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The influence of a poroelastic till on rapid subglacial flooding and cavity formation

Published online by Cambridge University Press:  24 September 2018

Duncan R. Hewitt Open the ORCID record for Duncan R. Hewitt [Opens in a new window] ,
Gregory P. Chini Open the ORCID record for Gregory P. Chini [Opens in a new window]  and
Jerome A. Neufeld
Duncan R. Hewitt*
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, CambridgeCB3 0WA, UK
Gregory P. Chini
Affiliation:
Department of Mechanical Engineering, Program in Integrated Applied Mathematics and Centre for Fluid Physics, University of New Hampshire, DurhamNH 03824, USA
Jerome A. Neufeld
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, CambridgeCB3 0WA, UK BP Institute, University of Cambridge, Madingley Rise, CambridgeCB3 0EZ, UK Department of Earth Sciences, Bullard Laboratories, University of Cambridge, Madingley Rise, CambridgeCB3 0EZ, UK
*
†Email address for correspondence: [email protected]
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Abstract

We develop a model of the rapid propagation of water at the contact between elastic glacial ice and a poroelastic subglacial till, motivated by observations of the rapid drainage of supraglacial lakes in Greenland. By treating the ice as an elastic bending beam, the fluid dynamics of contact with the subglacial hydrological network, which is modelled as a saturated poroelastic till, can be examined in detail. The model describes the formation and dynamics of an axisymmetric subglacial cavity, and the spread of pore pressure, in response to injection of fluid. A combination of numerical simulation and asymptotic analysis is used to describe these dynamics for both a rigid and a deformable porous till, and for both laminar and turbulent fluid flow. For constant injection rates and laminar flow, the cavity is isostatic and its spread is controlled by bending of the ice and suction of pore water in the vicinity of the ice–till contact. For a deformable till, this control can be modified: generically, a flexural wave that is initially trapped in advance of the contact point relaxes over time by diffusion of pore pressure ahead of the cavity. While the dynamics are found to be relatively insensitive to the properties of the subglacial till during injection with a constant flux, significant dependence on the till properties is manifest during the subsequent spread of a constant volume. A simple hybrid turbulent–laminar model is presented to account for fast injection rates of water: in this case, self-similar turbulent propagation can initially control the spread of the cavity, but there is a transition to laminar control in the vicinity of the ice–till contact point as the flow slows. Finally, the model results are compared with recent geophysical observations of the rapid drainage of supraglacial lakes in Greenland; the comparison provides qualitative agreement and raises suggestions for future quantitative comparison.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Ice sheets Low-Reynolds-number flows: Porous media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 855 , 25 November 2018 , pp. 1170 - 1207
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Copyright
© 2018 Cambridge University Press 

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