Hostname: page-component-77c89778f8-cnmwb Total loading time: 0 Render date: 2024-07-18T06:30:10.305Z Has data issue: false hasContentIssue false
  • English
  • Français

An experimental and theoretical study of the dynamics of grounding lines

Published online by Cambridge University Press:  01 July 2013

Samuel S. Pegler  and
M. Grae Worster
Samuel S. Pegler*
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, Wilberforce Road, Cambridge CB3 0WA, UK
M. Grae Worster
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: ssp23@cam.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

We present an experimental and theoretical study of a thin, viscous fluid layer that flows radially under gravity from a point source into a denser inviscid fluid layer of uniform depth above a rigid horizontal surface. Near the source, the viscous layer lies in full contact with the surface, forming a vertical-shear-dominated viscous gravity current. At a certain distance from the source, the layer detaches from the surface to form a floating current whose dynamics are controlled by the viscous stresses due to longitudinal extension. We describe the dynamics of the grounded and floating components using distinct thin-layer theories. Separating the grounded and floating regions is the freely moving line of detachment, or grounding line, whose evolution we model by balancing the horizontal forces between the two regions. Using numerical and asymptotic analysis, we calculate the evolution of the system from a self-similar form at early times towards a steady state at late times. We use our solutions to illustrate how three-dimensional stresses within marine ice sheets, such as that of West Antarctica, can lead to stabilization of the grounding line. To assess the validity of the assumptions underlying our model, we compare its predictions with data from a series of laboratory experiments.

JFM classification

Geophysical and Geological Flows: Ice sheets Interfacial Flows (free surface): Interfacial Flows (free surface) Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 728 , 10 August 2013 , pp. 5 - 28
Copyright
©2013 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

Alley, R. B. & Bindschadler, R. A. 2001 The West Antarctic Ice Sheet: Behavior and Environment, Antarct. Res. Ser., vol. 77.Google Scholar
Bamber, J. L., Riva, R. E. M., Vermeersen, B. L. A. & LeBrocq, A. M. 2009 Reassessment of the potential sea-level rise from a collapse of the West Antarctic Ice Sheet. Science 324 (5929), 901–903.Google Scholar
DiPietro, N. D. & Cox, R. G. 1979 The spreading of a very viscous liquid on a quiescent water surface. Q. J. Mech. Appl. Maths 32, 355–381.Google Scholar
Fowler, A. C. & Larson, D. A. 1978 On the flow of polythermal glaciers. I. Model and preliminary analysis. Proc. R. Soc. Lond. A 363, 217–242.Google Scholar
Howell, P. D. 1996 Models for thin viscous sheets. Eur. J. Appl. Maths 7, 321–343.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
MacAyeal, D. R. 1989 Large-scale ice flow over a viscous basal sediment: theory and application to ice stream B, Antarctica. J. Geophys. Res. 94, 4071–4087.Google Scholar
Nowicki, S. M. J. & Wingham, D. J. 2008 Conditions for a steady ice sheet–ice shelf junction. Earth Planet Sci. Lett. 265, 246–255.Google Scholar
Paterson, W. S. B. 1994 The Physics of Glaciers, 3rd edn. Pergamon.Google Scholar
Pegler, S. S. 2012 The fluid mechanics of ice-shelf buttressing. PhD thesis, University of Cambridge.Google Scholar
Pegler, S. S., Kowal, K. N., Hasenclever, L. Q. & Worster, M. G. 2013 Lateral controls on grounding-line dynamics. J. Fluid Mech. 722, R1.Google Scholar
Pegler, S. S., Lister, J. R. & Worster, M. G. 2012 Release of a viscous power-law fluid over a denser inviscid ocean. J. Fluid Mech. 700, 63–76.Google Scholar
Pegler, S. S. & Worster, M. G. 2012 Dynamics of a viscous layer flowing radially over an inviscid ocean. J. Fluid Mech. 696, 152–174.Google Scholar
Ribe, N. M. 2001 Bending and stretching of thin viscous sheets. J. Fluid Mech. 433, 135–160.Google Scholar
Richardson, S. 1970 A ‘stick-slip’ problem related to the motion of a free jet at low Reynolds numbers. Proc. Camb. Phil. Soc. 67, 477–489.Google Scholar
Robison, R. A. V., Huppert, H. E. & Worster, M. G. 2010 Dynamics of viscous grounding lines. J. Fluid Mech. 648, 363–380.Google Scholar
Schoof, C. 2007 Marine ice sheet dynamics. Part 1. The case of rapid sliding. J. Fluid Mech. 573, 27–55.Google Scholar
Schoof, C. 2011 Marine ice sheet dynamics. Part 2. A Stokes flow contact line problem. J. Fluid Mech. 679, 122–255.Google Scholar
Weertman, J. 1957 Deformation of floating ice shelves. J. Glaciol. 3, 38–42.Google Scholar
Weertman, J. 1974 Stability of the junction of an ice sheet and an ice shelf. J. Glaciol. 31, 3–11.Google Scholar
Wilchinsky, A. V. & Chugunov, V. A. 2000 Ice stream–ice shelf transition: theoretical analysis of two-dimensional flow. Ann. Glaciol. 30, 153–162.Google Scholar
Wingham, D., Wallis, D. & Shepherd, A. 2009 Spatial and temporal evolution of Pine Island Glacier thinning, 1995–2006. Geophys. Res. Lett. 36, L17 501.Google Scholar

Pegler and M. Grae Worster supplementary movie

Movie of an experiment viewed from the side, showing the evolution of the grounding

Download Pegler and M. Grae Worster supplementary movie(Video)
Video 671.8 KB