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Glaciers and Ice Sheets

  • Andrew Fowler
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 36)

Abstract

Chapter 10 begins with an overview of various phenomena which are of interest in glaciology: waves, surges, ice shelf collapse, and so on. Following this, the shallow ice approximation is derived in detail for both glaciers and ice sheets, and also for ice shelves. Theories for subglacial sliding and drainage are presented, and the resulting theories used to describe waves and surges. The chapter finishes with theoretical discussions of drumlins, eskers and the Martian polar ice caps.

Keywords

Effective Pressure Steep Descent Path Tidewater Glacier Geothermal Heat Flux Basal Shear Stress 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Allen JRL (1971) Transverse erosional marks of mud and rock: their physical basis and geological significance. Sediment Geol 5:167–385 CrossRefGoogle Scholar
  2. Alley RB (1989) Water-pressure coupling of sliding and bed deformation: I. Water system. J Glaciol 35:108–118 CrossRefGoogle Scholar
  3. Alley RB (2002) The two-mile time machine: ice cores, abrupt climate change, and our future. Princeton University Press, Princeton Google Scholar
  4. Altuhafi FN, Baudet BA, Sammonds P (2009) On the time-dependent behaviour of glacial sediments. Quat Sci Rev 28:693–707 CrossRefGoogle Scholar
  5. Barcilon V, MacAyeal DR (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
  6. Benn DA, Evans DJA (1998) Glaciers and glaciation. Edward Arnold, London Google Scholar
  7. Bennett MR, Glasser NF (2010) Glacial geology: ice sheets and landforms, 2nd edn. Wiley, London Google Scholar
  8. Bentley CR (1987) Antarctic ice streams: a review. J Geophys Res 92:8843–8858 CrossRefGoogle Scholar
  9. Blatter H (1995) Velocity and stress fields in grounded glaciers: a simple algorithm for including deviatoric stress gradients. J Glaciol 41:333–344 Google Scholar
  10. Blumberg PN, Curl RL (1974) Experimental and theoretical studies of dissolution roughness. J Fluid Mech 65:735–751 CrossRefGoogle Scholar
  11. Bond G et al. (1992) Evidence for massive discharges of icebergs into the North Atlantic ocean during the last glacial period. Nature 360:245–249 CrossRefGoogle Scholar
  12. Boulton GS, Hindmarsh RCA (1987) Sediment deformation beneath glaciers: rheology and geological consequences. J Geophys Res 92:9059–9082 CrossRefGoogle Scholar
  13. Bryce J (1833) On the evidences of diluvial action in the north of Ireland. J Geol Soc Dublin 1:34–44 Google Scholar
  14. Bueler E, Brown J (2009) Shallow shelf approximation as a “sliding law” in a thermomechanically coupled ice sheet model. J Geophys Res 114:F03008. doi: 10.1029/2008JF001179 CrossRefGoogle Scholar
  15. Chugunov VA, Wilchinsky AV (1996) Modelling of a marine glacier and ice-sheet–ice-shelf transition zone based on asymptotic analysis. Ann Glaciol 23:59–67 Google Scholar
  16. Clark PU, Walder JS (1994) Subglacial drainage, eskers, and deforming beds beneath the Laurentide and Eurasian ice sheets. Geol Soc Amer Bull 106:304–314 CrossRefGoogle Scholar
  17. Clarke GKC (2005) Subglacial processes. Annu Rev Earth Planet Sci 33:247–276 CrossRefGoogle Scholar
  18. Clarke GKC, Nitsan U, Paterson WSB (1977) Strain heating and creep instability in glaciers and ice sheets. Rev Geophys Space Phys 15:235–247 CrossRefGoogle Scholar
  19. Clarke GKC, Collins SG, Thompson DE (1984) Flow, thermal structure, and subglacial conditions of a surge-type glacier. Can J Earth Sci 21:232–240 CrossRefGoogle Scholar
  20. Close MH (1867) Notes on the general glaciation of Ireland. J R Geol Soc Irel 1:207–242 Google Scholar
  21. Cuffey K, Paterson WSB (2010) The physics of glaciers, 4th edn. Elsevier, Amsterdam Google Scholar
  22. Dahl-Jensen D (1989) Steady thermomechanical flow along two-dimensional flow lines in large grounded ice sheets. J Geophys Res 94:10335–10362 Google Scholar
  23. Deeley RM, Parr PH (1914) On the Hintereis glacier. Philos Mag 27(6):153–176 Google Scholar
  24. Drozdowski E (1986) An international drumlin biography. Boreas 15:310 CrossRefGoogle Scholar
  25. Durand G, Gagliardini O, Zwinger T, Le Meur E, Hindmarsh RCA (2009) Full Stokes modeling of marine ice sheets: influence of the grid size. Ann Glaciol 50(52):109–114 CrossRefGoogle Scholar
  26. Embleton C, King CAM (1968) Glacial and periglacial geomorphology. Edward Arnold, London Google Scholar
  27. Engelhardt H, Humphrey N, Kamb B, Fahnestock M (1990) Physical conditions at the base of a fast moving Antarctic ice stream. Science 248:57–59 CrossRefGoogle Scholar
  28. Finsterwalder S (1907) Die Theorie der Gletscherschwankungen. Z Gletschkd 2:81–103 Google Scholar
  29. Flint RF (1930) The origin of the Irish “eskers”. Geogr Rev 20:615–630 CrossRefGoogle Scholar
  30. Fowler AC (1979) Glacier dynamics. DPhil thesis, University of Oxford Google Scholar
  31. Fowler AC (1986) A sliding law for glaciers of constant viscosity in the presence of subglacial cavitation. Proc R Soc Lond A 407:147–170 MATHCrossRefGoogle Scholar
  32. Fowler AC (1987a) A theory of glacier surges. J Geophys Res 92:9111–9120 CrossRefGoogle Scholar
  33. Fowler AC (1987b) Sliding with cavity formation. J Glaciol 33:255–267 Google Scholar
  34. Fowler AC (1989) A mathematical analysis of glacier surges. SIAM J Appl Math 49:246–262 MATHMathSciNetCrossRefGoogle Scholar
  35. Fowler AC (1992a) Modelling ice sheet dynamics. Geophys Astrophys Fluid Dyn 63:29–65 MathSciNetCrossRefGoogle Scholar
  36. Fowler AC (2000) An instability mechanism for drumlin formation. In: Maltman A, Hambrey MJ, Hubbard B (eds) Deformation of glacial materials. Spec pub geol soc, vol 176. Geological Society, London, pp 307–319 Google Scholar
  37. Fowler AC (2003) On the rheology of till. Ann Glaciol 37:55–59 CrossRefGoogle Scholar
  38. Fowler AC (2010) The formation of subglacial streams and mega-scale glacial lineations. Proc R Soc Lond A 466:3181–3201. doi: 10.1098/rspa.2010.0009 MATHMathSciNetCrossRefGoogle Scholar
  39. Fowler AC, Johnson C (1995) Hydraulic runaway: a mechanism for thermally regulated surges of ice sheets. J Glaciol 41:554–561 Google Scholar
  40. Fowler AC, Johnson C (1996) Ice sheet surging and ice stream formation. Ann Glaciol 23:68–73 Google Scholar
  41. Fowler AC, Larson DA (1978) On the flow of polythermal glaciers. I. Model and preliminary analysis. Proc R Soc Lond A 363:217–242 MathSciNetCrossRefGoogle Scholar
  42. Fowler AC, Larson DA (1980a) The uniqueness of steady state flows of glaciers and ice sheets. Geophys J R Astron Soc 63:333–345 MATHGoogle Scholar
  43. Fowler AC, Larson DA (1980b) On the flow of polythermal glaciers II. Surface wave analysis. Proc R Soc Lond A 370:155–171 MathSciNetCrossRefGoogle Scholar
  44. Fowler AC, Toja R, Vázquez C (2009) Temperature dependent shear flow and the absence of thermal runaway in valley glaciers. Proc R Soc Lond A 466:363–382 Google Scholar
  45. François B, Lacombe F, Herrmann HJ (2002) Finite width of shear zones. Phys Rev E 65:031311 CrossRefGoogle Scholar
  46. Frappé-Sénéclauze T-P, Clarke GKC (2007) Slow surge of Trapridge Glacier, Yukon Territory, Canada. J Geophys Res 112:F03S32. doi: 10.1029/2006JF000607 CrossRefGoogle Scholar
  47. Fudge TJ, Humphrey NF, Harper JT, Pfeffer WT (2008) Diurnal fluctuations in borehole water levels: configuration of the drainage system beneath Bench Glacier, Alaska, USA. J Glaciol 54:297–306 CrossRefGoogle Scholar
  48. Grigoryan SS, Krass MS, Shumskiy PA (1976) Mathematical model of a three-dimensional non-isothermal glacier. J Glaciol 17:401–417 Google Scholar
  49. Gudmundsson GH (2003) Transmission of basal variability to a glacier surface. J Geophys Res 108(B5):2253. doi: 10.1029/2002JB002107 CrossRefGoogle Scholar
  50. Hall J (1815) On the revolutions of the Earth’s surface. Trans R Soc Edinb 7:169–184 Google Scholar
  51. Hewitt IJ, Fowler AC (2008) Seasonal waves on glaciers. Hydrol Process 22:3919–3930 CrossRefGoogle Scholar
  52. Hindmarsh RCA (1993) Qualitative dynamics of marine ice sheets. In: Peltier WR (ed) Ice in the climate system. Springer, Berlin, pp 67–99 Google Scholar
  53. Hindmarsh RCA (1998) The stability of a viscous till sheet coupled with ice flow, considered at wavelengths less than the ice thickness. J Glaciol 44:285–292 Google Scholar
  54. Hindmarsh RCA (2009) Consistent generation of ice-streams via thermo-viscous instabilities modulated by membrane stresses. Geophys Res Lett 36:L06502 CrossRefGoogle Scholar
  55. Hindmarsh RCA, Le Meur E (2001) Dynamical processes involved in the retreat of marine ice sheets. J Glaciol 47:271–282 CrossRefGoogle Scholar
  56. Hodge SM (1974) Variations in the sliding of a temperate glacier. J Glaciol 13:349–369 Google Scholar
  57. Holland DM, Jacobs SS, Jenkins A (2003) Modelling the ocean circulation beneath the Ross Ice Shelf. Antarct Sci 15:13–23 CrossRefGoogle Scholar
  58. Holland DM, Thomas RH, de Young B, Ribergaard MH (2008) Acceleration of Jakobshavn Isbrae triggered by warm subsurface ocean waters. Nat Geosci 1:659–664 CrossRefGoogle Scholar
  59. Hooke RLeB (2005) Principles of glacier mechanics, 2nd edn. Cambridge University Press, Cambridge CrossRefGoogle Scholar
  60. Hooke RLeB, Hanson B, Iverson NR, Jansson P, Fischer UH (1997) Rheology of till beneath Storglaciären, Sweden. J Glaciol 43(143):172–179 Google Scholar
  61. Howard AD (1978) Origin of the stepped topography on the Martian poles. Icarus 34:581–599 CrossRefGoogle Scholar
  62. Hubbard BP, Sharp MJ, Willis IC, Nielsen MK, Smart CC (1995) Borehole water-level variations and the structure of the subglacial hydrological system of Haut Glacier d’Arolla, Valais, Switzerland. J Glaciol 41:572–583 Google Scholar
  63. Hughes TJ (1973) Is the West Antarctic ice sheet disintegrating? J Geophys Res 78:7884–7910 CrossRefGoogle Scholar
  64. Hutter K (1983) Theoretical glaciology. Reidel, Dordrecht Google Scholar
  65. Hutter K, Olunloyo VOS (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 MATHMathSciNetCrossRefGoogle Scholar
  66. Hutter K, Yakowitz S, Szidarovsky F (1986) A numerical study of plane ice sheet flow. J Glaciol 32:139–160 Google Scholar
  67. Iken A (1981) The effect of subglacial water pressure on the sliding velocity of a glacier in an idealized numerical model. J Glaciol 27:407–422 Google Scholar
  68. Imbrie J, Imbrie KP (1979) Ice ages; solving the mystery. Harvard University Press, Cambridge Google Scholar
  69. Innes R (1732) Miscellaneous letters on several subjects in philosophy and astronomy, I, p 4. S Birt, London Google Scholar
  70. Ivanov AB, Muhleman DO (2000) The role of sublimation for the formation of the Northern ice cap: results from the Mars Orbiter Laser Altimeter. Icarus 144:436–448 CrossRefGoogle Scholar
  71. Iverson NR, Baker RW, Hooyer TS (1997) A ring-shear device for the study of till deformation: tests on tills with contrasting clay contents. Quat Sci Rev 16(9):1057–1066 CrossRefGoogle Scholar
  72. Kamb B (1987) Glacier surge mechanism based on linked cavity configuration of the basal water conduit system. J Geophys Res 92:9083–9100 CrossRefGoogle Scholar
  73. Kamb B (1991) Rheological nonlinearity and flow instability in the deforming bed mechanism of ice stream motion. J Geophys Res 96(B10):16585–16595 CrossRefGoogle Scholar
  74. Kamb B, Raymond CF, Harrison WD, Engelhardt H, Echelmeyer KA, Humphrey N, Brugman MM, Pfeffer T (1985) Glacier surge mechanism: 1982–1983 surge of Variegated Glacier, Alaska. Science 227:469–479 CrossRefGoogle Scholar
  75. Kamb WB (1970) Sliding motion of glaciers: theory and observation. Rev Geophys Space Phys 8:673–728 CrossRefGoogle Scholar
  76. Kinahan GH, Close MH (1872) The general glaciation of Iar-Connaught and its neighbourhood, in the counties of Galway and Mayo. Hodges, Foster and Co, Dublin Google Scholar
  77. Kleman J, Hättestrand C (1999) Frozen-bed Fennoscandian and Laurentide ice sheets during the Last Glacial Maximum. Nature 402:63–66 CrossRefGoogle Scholar
  78. Li M, Richmond O (1997) Intrinsic instability and non-uniformity of plastic deformation. Int J Plast 13:765–784 MATHCrossRefGoogle Scholar
  79. Lighthill MJ, Whitham GB (1955a) On kinematic waves. I. Flood movement in long rivers. Proc R Soc Lond A 229:281–316 MATHMathSciNetCrossRefGoogle Scholar
  80. Lighthill MJ, Whitham GB (1955b) On kinematic waves. II. A theory of traffic flow on long, crowded roads. Proc R Soc Lond A 229:317–345 MATHMathSciNetCrossRefGoogle Scholar
  81. Lliboutry LA (1956) La mécanique des glaciers en particulier au voisinage de leur front. Ann Geophys 12:245–276 MathSciNetGoogle Scholar
  82. Lliboutry LA (1958a) La dynamique de la Mer de Glace et la vague de 1891–95 d’après les mésures de Joseph Vallot. In: Physics of the movement of ice (Chamonix symposium). IAHS publ, vol 47. IAHS Press, Wallingford, pp 125–138. Available to download at http://www.iahs.info/redbooks/047.htm Google Scholar
  83. Lliboutry LA (1958b) Glacier mechanics in the perfect plasticity theory. J Glaciol 3:162–169 Google Scholar
  84. Lliboutry LA (1964) Traité de glaciologie, vol I. Glace, neige, hydrologie nivale. Masson, Paris Google Scholar
  85. Lliboutry LA (1965) Traité de glaciologie, vol II. Glaciers, variations du climat, sols gelés. Masson, Paris Google Scholar
  86. Lliboutry LA (1968) General theory of subglacial cavitation and sliding of temperate glaciers. J Glaciol 7:21–58 Google Scholar
  87. Lliboutry LA (1979) Local friction laws for glaciers: a critical review and new openings. J Glaciol 23:67–95 Google Scholar
  88. Lliboutry LA (1987) Very slow flows of solids. Basics of modeling in geodynamics and glaciology. Martinus Nijhoff, Dordrecht MATHGoogle Scholar
  89. MacAyeal DR (1989) Large-scale ice flow over a viscous basal sediment. J Geophys Res 94:4071–4087 CrossRefGoogle Scholar
  90. MacAyeal DR (1993) Binge/purge oscillations of the Laurentide ice sheet as a cause of the North Atlantic’s Heinrich events. Paleoceanography 8:775–784 CrossRefGoogle Scholar
  91. Menzies J (1984) Drumlins: a bibliography. Geo Books, Norwich Google Scholar
  92. Moore PL, Iverson NR (2002) Slow episodic shear of granular materials regulated by dilatant strengthening. Geology 30:843–846 CrossRefGoogle Scholar
  93. Morland LW (1976a) Glacier sliding down an inclined wavy bed. J Glaciol 17:447–462 Google Scholar
  94. Morland LW (1976b) Glacier sliding down an inclined wavy bed with friction. J Glaciol 17:463–477 Google Scholar
  95. Morland LW (1984) Thermo-mechanical balances of ice sheet flow. Geophys Astrophys Fluid Dyn 29:237–266 MATHCrossRefGoogle Scholar
  96. Morland LW, Johnson IR (1980) Steady motion of ice sheets. J Glaciol 25:229–246 Google Scholar
  97. Morland LW, Shoemaker EM (1982) Ice shelf balances. Cold Reg Sci Technol 5:235–251 CrossRefGoogle Scholar
  98. Ng FSL, Zuber MT (2003) Albedo feedback in the patterning mechanisms of Martian polar caps. In: 3rd international conference on Mars polar science and exploration, abstract #8061, Lunar and Planetary Science Institute, Houston (CD-ROM) Google Scholar
  99. Ng FSL, Zuber MT (2006) Patterning instability on the Mars polar ice caps. J Geophys Res 111:E02005. doi: 10.1029/2005JE002533 CrossRefGoogle Scholar
  100. Nicolussi K (1990) Bilddokumente zur Geschichte des Vernagtferners im 17. Jahrhundert. Zeit Gletschkd Glazialgeol 26(2):97–119 Google Scholar
  101. Nienow P, Sharp M, Willis I (1998) Seasonal changes in the morphology of the subglacial drainage system, Haut Glacier d’Arolla. Switz Earth Surf Process Landf 23:825–843 CrossRefGoogle Scholar
  102. Nowicki SMJ, Wingham DJ (2008) Conditions for a steady ice sheet–ice shelf junction. Earth Planet Sci Lett 265:246–255 CrossRefGoogle Scholar
  103. Nye JF (1957) Glacier mechanics; comments on Professor L Lliboutry’s paper. J Glaciol 3:91–93 Google Scholar
  104. Nye JF (1958) Comments on Professor Lliboutry’s paper. J Glaciol 3:170–172 Google Scholar
  105. Nye JF (1959) The motion of ice sheets and glaciers. J Glaciol 3:493–507 Google Scholar
  106. Nye JF (1960) The response of glaciers and ice sheets to seasonal and climatic changes. Proc R Soc Lond A 256:559–584 MathSciNetCrossRefGoogle Scholar
  107. Nye JF (1963) The response of a glacier to changes in the rate of nourishment and wastage. Proc R Soc Lond A 275:87–112 MATHCrossRefGoogle Scholar
  108. Nye JF (1969) A calculation on the sliding of ice over a wavy surface using a Newtonian viscous approximation. Proc R Soc Lond A 311:445–477 CrossRefGoogle Scholar
  109. Nye JF (1970) Glacier sliding without cavitation in a linear viscous approximation. Proc R Soc Lond A 315:381–403 CrossRefGoogle Scholar
  110. Nye JF (1973) Water at the bed of a glacier. IASH Publ 95:189–194 Google Scholar
  111. Nye JF (1976) Water flow in glaciers: jökulhlaups, tunnels, and veins. J Glaciol 17:181–207 Google Scholar
  112. Paterson WSB (1994) The physics of glaciers, 3rd edn. Pergamon, Oxford Google Scholar
  113. Pattyn F, de Smedt B, Souchez R (2004) Influence of subglacial Vostok lake on the regional ice dynamics of the Antarctic ice sheet: a model study. J Glaciol 50:583–589 CrossRefGoogle Scholar
  114. Payne AJ, Dongelmans PW (1997) Self-organization in the thermomechanical flow of ice sheets. J Geophys Res 102:12219–12233 CrossRefGoogle Scholar
  115. Pelletier JD (2004) How do spiral troughs form on Mars? Geology 32(4):365–367 MathSciNetCrossRefGoogle Scholar
  116. Pelletier JD (2008) Quantitative modeling of Earth surface processes. Cambridge University Press, Cambridge MATHGoogle Scholar
  117. Rathbun AP, Marone C, Alley RB, Anandakrishnan S (2008) Laboratory study of the frictional rheology of sheared till. J Geophys Res 113:F02020. doi: 10.1029/2007JF000815 CrossRefGoogle Scholar
  118. Robin G de Q (1955) Ice movement and temperature distribution in glaciers and ice sheets. J Glaciol 2:523–532 CrossRefGoogle Scholar
  119. Röthlisberger H (1972) Water pressure in intra- and subglacial channels. J Glaciol 11:177–203 Google Scholar
  120. 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. doi: 10.1029/2007JB005228 CrossRefGoogle Scholar
  121. Schoof C (2005) The effect of cavitation on glacier sliding. Proc R Soc Lond A 461:609–627 MATHMathSciNetCrossRefGoogle Scholar
  122. Schoof C (2007a) Pressure-dependent viscosity and interfacial instability in coupled ice-sediment flow. J Fluid Mech 570:227–252 MATHMathSciNetCrossRefGoogle Scholar
  123. Schoof C (2007b) Marine ice-sheet dynamics. Part 1. The case of rapid sliding. J Fluid Mech 573:27–55 MATHMathSciNetCrossRefGoogle Scholar
  124. Schoof C (2007c) Ice sheet grounding line dynamics: steady states, stability and hysteresis. J Geophys Res 112:F03S28. doi: 10.1029/2006JF000664 CrossRefGoogle Scholar
  125. Schoof C, Hindmarsh RCA (2010) Thin-film flows with wall slip: an asymptotic analysis of higher order glacier flow models. Q J Mech Appl Math 63:73–114 MATHMathSciNetCrossRefGoogle Scholar
  126. Shaw J (1983) Drumlin formation related to inverted meltwater erosional marks. J Glaciol 29:461–479 Google Scholar
  127. Shaw J, Kvill D, Rains B (1989) Drumlins and catastrophic subglacial floods. Sediment Geol 62:177–202 CrossRefGoogle Scholar
  128. Shreve RL (1985) Esker characteristics in terms of glacier physics, Katahdin esker system, Maine. Geol Soc Amer Bull 96:639–646 CrossRefGoogle Scholar
  129. Sinclair, Sir John (ed) (1791–1799) The statistical account of Scotland: drawn up from the communications of the ministers of the different parishes, 21 vols. William Creech, Edinburgh Google Scholar
  130. Sugden DE, John BS (1976) Glaciers and landscape: a geomorphological approach. Edward Arnold, London Google Scholar
  131. Thomas RH (1979) The dynamics of marine ice sheets. J Glaciol 24:167–177 Google Scholar
  132. Tulaczyk SM, Kamb B, Engelhardt HF (2000) Basal mechanics of Ice Stream B, West Antarctica. I. Till mechanics. J Geophys Res 105(B1):463–481 CrossRefGoogle Scholar
  133. Van der Veen CJ (1999) Fundamentals of glacier dynamics. Balkema, Rotterdam Google Scholar
  134. Waddington ED (1986) Wave ogives. J Glaciol 32:325–334 Google Scholar
  135. Walder JS (1982) Stability of sheet flow of water beneath temperate glaciers and implications for glacier surging. J Glaciol 28:273–293 Google Scholar
  136. Walder JS (1986) Hydraulics of subglacial cavities. J Glaciol 32:439–446 Google Scholar
  137. Walder JS, Fowler A (1994) Channelised subglacial drainage over a deformable bed. J Glaciol 40:3–15 Google Scholar
  138. Walder J, Hallet B (1979) Geometry of former subglacial water channels and cavIties. J Glaciol 23:335–346 Google Scholar
  139. Walker G (2003) Snowball Earth: the story of the great global catastrophe that spawned life as we know it. Bloomsbury, London Google Scholar
  140. Warren WP, Ashley GM (1994) Origins of the ice-contact stratified ridges (eskers) of Ireland. J Sediment Res A 64:433–449 Google Scholar
  141. Weertman J (1957a) On the sliding of glaciers. J Glaciol 3:33–38 Google Scholar
  142. Weertman J (1957b) Deformation of floating ice shelves. J Glaciol 3:39–42 Google Scholar
  143. Weertman J (1958) Travelling waves on glaciers. In: IUGG symposium, Chamonix. Int assoc hydrol sci publ, vol 47, pp 162–168 Google Scholar
  144. Weertman J (1972) General theory of water flow at the base of a glacier or ice sheet. Rev Geophys Space Phys 10:287–333 CrossRefGoogle Scholar
  145. Weertman J (1974) Stability of the junction of an ice sheet and an ice shelf. J Glaciol 13:3–11 Google Scholar
  146. Weertman J (1979) The unsolved general glacier sliding problem. J Glaciol 23:97–115 Google Scholar
  147. Wilchinsky AV (2007) The effect of bottom boundary conditions in the ice-sheet to ice-shelf transition zone problem. J Glaciol 53:363–367 CrossRefGoogle Scholar
  148. Wilchinsky AV (2009) Linear stability analysis of an ice sheet interacting with the ocean. J Glaciol 55:13–20 CrossRefGoogle Scholar
  149. Wilchinsky AV, Chugunov VA (2000) Ice-stream–ice-shelf transition: theoretical analysis of two-dimensional flow. Ann Glaciol 30:153–162 CrossRefGoogle Scholar
  150. Wilchinsky AV, Chugunov VA (2001) Modelling ice flow in various glacier zones. J Appl Math Mech 65:479–493. In Russian: Prikl Mat Mekh 65:495–510 CrossRefGoogle Scholar
  151. Yuen DA, Schubert G (1979) The role of shear heating in the dynamics of large ice masses. J Glaciol 24:195–212 Google Scholar

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© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.MACSI, Department of Mathematics & StatisticsUniversity of LimerickLimerickIreland

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