In this talk, I will present two volcanologically motivated modelling problems. In the first, I will detail how thermoviscous localisation of volcanic eruptions is influenced by the irregular geometry of natural volcanic fissures. Fissure eruptions typically start with the opening of a linear fissure that erupts along its entire length, following which activity localises to one or more isolated vents within a few hours or days. Previous work has proposed that localisation can arise through a thermoviscous fingering instability driven by the strongly temperature dependent viscosity of the rising magma. I will show that, even for relatively modest variations of the fissure width, a non-planar geometry supports strongly localised steady states, in which the wider parts of the fissure host faster, hotter flow, and the narrower parts of the fissure host slower, cooler flow. This geometrically-driven localisation is different from, and typically more potent than, the thermoviscous fingering localisation observed in planar geometries.

The second problem concerns lava delta formation. A lava delta arises when a volcanic lava flow enters a body of water, extending the pre-eruption shoreline via the creation of new, flat land. A combination of cooling induced rheological changes and the reduction in gravitational driving forces controls the morphology and evolution of the delta. I will present shallow-layer continuum models for this process, highlighting how different modes of delta formation manifest in different late-time behaviours.