Water Flow in Glaciers: Jökulhlaups, Tunnels and Veins

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Abstract
The physics of water flow within and under glacier ice is examined with special reference to the periodic catastrophic outbursts of water (jökulhlaups) from the subglacial lake Grímsvötn, Vatnajökull, Iceland. The lake is sealed until it reaches a critical level which enables it to lift the glacier, helped by a hydrostatic cantilever effect. The differential equations for non-steady water flow in a subglacial tunnel are derived and applied to the 1972 Grímsvötn outburst. The discharge: time relation observed during the growth stage, and the abrupt ending of the flood, are both very well accounted for by a theory which is insensitive to the details of the subglacial tunnel system. The steady state, in which an intergranular vein or tunnel is simultaneously melted open by frictional heat and closed by plastic deformation, may be stable or unstable according to the conditions imposed at the ends. This explains why the flow of water in a vein does not normally increase unstably as in a jökulhlaup. An ice-dammed lake does not drain away through the vein system because the driving force on the vein-water is towards the lake rather than away from it.

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