Modelling Surtseyan Ejecta

Eruptions through crater lakes or shallow sea water, known as Subaqueous or Surtseyan eruptions, are some of the most dangerous eruptions in the world. These eruptions can cause tsunamis, lahars and base surges, but the phenomenon of interest to this research is that of the Surtseyan ejecta. Surtseyan ejecta are balls of highly viscous magma containing entrained material. They occur when a slurry of previously erupted material and water washes back into the volcanic vent. This slurry is incorporated into the magma and ejected from the volcano inside a ball of lava. The large variation in temperature between the slurry and the lava causes the water in the slurry to vaporise. This results in a pressure build-up which is released by vapour either escaping through the pores of the lava or the ejectum exploding. The volcanological question of interest is under what conditions these ejecta rupture. During this thesis the aim is to improve on the existing highly simplified model of partial differential equations that describe the transient changes in temperature and pressure in Surtseyan ejecta. This is achieved by returning to the basics and developing a model that is more soundly based on the physics and mathematics of Surtseyan ejecta behaviour. This model is developed through the systemic reduction of the coupled nonlinear partial differential equations that arise from the mass, momentum and energy conservation equations to form a fully coupled model for the behaviour of Surtseyan ejecta. The fully coupled model has been solved numerically as well as reduced further to produce analytical solutions for temperature and pressure. The numerical solutions show a boundary layer of rapidly varying temperatures and pressures around the steam generation boundary. This allows for a boundary layer analysis to be used in both the magma and the inclusion to estimate the temperature profile at early times. The numerical solution also showed a rapid increase in pressure at the flash front that allowed for a quasi steady state approximation in pressure to be used to form a reduced model that could be analytically solved. This produced an updated criterion for rupture and a criterion for the lower limit of permeability. The analytical and numerical results were then compared to the data from existing intact ejecta for verification.