Fannon_2020_Mathematical.pdf (23.3 MB)
Mathematical modelling of subglacial bedform formation and dense granular flows
thesisposted on 2023-01-30, 09:29 authored by James S. Fannon
Subglacial bedforms,which include drumlins,ribbed moraine,and mega scale glacial lineations, are ubiquitous features in regions which were once covered by ice sheets, and their genesis is a long-standing and controversial problem in geophysics. In the ﬁrst part of this thesis, a mathematical model for subglacial bedform formation is rigorously derived, which describes the coupled ﬂow of ice, subglacial water, and sediment. We perform a linear stability analysis of the model and demonstrate that it can plausibly account for the formation of self-organised subglacial bedforms. We outline a novel numerical method to solve the model which is capable of providing three-dimensional simulations of the subglacial system for a restricted range of model parameters. The ﬂow of granular material is a common occurrence in our everyday lives and understanding its behaviour is of critical importance for several industrial and geophysical applications. In part two of this thesis, we outline a popular local rheology for dense granular ﬂows and present a recent compressible generalisation of this rheology. By using various analytical, asymptotic, and numerical techniques, we apply the model to two non-trivial ﬂow phenomena; free-surface instability for inclined plane ﬂows and spontaneous oscillations in plane shear ﬂows, and compare model results to existing experimental and numerical data.
- Faculty of Science and Engineering
First supervisorFowler, Andrew C.
Second supervisorMoyles, Iain R.
Department or School
- Mathematics & Statistics