Hostname: page-component-76fb5796d-vvkck Total loading time: 0 Render date: 2024-04-26T04:01:17.424Z Has data issue: false hasContentIssue false
  • English
  • Français

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: drh39@cam.ac.uk
Get access Rights & Permissions [Opens in a new window]

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
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adhikari, S. & Tsai, V. C. 2015 A model for subglacial flooding through a preexisting hydrological network during the rapid drainage of supraglacial lakes. J. Geophys. Res. 120, 580–603.Google Scholar
Beavers, G. S. & Joseph, D. D. 1967 Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197–207.Google Scholar
Clarke, G. K. C. 2005 Subglacial processes. Annu. Rev. Earth Planet. Sci. 33, 247–276.Google Scholar
Das, S. B., Joughin, I., Behn, M. D., Howat, I. M., King, M. A., Lizarralde, D. & Bhatia, M. P. 2008 Fracture propagation to the base of the Greenland ice sheet during supraglacial lake drainage. Science 320 (5877), 778–781.Google Scholar
Dontsov, E. V. 2016 Tip region of a hydraulic fracture driven by a laminar-to-turbulent fluid flow. J. Fluid Mech. 797, R2.Google Scholar
Dow, C. F., Kulessa, B., Rutt, I. C., Tsai, V. C., Pimentel, S., Doyle, S. H., van As, D., Lindback, K., Pettersson, R., Jones, G. A. & Hubbard, A. 2015 Modeling of subglacial hydrological development following rapid supraglacial lake drainage. J. Geophys. Res. 120 (6), 1127–1147.Google Scholar
Fischer, U. H., Iverson, N. R., Hanson, B., Hooke, R. LeB. & Jansson, P. 1998 Estimation of hydraulic properties of subglacial till from ploughmeter measurements. J. Glac. 44 (148), 517–522.Google Scholar
Hewitt, D. R., Neufeld, J. A. & Balmforth, N. J. 2015a Shallow, gravity-driven flow in a poro-elastic layer. J. Fluid Mech. 778, 335–360.Google Scholar
Hewitt, I. J., Balmforth, N. J. & De Bruyn, J. R. 2015b Elastic-plated gravity currents. Eur. J. Appl. Maths 26, 1–31.Google Scholar
Huppert, H. E. 1982 The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface. J. Fluid Mech. 121, 43–58.Google Scholar
Krawczynski, M. J., Behn, M. D., Das, S. B. & Joughin, I. 2009 Constraints on the lake volume required for hydro-fracture through ice sheets. Geophys. Res. Lett. 36, 10501.Google Scholar
Larour, E., Seroussi, H., Morlighem, M. & Rignot, E. 2012 Continental scale, high order, high spatial resolution, ice sheet modeling using the Ice Sheet System Model (ISSM). J. Geophys. Res. 117, F01022.Google Scholar
Le Bars, M. & Worster, M. G. 2006 Interfacial conditions between a pure fluid and a porous medium: implications for binary alloy solidification. J. Fluid Mech. 550, 149–173.Google Scholar
Lister, J. R., Peng, G.G. & Neufeld, J. A. 2013 Viscous control of peeling an elastic sheet by bending and pulling. Phys. Rev. Lett. 111, 154501.Google Scholar
Peng, G. G., Pihler-Puzovic, D., Juel, A. & Heil, M. 2015 Displacement flows under elastic membranes. Part 2. Analysis of interfacial effects. J. Fluid Mech. 784, 512–547.Google Scholar
Pihler-Puzovic, D., Juel, A. & Heil, M. 2014 The interaction between viscous fingering and wrinkling in elastic-walled Hele-Shaw cells. Phys. Fluids 26, 022102.Google Scholar
Pimentel, S. & Flowers, G. E. 2011 A numerical study of hydrologically driven glacier dynamics and subglacial flooding. Proc. R. Soc. Lond. A 467, 537–558.Google Scholar
Rice, J. R., Tsai, V. C., Fernandes, M. C. & Platt, J. D. 2015 Time scale for rapid drainage of a surficial lake into the Greenland ice sheet. Trans. ASME J. Appl. Mech. 82, 071001.Google Scholar
Rignot, E., Mouginot, J. & Scheuchl, B. 2011 Ice flow of the Antarctic ice sheet. Science 333, 1427–1430.Google Scholar
Rubin, S., Tulchinsky, A., Gat, A. D. & Bercovici, M. 2017 Elastic deformations driven by non-uniform lubrication flows. J. Fluid Mech. 812, 841–865.Google Scholar
Schoof, C. & Hewitt, I. 2013 Ice-sheet dynamics. Ann. Rev. Fluid Mech. 45 (1), 217–239.Google Scholar
Sergienko, O. V., Creyts, T. T. & Hindmarsh, R. C. A. 2014 Similarity of organized patterns in driving and basal stresses of Antarctic and Greenland ice sheets beneath extensive areas of basal sliding. Geophys. Res. Lett. 41, 3925–3932.Google Scholar
Sergienko, O. V. & Hindmarsh, R. C. A. 2013 Regular patterns in frictional resistance of ice-stream beds seen by surface data inversion. Science 342, 1086–1089.Google Scholar
Stevens, L. A., Behn, M. D., Das, S. B., I., Joughin, Noel, B. P. Y., van den Broeke, M. R. & Herring, T. 2016 Greenland Ice Sheet flow response to runoff variability. Geophys. Res. Lett. 43, 11295–11303.Google Scholar
Stevens, L. A., Behn, M. D., McGuire, J. J., Das, S. B., Joughin, I., Herring, T., Shean, D. E. & King, M. A. 2015 Greenland supraglacial lake drainages triggered by hydrologically induced basal slip. Nature 522, 73–76.Google Scholar
Thorey, C. & Michaut, C. 2016 Elastic-plated gravity currents with a temperature-dependent viscosity. J. Fluid Mech. 805, 88–117.Google Scholar
Tsai, V. C. & Rice, J. R. 2010 A model for turbulent hydraulic fracture and application to crack propagation at glacier beds. J. Geophys. Res. 115 (F3), F03007.Google Scholar
Tsai, V. C. & Rice, J. R. 2012 Modeling turbulent hydraulic fracture near a free surface. Trans. ASME J. Appl. Mech. 79, 031003.Google Scholar
Vaughan, D. G. 1995 Tidal flexure at ice shelf margins. J. Geophys. Res. 100, 6213–6224.Google Scholar
Wang, H. F. 2000 Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology. Princeton University Press.Google Scholar
Wang, Z.-Q. & Detournay, E. 2018 The tip region of a near-surface hydraulic fracture. J. Appl. Mech. 85, 041010.Google Scholar