Volcanic fissure localisation: Thermoviscous focussing in non-uniform geometries

Volcanic fissure eruptions, which occur when a magma-filled crack intersects the surface, typically evolve from a continuous curtain of lava to one or more point-source lava fountains at distinct vents. One proposed mechanism for localisation is via a thermoviscous fingering instability, in which hot, low-viscosity magma forms finger-like preferential pathways through cooler, higher-viscosity magma, analogously to the classical Saffman-Taylor instability. Previous work has considered the flow of hot fluid driven by an imposed pressure drop through a planar fissure with walls held at a constant, colder temperature.

These results have demonstrated non-uniqueness of steady-state solutions, and explored the instability of solutions to non-planar perturbations. In this talk I will extend these results to non-uniform fissure width, as is often the case for real-world volcanic fissures. I will show how the inclusion of a sinusoidal perturbation modifies the bifurcation diagram of the system and the conditions for instability, in particular resulting in a stable flow-focussed solution branch on which the system exhibits significant flow localisation above the critical pressure drop for the onset of the thermoviscous fingering instability. I will further consider the behaviour of a rough fissure geometry containing a spectrum of Fourier modes, discussing the implications for the localisation behaviour of volcanic fissure eruptions.