Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-14T13:20:25.268Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamics of viscous grounding lines

Published online by Cambridge University Press:  07 April 2010

ROSALYN A. V. ROBISON ,
HERBERT E. HUPPERT  and
M. GRAE WORSTER
ROSALYN A. V. ROBISON
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, CMS, Wilberforce Road, Cambridge CB3 0WA, UK
HERBERT E. HUPPERT
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, CMS, Wilberforce Road, Cambridge CB3 0WA, UK
M. GRAE WORSTER*
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, CMS, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We have used viscous fluids in simple laboratory experiments to explore the dynamics of grounding lines between marine ice sheets and the freely floating ice shelves into which they develop. We model the ice sheets as shear-dominated gravity currents, and the ice shelves as extensional gravity currents having zero shear to leading order. We consider the flow of viscous fluid down an inclined plane into a dense inviscid ‘ocean’. A fixed flux of fluid is supplied at the top of the plane, which is at ‘sea level’. The fluid forms a gravity current flowing down and attached to the plane for some distance before detaching to form a freely floating extensional current. We have derived a mathematical model of the flow that incorporates a new dynamic boundary condition for the position of the grounding line, where the gravity current loses contact with the solid base. The grounding line initially advances and eventually reaches a steady position. Good agreement between our theoretical predictions and experimental measurements and observations gives confidence in the fundamental assumptions of our model.

JFM classification

Geophysical and Geological Flows: Ice sheets Geophysical and Geological Flows: Gravity currents
Type
Papers
Information
Journal of Fluid Mechanics , Volume 648 , 10 April 2010 , pp. 363 - 380
Copyright
Copyright © Cambridge University Press 2010

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

REFERENCES

Acton, J. M., Huppert, H. E. & Worster, M. G. 2001 Two-dimensional viscous gravity currents flowing over a deep porous medium. J. Fluid Mech. 440, 359–380.CrossRefGoogle 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.CrossRefGoogle Scholar
Huppert, H. E. 2000 Geological fluid mechanics. In Perspectives in Fluid Dynamics: A Collective Introduction to Current Research (ed. Batchelor, G. K., Moffatt, H. K. & Worster, M. G.), pp. 447–506. Cambridge University Press.Google Scholar
IPCC report 2007 Intergovernmental Panel on Climate Change Fourth Assessment Report.Google Scholar
Nowicki, S. M. J. & Wingham, D. J. 2008 Conditions for a steady ice sheet–ice shelf junction. Earth Planet Sc. Lett. 265, 246–255.CrossRefGoogle Scholar
Paterson, W. S. B. 1994 The Physics of Glaciers, 3rd edn. Pergamon.Google Scholar
Schoof, C. 2007 Marine ice sheet dynamics. Part I: the case of rapid sliding. J. Fluid Mech. 573, 27–55.CrossRefGoogle Scholar
Vieli, A. & Payne, A. J. 2005 Assessing the ability of numerical ice sheet models to simulate grounding line migration. J. Geophys. Res.-Earth 110, F01003.Google Scholar
Weertman, J. 1974 Stability of the junction of an ice sheet and an ice shelf. J. Glac. 13 (67), 3–11.CrossRefGoogle Scholar
Wilchinsky, A. V. 2001 Studying ice sheet stability using the method of separation of variables. Geophys. Astrophys. Fluid Dyn. 94, 15–45.CrossRefGoogle Scholar
Wilchinsky, A. V. & Chugunov, V. A. 2000 Ice stream-ice shelf transition: theoretical analysis of two-dimensional flow. Ann. Glaciol. 30, 153–162.CrossRefGoogle Scholar

Robison et al. supplementary movie

Movie 1. Experiment of a viscous sheet of golden syrup flowing down a rigid slope into a dense ocean of potassium carbonate solution. The syrup is supplied to the reservoir at the left from a container (red plastic box at top left) maintained at a constant head. Note that the sheet detaches from the slope to form a freely floating shelf at a 'grounding line' that migrates down slope before reaching a steady position. The movie is shown at five times actual speed.

Download Robison et al. supplementary movie(Video)
Video 997.2 KB