Developing mathematical models to incorporate microstructural heterogeneities into viscous flow

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Ice and rocks flow viscously as complex non-Newtonian fluids. Current models commonly neglect several key rheological effects introduced by the heterogeneity of the materials' (micro)structure. The incorporation of these complex features into viscous fluid dynamics presents exciting research opportunities, to be addressed in this PhD project. An example concerns our ability to predict the rate of collapse of the Earth's ice sheets, which depends centrally on the dependence of ice rheology on the heterogeneities of its microstructure. Another is the movement of tectonic plates, which controls the occurrence and severity of earthquakes. Simulations in solid-Earth viscous flows typically apply isotropic models that are insufficient to describe leading-order characteristics of ice and rock flow dynamics because of the presence of microstructural heterogeneities: complexities at a small scale due to the presentence of differing material types (e.g. layering) and polycrystal arrangement (crystal grains, each oriented/slipping in different directions). This project presents an opportunity to address key open questions needed to close this gap in fluid-mechanical modelling of environmental systems. The effects of polycrystalline arrangement involves coupling a statistical representation of the material's microstructure with viscous anisotropy. The evolution of layers involves the analysis of the folding and necking instabilities associated with elastic and viscous beams separated by interstitial fluid of different material properties. The project thus presents a variety of directions, and the specific focus will be primarily mathematical, but otherwise tailored to the interests of the student.