Skip to main content

Developing mathematical models to incorporate microstructural heterogeneities into viscous flow

Academic lead
Sam Pegler, Maths
Sandra Piazolo, Earth and Environment, Oliver Harlen, Maths
Project themes
Environmental Flows, Geophysical and Astrophysical Flows, Underpinning Methods for Fluid Dynamics

This project will address fundamental aspects of viscous flow arising from the evolution of a complex microstructure in the material, eventually informing efforts to predict the evolution of the Earth’s ice sheets in a changing climate, and the effects of the Earths’ interior which governs the movement of tectonic plates, each problems of considerable societal importance. For example, our ability to predict future sea-level rise is at present limited by our ability to model the evolution of ice microstructure and couple it with flow, which is necessary to predict the rate at which Earth’s ice sheets flow into the ocean, a contribution likely to dominate sea-level rise over the next century and beyond. Ice and rock flow viscously (like honey) as complex non-Newtonian fluids. However, their simulation typically assumes an isotropic rheology that neglects a host of effects caused by small-scale heterogeneities in the material’s structure. These complexities arise at the microscale from crystal orientations and/or internal layering. The result is to introduce viscosity variations spanning orders of magnitude as well as an inherent viscous anisotropy (a dependence of fluid mechanical stresses on flow direction) that requires modelling the internal crystal structure of the material. The way this coupling is performed presents an exciting mathematical challenge and would lead to significant developments in how ice and rock are modelled. The key question of the rate at which ice flows into the ocean from Antarctica, for example, is inherently dependent on addressing this problem. 

The project will explore new research directions focusing on the development of heterogeneities and their effects on large-scale flow. The project is flexible, but the central focus will be the development and analysis of new mathematical models using a combination of analytical, asymptotic, and numerical approaches. It is likely to be of particular interest to students with an interest in mathematical analysis, low-Reynolds number fluid dynamics, non-Newtonian fluid dynamics, and applications to environmental dynamics with high societal impact.