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Title: Glacier dynamics
Author: Fowler, A. C.
ISNI:       0000 0001 2409 8450
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 1977
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A model is proposed for the study of general two-dimensional 'polythermal' glacial ice flows. It consists of equations of conservation of mass, momentum and energy together with a constitutive relation between stress and strain rate and a full set of boundary conditions. A novel aspect is the consideration of the moisture content of temperate ice as an enthalpy variable: this represents a first attempt at incorporating the glacial hydrology in a dynamical model. One of the bedrock boundary conditions requires a knowledge of the so-called 'sliding law' relating the basal shear stress to the basal velocity (when the ice is temperate). A detailed model is proposed to determine this law, and upper and lower bounds for the basal velocity in terms of the stress are given by using a variational principle. The effect of cavitation on the sliding law is considered in the case of Newtonian flow, and it is shown to have a dramatic effect on the basal sliding. We then turn to our analysis of the glacier flow model. Firstly we consider kinematic waves: an analogue of Nye's (1960) equation is derived and analysed from a nonlinear viewpoint. The formation and evolution of surface shocks is studied, and explicit results given for small perturbations to the surface profile. Secondly, we show how the modal may be used to predict a finite slope at the glacier snout by use of the method of strained coordinates. Finally, steady state solutions are examined in the cases of large and small conduction. We demonstrate that there generally exists a large patch of basal ice which is almost temperate, but which slides at a velocity lower than that predicted by the sliding law: this is probably the most important result of the present work.
Supervisor: Tayler, A. B. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available