Hostname: page-component-8448b6f56d-gtxcr Total loading time: 0 Render date: 2024-04-19T04:36:18.767Z Has data issue: false hasContentIssue false
  • English
  • Français

Lateral controls on grounding-line dynamics

Published online by Cambridge University Press:  04 April 2013

Samuel S. Pegler ,
Katarzyna N. Kowal ,
Leonard Q. Hasenclever  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
Katarzyna N. Kowal
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, Wilberforce Road, Cambridge CB3 0WA, UK
Leonard Q. Hasenclever
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 a theoretical and experimental study of viscous gravity currents introduced at the surface of a denser inviscid fluid layer of finite depth inside a vertical Hele-Shaw cell. Initially, the viscous fluid floats on the inviscid fluid, forming a self-similar, buoyancy-driven current resisted predominantly by the viscous stresses due to shear across the width of the cell. Once the viscous current contacts the base of the cell, the flow can be considered in two regions: a grounded region in which the current lies in full contact with the base; and a floating region. The subsequent advance of the grounding line separating these regions is shown to be controlled by the thickening of the current associated with balancing the local shear stresses. An understanding of the flow transitions is developed using asymptotic and numerical analysis of a model based on lubrication theory.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Low-Reynolds-number flows: Hele-Shaw flows Geophysical and Geological Flows: Ice sheets
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 722 , 10 May 2013 , R1
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

Bamber, J. L., Riva, R. E. M., Vermeersen, B. L. A. & LeBroq, 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
Budd, W. F. 1966 The dynamics of the Amery Ice Shelf. J. Glaciol. 5, 335–358.CrossRefGoogle 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
Dupont, T. K. & Alley, R. B. 2005 Assessment of the importance of ice-shelf buttressing to ice-sheet flow. Geophys. Res. Lett. 32, F03009.Google Scholar
Goldberg, D., Holland, D. M. & Schoof, C. 2009 Grounding line movement and ice shelf buttressing in marine ice sheets. J. Geophys. Res. 114, F0402.Google Scholar
Happel, J. & Brenner, H. 1991 Low Reynolds Number Hydrodynamics: with Special Applications to Particulate Media, 2nd edn. Kluwer Academic.Google Scholar
Huppert, H. E. 1986 The intrusion of fluid mechanics into geology. J. Fluid Mech. 173, 557–594.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
Pegler, S. S. 2012 The fluid mechanics of ice-shelf buttressing. PhD thesis, University of Cambridge.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, 261–281.CrossRefGoogle 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
Pegler, S. S. & Worster, M. G. 2013 An experimental and theoretical study of the dynamics of grounding lines. J. Fluid Mech. (submitted).Google Scholar
Rignot, E., Casassa, G., Gogineni, P., Krabill, W., Rivera, A. & Thomas, R. 2004 Accelerated ice discharge from the Antarctic Peninsula following the collapse of Larsen B ice shelf. Geophys. Res. Lett. 31, L18401.Google Scholar
Robison, R. A. V., Huppert, H. E. & Worster, M. G. 2010 Dynamics of viscous grounding lines. J. Fluid Mech. 648, 363–380.CrossRefGoogle 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.CrossRefGoogle 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. Geophys. Res. Lett. 36, L17–501.Google Scholar

Pegler et al. supplementary movie

Movie of an experiment showing the evolution of the grounding line.

Download Pegler et al. supplementary movie(Video)
Video 1.9 MB