Thermodynamics and fluid dynamics of effusive subglacial eruptions

We consider the thermodynamic and fluid dynamic processes that occur during subglacial effusive eruptions. Subglacial eruptions typically generate catastrophic floods (jökulhlaups) due to melting of ice by lava and generation of a large water cavity. We consider the heat transfer from basaltic and rhyolitic lava eruptions to the ice for typical ranges of magma discharge and geometry of subglacial lavas in Iceland. Our analysis shows that the heat flux out of cooling lava is large enough to sustain vigorous natural convection in the surrounding meltwater. In subglacial eruptions the temperature difference driving convection is in the range 10–100??°C. Average temperature of the meltwater must exceed 4??°C and is usually substantially greater. We calculate melting rates of the walls of the ice cavity in the range 1–40?m/day, indicating that large subglacial lakes can form rapidly as observed in the 1918 eruption of Katla and the 1996 eruption of Gjálp fissure in Vatnajökull. The volume changes associated with subglacial eruptions can cause large pressure changes in the developing ice cavity. These pressure changes can be much larger than those associated with variation of bedrock and glacier surface topography. Previous models of water-cavity stability based on hydrostatic and equilibrium conditions may not be applicable to water cavities produced rapidly in volcanic eruptions. Energy released by cooling of basaltic lava at the temperature of 1200??°C results in a volume deficiency due to volume difference between ice and water, provided that heat exchange efficiency is greater than approximately 80%. A negative pressure change inhibits escape of water, allowing large cavities to build up. Rhyolitic eruptions and basaltic eruptions, with less than approximately 80% heat exchange efficiency, cause positive pressure changes promoting continual escape of meltwater. The pressure changes in the water cavity can cause surface deformation of the ice. Laboratory experiments were carried out to investigate the development of a water cavity by melting ice from a finite source area at its base. The results confirm that the water cavity develops by convective heat transfer.