Skip to main content Accessibility help
×
Home
Hostname: page-component-cf9d5c678-5tm97 Total loading time: 0.209 Render date: 2021-08-04T17:08:43.461Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

An experimental and theoretical study of the dynamics of grounding lines

Published online by Cambridge University Press:  01 July 2013

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
Corresponding
E-mail address:

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.

Type
Papers
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.CrossRefGoogle 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), 901903.CrossRefGoogle ScholarPubMed
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, 355381.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, 217242.CrossRefGoogle Scholar
Howell, P. D. 1996 Models for thin viscous sheets. Eur. J. Appl. Maths 7, 321343.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, 4358.CrossRefGoogle 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, 40714087.CrossRefGoogle Scholar
Nowicki, S. M. J. & Wingham, D. J. 2008 Conditions for a steady ice sheet–ice shelf junction. Earth Planet Sci. Lett. 265, 246255.CrossRefGoogle 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.CrossRefGoogle 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, 6376.CrossRefGoogle Scholar
Pegler, S. S. & Worster, M. G. 2012 Dynamics of a viscous layer flowing radially over an inviscid ocean. J. Fluid Mech. 696, 152174.CrossRefGoogle Scholar
Ribe, N. M. 2001 Bending and stretching of thin viscous sheets. J. Fluid Mech. 433, 135160.CrossRefGoogle 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, 477489.CrossRefGoogle Scholar
Robison, R. A. V., Huppert, H. E. & Worster, M. G. 2010 Dynamics of viscous grounding lines. J. Fluid Mech. 648, 363380.CrossRefGoogle Scholar
Schoof, C. 2007 Marine ice sheet dynamics. Part 1. The case of rapid sliding. J. Fluid Mech. 573, 2755.CrossRefGoogle Scholar
Schoof, C. 2011 Marine ice sheet dynamics. Part 2. A Stokes flow contact line problem. J. Fluid Mech. 679, 122255.CrossRefGoogle Scholar
Weertman, J. 1957 Deformation of floating ice shelves. J. Glaciol. 3, 3842.CrossRefGoogle Scholar
Weertman, J. 1974 Stability of the junction of an ice sheet and an ice shelf. J. Glaciol. 31, 311.CrossRefGoogle Scholar
Wilchinsky, A. V. & Chugunov, V. A. 2000 Ice stream–ice shelf transition: theoretical analysis of two-dimensional flow. Ann. Glaciol. 30, 153162.CrossRefGoogle 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.CrossRefGoogle 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 672 KB
8
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

An experimental and theoretical study of the dynamics of grounding lines
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

An experimental and theoretical study of the dynamics of grounding lines
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

An experimental and theoretical study of the dynamics of grounding lines
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *