Thermoviscous localisation of volcanic eruptions is enhanced by variations in fissure width

Volcanic 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. Localisation is important because it influences the spatiotemporal evolution of the hazard posed by the eruption. Previous work has proposed that localisation can arise through a thermoviscous fingering instability driven by the strongly temperature dependent viscosity of the rising magma. Here, we explore how thermoviscous localisation is influenced by the irregular geometry of natural volcanic fissures. We model the pressure driven flow of a viscous fluid with temperature dependent viscosity through a narrow fissure with either sinusoidal or randomised deviations from a uniform width. We identify steady states, determine their stability, and quantify the degree of flow enhancement associated with localised flow. We find that, even for relatively modest variations of the fissure width (<10%), the 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 differs from the spontaneous thermoviscous fingering observed in planar geometries and can strongly impact the localisation process. We delineate the regions of parameter space under which geometrically-driven localisation is significant, showing that it is a viable mechanism for the observed localisation under conditions typical of basaltic eruptions, and that it has the potential to dominate the effects of spontaneous thermoviscous fingering in these cases.