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Mathematical modelling of subglacial drainage and erosion

By F. S. L. Ng


The classical theory of channelized subglacial drainage,due orginally to Röthlisberger (1972) and Nye (1976), considers water flow in an ice channel overlying a rigid, impermeable bed. At steady flow, creep closure of the channel walls is counteracted by melt-back due to heat dissipation, and this leads to an equilibrium relation between channel water pressure and discharge. More generally, such a balance exhibits an instability that can be used to describe the mechanics of catastrophic flood events known as `jökulhlaups'. In this thesis, we substantiate these developments by exploring a detailed model where the channel is underlain by subglacial till and the flow supports a sediment load. Attention is given to the physics of bed processes and its effect on channel morphology. In particular, we propose a theory in which the channel need not be semi-circular, but has independently evolving depth and width determined by a local balance between melting and closure, and in which sediment erosion and deposition is taken into account. The corresponding equilibrium relation indicates a reverse dependence to that in the classical model, justifying the possibility of the subglacial canals envisaged by Walder and Fowler (1994). Theoretical predictions for sediment discharge are also derived. Regarding time-dependent flood drainage, we demonstrate how rapid channel widening caused by bank erosion can explain the abrupt recession observed in the flood hydrographs. This allows us to produce an improved simulation of the 1972 jökulhlaup from Grímsvötn, Iceland, and self-consistently, a plausible estimate for the total sediment yield. We also propose a mechanism for the observed flood initiation lake-level at Grímsvötn. These investigations expose the intimate interactions between drainage and sediment transport, which have profound implications on the hydrology, sedimentology and dynamics of ice masses, but which have received little attention

Topics: Geophysics, Partial differential equations, Approximations and expansions, Fluid mechanics
Year: 1998
OAI identifier:

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  1. (1969). A calculation on the sliding of ice over a wavy surface using a Newtonian viscous approximation.
  2. (1996). A conceptually based model of the interaction between flowing meltwater and subglacial sediment.
  3. (1985). A history of jo¨kulhlaups from Strandline Lake,
  4. (1994). A new vectorial bedload formulation and its application to the time evolution of straight river channels.
  5. (1986). A sliding law for glaciers of constant viscosity in the presence of subglacial cavitation.
  6. (1987). A subglacial aquifer bed model and water pressure dependent basal sliding relationship for a West Antarctic ice stream.
  7. (1965). An investigation of the elastic strip and the annulus. doi
  8. (1936). Anwendung der Aehnlichkeitsmechanik und der turbulenzforschung auf die geschiebebewegung.
  9. (1997). Basal hydraulic system of a West Antarctic ice stream: constraints from borehole observations.
  10. (1981). Basal stress concentrations due to abrupt changes in boundary conditions: a cause for high till concentration at the bottom of a glacier.
  11. (1993). Binge/purge oscillations of the Laurentide Ice Sheet as a cause of the North Atlantic’s Heinrich events.
  12. (1960). Boundary Layer Theory.
  13. (1983). Calculation of fully developed turbulent flows in ducts of arbitrary cross-section.
  14. (1997). Center of the Iceland hotspot experiences volcanic unrest.
  15. (1994). Channelized subglacial drainage over a deformable bed.
  16. (1980). Comparison of sediment load transport
  17. (1971). Complex Variable Methods in Elasticity. Wiley–Interscience,
  18. (1981). Conduit flow of a fluid through its solid phase and its application to intraglacial channel flow.
  19. (1993). Creep closure of channels in deforming subglacial till.
  20. (1982). Dynamics of glaciers and large ice masses.
  21. Dynamics of the West Antarctic Ice Sheet,
  22. (1974). Erosion by catastrophic floods on Mars and on Earth.
  23. (1974). Explanation of jo¨kulhlaups from
  24. (1988). Flood Geomorphology.
  25. (1995). Flow mechanism of glaciers on soft beds.
  26. (1984). Flow, thermal structure, and subglacial conditions of a surge-type glacier.
  27. (1948). Formulas for bed-load transport.
  28. (1951). Fourier Transforms.
  29. (1983). Functions of a Complex Variable. Hod Books, doi
  30. (1972). General theory of water flow at the base of a glacier or ice sheet. doi
  31. (1993). Geometry, bed topography and drainage system structure of the Haut Glacier d’Arolla,
  32. (1986). Glacial Geologic Processes.
  33. (1971). Glacier dammed lakes and outburst floods in Alaska.
  34. (1982). Glacier outburst floods from ‘Hazard Lake’, Yukon Territory, and the problem of flood magnitude prediction. doi
  35. (1970). Glacier sliding without cavitation in a linear viscous approximation.
  36. (1987). Glacier surge mechanism based on linked cavity configuration of the basal water conduit system.
  37. (1930). Heat transfer in automobile radiators of the tubular type.
  38. (1947). Heat transfer to molten metals.
  39. (1992). How can low-pressure channels and deforming tills coexist subglacially?
  40. (1995). Hydraulic run-away: a mechanism for thermally regulated surges of ice sheets.
  41. (1986). Hydraulics of subglacial cavities.
  42. (1988). Hydrology of ice caps in volcanic regions. V´ısindafe´lag I´sl.
  43. (1996). Ice sheet surging and ice stream formation.
  44. (1997). Iceland’s trial by fire. National Geographic,
  45. (1957). Integral Equations. Interscience,
  46. (1992). Jo¨kulhlaups in Iceland: prediction, characteristics and simulation.
  47. (1979). Local friction laws for glaciers: a critical review and new openings.
  48. (1997). Mathematical Models in the Applied Sciences.
  49. (1989). Mechanics of Fluids, 6th edition.
  50. (1972). Movement of water in glaciers.
  51. (1974). Numerical Solution of Integral Equations.
  52. (1981). Numerical studies of jo¨kulhlaups.
  53. (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.
  54. (1986). On the mechanics of surging glaciers.
  55. (1957). On the sliding of glaciers. doi
  56. (1996). Outburst floods from glacier-dammed lakes: the effect of mode of lake drainage on flood magnitude. doi
  57. (1988). Partial Differential Equations, 2nd edition.
  58. (1982). Rivers: Form and Process in Alluvial Channels.
  59. (1987). Sediment deformation beneath glaciers: rheology and geological consequences. doi
  60. (1972). Sedimentation. In
  61. (1989). Sedimentology and paleohydrology of Holocene flood deposits in front of a jo¨kulhlaup glacier, Southern Iceland.
  62. (1989). Sedimentology, paleoflow dynamics and flood history of jo¨kulhlaup deposits: paleohydrology of Holocene sediment sequences in Southern Iceland sandur deposits.
  63. (1978). Self-formed straight rivers with equilibrium banks and mobile bed. Part 1. The sand–silt river.
  64. (1953). Singular Integral Equations, translated by
  65. (1955). Skeiðara´rhlaup
  66. (1970). Sliding motion of glaciers: theory and observation.
  67. (1987). Sliding with cavity formation.
  68. (1982). Stability of sheet flow of water beneath temperate glaciers and implications for glacier surging.
  69. (1986). Subglacial hydrology for an ice sheet resting on a deformable aquifer.
  70. (1974). Subglacial shearing and crushing, and the roˆle of water pressures in tills from south-east Iceland. doi
  71. (1987). Subglacial till: a physical framework for its properties and processes. doi
  72. (1990). Subglacial water pressures and the shape of subglacial conduits.
  73. (1980). Table of Integrals, Series and Products, 2nd edition.
  74. (1923). The channeled scablands of the Columbia Plateau. doi
  75. (1981). The effect of the subglacial water pressure on the sliding velocity of a glacier in an idealized numerical model.
  76. (1953). The flow law of ice from measurements in glacier tunnels, laboratory experiments and the Jungfraufirn borehole experiment.
  77. (1956). The flow of cohesionless grains in fluids.
  78. (1969). The Lake Missoula floods and the channeled scabland. doi
  79. (1973). The magnitude of jo¨kulhlaups.
  80. (1981). The nature of piping soils: a review of research.
  81. (1994). The Physics of Glaciers, 3rd edition. Pergamon,
  82. (1964). The production and diffusion of vorticity in duct flow. doi
  83. (1996). The roˆle of sediment transport in the mechanics of jo¨kulhlaups.
  84. (1978). The Spokane Flood controversy and the Martian outflow channels.
  85. (1987). Till deformation: evidence and implications.
  86. (1974). Vo¨tnin str´ıdh. Reykjav´ık, Bo´kau´tga´fa Menningarsjo´ds.
  87. (1982). Waiting-time’ solutions of a non-linear diffusion equation.
  88. (1976). Water flow in glaciers: jo¨kulhlaups, tunnels and veins.
  89. (1972). Water pressure in intra- and subglacial channels.
  90. (1989). Water-pressure coupling of sliding and bed deformation: 1. Water system.

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