Mathematical modelling of lava flows undergoing rheological evolution

Lava flows are the most common product of volcanic eruptions and pose a substantial hazard to property and infrastructure; as such, predicting the path of lava flows is a major goal in volcanological hazard management. Furthermore, volcanic lava flows can act as a "laboratory" for exploring how to include cooling and phase changes in the modelling of wide-ranging industrial fluid flows that also exhibit evolution of rheology (the manner in which a material deforms under imposed stress). Recent high-profile eruptions in Hawaii (2020-2021), Iceland (2021), and the Canary Islands (2021) have reinvigorated public interest in these flows, and have also provided significant quantities of data for the motivation and validation of fluid dynamical models, both in the form of research field data and in amateur videography. Prediction of lava emplacement requires fluid dynamic models that account for rheological changes during flow, particularly the progressive formation of a cooled crust. This project will achieve a transformation in our capacity to model lava flow emplacement through the modelling of three complex flow behaviours exhibited by volcanic lava flows: the intermittent emplacement of a Pahoehoe style lava flow in which successive toes inflate, stagnate and rupture to produce new toes; the formation of solidified levees at the boundaries of lava flows, resulting in self-channelisation and an enhanced supply of molten lava to the flow front; and transitions between ropy, consistent crust and rubbly, fragmented crust formation. The proposed project will use a mixture of novel asymptotic, numerical and experimental methods to model these enigmatic phenomena, using my own expertise in viscoplastic and shallow-layer flows and the support of a network of experts in non-Newtonian fluid dynamics and volcanology from the UK and abroad. The outcome of this work will be improved modelling of flows undergoing rheological evolution which will allow for improved prediction of lava flow paths and more efficient production processes in industries that involve cooling viscoplastic flows, including food processing and 3D printing.