. and Johnsen, S.J.. 1969. A flow model and a time scale for the ice core from Camp Century, Greenland. J. Glaciol., 8(53), 215223.
Duval, P., Ashby, M.F. and Anderman, I.. 1983. Rate-controlling processes in the creep of polycrystalline ice. J. Phys. Chem., 87(21), 40664074.
Eisen, O., Hamann, I., Kipfstuhl, S., Steinhage, D. and Wilhelms, F.. 2007. Direct evidence for continuous radar reflector originating from changes in crystal-orientation fabric. Cryosphere, 1(1), 110.
EPICA community members. 2006. One-to-one coupling of glacial climate variability in Greenland and Antarctica. Nature, 444(7116), 195198.
Faria, S.H. 2003. Mechanics and thermodynamics of mixtures with continuous diversity. (Doctoral thesis, Technical University Darmstadt.)
Faria, S.H. 2006a. Creep and recrystallization of large polycrystalline masses. I. General continuum theory. Proc. R. Soc. London, Ser. A, 462(2069), 14931514.
Faria, S.H. 2006b. Creep and recystallization of large polycrystalline masses. III. Continuum theory of ice sheets. Proc. R. Soc. London, Ser. A, 462(2073), 27972816.
Faria, S.H., Kremer, G.M. and Hutter, K.. 2006. Creep and recrystallization of large polycrystalline masses. II. Constitutive theory for crystalline media with transversely isotropic grains. Proc. R. Soc. London, Ser. A, 462(2070), 16991720.
Gagliardini, O., Gillet-Chaulet, F. and Montagnat, M.. In press. A review of anisotropic polar ice models: from crystal to ice-sheet flow models. In Hondoh, T., ed. Proceedings of the 2nd International Workshop on Physics of Ice Core Records (PICR-2). Sapporo, Hokkaido University, Institute of Low Temperature Science.
Gillet-Chaulet, F., Gagliardini, O., Meyssonnier, J., Montagnat, M. and Castelnau, O.. 2005. A user-friendly anisotropic flow law for ice-sheet modelling. J. Glaciol., 51(172), 314.
Gillet-Chaulet, F., Gagliardini, O., Meyssonnier, J., Zwinger, T. and Ruokolainen, J.. 2006. Flow-induced anisotropy in polar ice and related ice-sheet flow modelling. J. Non-Newtonian FluidMech., 134(1–3), 3343.
Gödert, G. and Hutter, K.. 1998. Induced anisotropy in large ice shields: theory and its homogenization. Contin. Mech. Thermodyn., 10(5), 293318.
Greve, R. 1997. A continuum-mechanical formulation for shallow polythermal ice sheets. Philos. Trans. R. Soc. London, Ser. A, 355(1726), 921974.
Greve, R. 2005. Relation of measured basal temperatures and the spatial distribution of the geothermal heat flux for the Greenland ice sheet. Ann. Glaciol., 42, 424432.
Greve, R. and Blatter, H.. In press. Dynamics of ice sheets and glaciers. Berlin, etc, Springer.
Greve, R., Wang, Y. and Mügge, B.. 2002. Comparison of numerical schemes for the solution of the advective age equation in ice sheets. Ann. Glaciol., 35, 487494.
Greve, R., Placidi, L. and Seddik, H.. In press. A continuum-mechanical model for the flow of anisotropic polar ice. In Hon-doh, T., ed. Proceedings of the 2nd International Workshop on Physics of Ice Core Records (PICR-2). Sapporo, Hokkaido University, Institute of Low Temperature Science.
Hooke, R.LeB. 2005. Principles of glacier mechanics. Second edition. Cambridge, etc., Cambridge University Press.
Hutter, K. 1983. Theoretical glaciology; material science of ice and the mechanics of glaciers and ice sheets. Dordrecht, D. Reidel Publishing.
Huybrechts, P., Rybak, O., Pattyn, F., Ruth, U. and Steinhage, D.. 2007. Ice thinning, upstream advection, and non-climatic biases for the upper 89% of the EDML ice core from a nested model of the Antarctic ice sheet. Climate Past, 3(4), 577589.
Jacka, T.H. and Budd, W.F.. 1989. Isotropic and anisotropic flow relations for ice dynamics. Ann. Glaciol., 12, 8184.
Ktitarev, D., Godert, G. and Hutter, K.. 2002. Cellular automaton model for recrystallization, fabric, and texture development in polar ice. J. Geophys. Res., 107(B8), 2165. (10.1029/2001JB000621.)
Lebensohn, R.A., Liu, Y. and Ponte Castañeda, P.. 2004a. Macroscopic properties and field fluctuations in model power-law poly-crystals: full-field solutions versus self-consistent estimates. Proc. R. Soc. London, Ser. A, 460(2045), 13811405.
Lebensohn, R.A., Liu, Y. and Ponte Castañeda, P.. 2004b. On the accuracy of the self-consistent approximation for polycrystals: comparison with full-field numerical simulations. Acta Mater., 52(18), 53475361.
Liu, I.S. 2002. Continuum mechanics. New York, Springer.
Lliboutry, L. 1993. Anisotropic, transversely isotropic nonlinear viscosity of rock ice and rheological parameters inferred from homogenization. Int. J. Plasticity, 9(5), 619632.
Lliboutry, L. and Duval, P.. 1985. Various isotropic and anisotropic ices found in glaciers and polar ice caps and their corresponding rheologies. Ann. Geophys., 3(2), 207224.
Mangeney, A., Califano, F. and Castelnau, O.. 1996. Isothermal flow of an anisotropic ice sheet in the vicinity of an ice divide. J. Geophys. Res., 101(B12), 28,18928,204.
Mansuy, P., Meyssonnier, J. and Philip, A.. 2002. Localization of deformation in polycrystalline ice: experiments and numerical simulations with a simple grain model. Comput. Mat. Sci., 25(1–2), 142150.
Meyssonnier, J. and Philip, A.. 2000. Comparison of finite-element and homogenization methods for modelling the viscoplastic behaviour of a S2-columnar-ice polycrystal. Ann. Glaciol., 30, 115120.
Miyamoto, A. 1999. Mechanical properties and crystal textures of Greenland deep ice cores. (Doctoral thesis, Hokkaido University.)
Morland, L.W. 1984. Thermomechanical balances of ice sheet flows. Geophys. Astrophys. Fluid Dyn., 29(1–4), 237266.
Morland, L.W. and Staroszczyk, R.. 1998. Viscous response of polar ice with evolving fabric. Contin. Mech. Thermodyn., 10, 135152.
Morland, L.W. and Staroszczyk, R.. 2003. Stress and strain-rate formulations for fabric evolution in polar ice. Contin. Mech. Thermodyn., 15(1), 5571.
Motoyama, H. 2007. The second deep ice coring project at Dome Fuji, Antarctica. Sci. Drilling 5, 4143.
Paterson, W.S.B. 1991. Why ice-age ice is sometimes “soft”. Cold Reg. Sci. Technol., 20(1), 7598.
Paterson, W.S.B. 1994. The physics of glaciers. Third edition. Oxford, etc., Elsevier.
Pimienta, P., Duval, P., and Lipenkov, V.Y.. 1987. Mechanical behavior of anisotropic polar ice. IAHS Publ. 170 (Symposium at Vancouver 1987 – The Physical Basis of Ice Sheet Modelling), 5766.
Placidi, L. 2004. Thermodynamically consistent formulation of induced anisotropy in polar ice accounting for grain-rotation, grain-size evolution and recrystallization. (Doctoral thesis, Darmstadt University of Technology.)
Placidi, L. 2005. Microstructured continua treated by the theory of mixtures. (Doctoral thesis, University of Rome La Sapienza.)
Placidi, L. and Hutter, K.. 2006a. An anisotropic flow law for incompressible polycrystalline materials. Z. Angew. Math. Phys., 57(1), 160181.
Placidi, L. and Hutter, K.. 2006b. Thermodynamics of polycrystalline materials treated by the theory of mixtures with continuous diversity. Contin. Mech. Thermodyn., 17(6), 409451.
Russell-Head, D.S. and Budd, W.F., 1979. Ice sheet flow properties derived from borehole shear measurements combined with ice core studies. J. Glaciol., 24(90), 117130.
Saito, F. and Abe-Ouchi, A.. 2004. Thermal structure of Dome Fuji and east Dronning Maud Land, Antarctica, simulated by a three-dimensional ice-sheet model. Ann. Glaciol., 39, 433438.
Seddik, H. 2008. A full-Stokes finite-element model for the vicinity of Dome Fuji with flow-induced ice-anisotropy and fabric evolution. (Doctoral thesis, Hokkaido University.)
Svendsen, B. and Hutter, K.. 1996. A continuum approach for modelling induced anisotropy in glaciers and ice sheets. Ann. Glaciol., 23, 262269.
Thorsteinsson, T. 2001. An analytical approach to deformation of anisotropic ice-crystal aggregates. J. Glaciol., 47(158), 507516.
Thorsteinsson, T. 2002. Fabric development with nearest-neighbour interaction and dynamic recrystallization. J. Geophys. Res., 107(B1), 2014. (10.1019/2001JB000244.)
Van der Veen, C.J. 1999. Fundamentals of glacier dynamics. Rotterdam, A.A. Balkema.
Wesche, C., Eisen, O., Oerter, H., Schulte, D. and Steinhage, D.. 2007. Surface topography and ice flow in the vicinity of the EDML deep-drilling site, Antarctica. J. Glaciol., 53(182), 442448.
Wilson, C.J.L., Russell-Head, D.S. and Sim, H.M.. 2003. The application of an automated fabric analyzer system to the textural evolution of folded ice layers in shear zones. Ann. Glaciol., 37, 717.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Glaciology
  • ISSN: 0022-1430
  • EISSN: 1727-5652
  • URL: /core/journals/journal-of-glaciology
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 6
Total number of PDF views: 28 *
Loading metrics...

Abstract views

Total abstract views: 75 *
Loading metrics...

* Views captured on Cambridge Core between 8th September 2017 - 18th September 2018. This data will be updated every 24 hours.