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Ice-shelf vibrations modeled by a full 3-D elastic model

  • Yuri V. Konovalov (a1)

Abstract

Forced ice-shelf vibration modeling is performed using a full 3-D finite-difference elastic model, which also takes into account sub-ice seawater flow. The sea water flow is described by the wave equation. Ice-shelf flexure therefore results from hydrostatic pressure perturbations in the sub-ice seawater layer. Numerical experiments were undertaken for idealized rectangular ice-shelf geometry. The ice-plate vibrations were modeled for harmonic incoming pressure perturbations and for a wide range of incoming wave frequencies. The spectra showed distinct resonant peaks, which demonstrate the ability of the model to simulate a resonant-like motion. The spectra obtained by the full 3-D model are compared with exact solutions for the elastic thin plate with two fixed edges and two free edges. The spectra are also compared with the spectra modeled by the thin-plate Holdsworth and Glynn model (1978).

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Copyright

This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

References

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Balmforth, NJ and Craster, RV (1999) Ocean waves and ice sheets. J. Fluid Mech., 395, 89124 (doi: 10.1017/S0022112099005145)
Bassis, JN, Fricker, HA, Coleman, R and Minster, J-B (2008) An investigation into the forces that drive ice-shelf rift propagation on the Amery Ice Shelf, East Antarctica. J. Glaciol., 54(184), 172710.3189/002214308784409116
Bromirski, PD, Sergienko, OV and MacAyeal, DR (2009) Transoceanic infragravity waves impacting Antarctic ice shelves. Geophys. Res. Lett., 37, L02502 (doi: 10.1029/2009GL041488)
Goodman, DJ, Wadhams, P and Squire, VA (1980) The flexural response of a tabular ice island to ocean swell. Ann. Glaciol., 1, 2327
Holdsworth, G (1977) Tidal interaction with ice shelves. Ann. Geophys., 33, 133146
Holdsworth, G and Glynn, (1978) Iceberg calving from floating glaciers by a vibrating mechanism. Nature, 274, 46446610.1038/274464a0
Hughes, TJ (1977) West Antarctic ice streams. Rev. Geophys. Space Phys., 15(1), 146
Konovalov, YV (2015) The eigenvalue problem for ice-shelf vibrations: comparison of a full 3-D model with the thin plate approximation. Earth Syst. Dyn. Discuss., 6, 16051633 (doi: 10.5194/esdd-6-1605-2015)
Konovalov, YV (2016) The eigen value problem for ice-tongue vibrations in 3-D and thin-plate elastic models. J. Geogr. Earth Sci., 4(2), 7598 (doi: 10.15640/jges.v4n2a5)
Lamb, H (1994) Hydrodynamics, 6th edn. Cambridge University Press, Cambridge
Landau, LD and Lifshitz, EM (1986) Theory of elasticity, Vol. 7, 3rd edn. Butterworth-Heinemann, Oxford
Landau, LD and Lifshitz, EM (1987) Fluid mechanics, Vol. 6, 2nd edn. Pergamon Press, Oxford
Lingle, CS, Hughes, TJ and Kollmeyer, RC (1981) Tidal flexure of Jakobshavns Glacier, West Greenland. J. Geophys. Res., 86(B5), 39603968
Lurie, AI (2005) Theory of elasticity. Foundations of engineering mechanics. Springer, Heidelberg, Berlin10.1007/978-3-540-26455-2
MacAyeal, DR and 13 others (2006) Transoceanic wave propagation links iceberg calving margins of Antarctica with storms in tropics and Northern Hemisphere. Geophys. Res. Lett., 33, L17502 (doi: 10.1029/2006GL027235)
Meylan, M, Squire, VA and Fox, C (1997) Towards realism in modelling ocean wave behavior in marginal ice zones. J. Geophys. Res., 102(C10), 2298122991
Reeh, N, Christensen, EL, Mayer, C and Olesen, OB (2003) Tidal bending of glaciers: a linear viscoelastic approach. Ann. Glaciol., 37, 838910.3189/172756403781815663
Robin, G de Q (1958) Seismic shooting and related investigations. Norwegian-British-Swedish Antarctic Expedition, 1949-1952, Glaciology 3, Scientific Results 5, Norsk Polarinstitutt, Oslo
Rosier, SHR, Gudmundsson, GH and Green, JAM (2014) Insights into ice stream dynamics through modeling their response to tidal forcing. Cryosphere, 8, 17631775
Schmeltz, M, Rignot, E and MacAyeal, DR (2001) Tidal flexure along ice-sheets margins: comparison of InSAR with an elastic plate model. Ann. Glaciol., 34, 20220810.3189/172756402781818049
Schulson, EM (1999) The structure and mechanical behavior of ice. JOM, 51(2), 2127
Sergienko, OV (2010) Elastic response of floating glacier ice to impact of long-period ocean waves. J. Geophys. Res., 115, F04028 (doi: 10.1029/2010JF001721)
Smith, AM (1991) The use of tiltmeters to study the dynamics of Antarctic ice shelf grounding lines. J. Glaciol., 37, 5158
Squire, VA, Dugan, JP, Wadhams, P, Rottier, PJ and Liu, AK (1995) Of ocean waves and sea ice. Annu. Rev. Fluid Mech., 27, 115168
Stephenson, SN (1984) Glacier flexure and the position of grounding lines: measurements by tiltmeter on Rutford Ice Stream, Antarctica. Ann. Glaciol., 5, 165169
Tikhonov, AN and Samarskii, AA (1963) Equations of mathematical physics. Pergamon Press Ltd., USA
Turcotte, DL and Schubert, G (2002) Geodynamics, 3rd edn. Cambridge University Press, Cambridge
Vaughan, DG (1995) Tidal flexure at ice shelf margins. J. Geophys. Res., 100(B4), 62136224 (doi: 10.1029/94JB02467)
Wadhams, P (1986) The seasonal ice zone. In Untersteiner, N ed. Geophysics of sea ice. Plenum Press, London, 82599110.1007/978-1-4899-5352-0_15
Walker, RT and 5 others (2013) Ice-shelf tidal flexure and subglacial pressure variations. Earth Planet. Sci. Lett., 361, 422428

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