Hostname: page-component-77c89778f8-m42fx Total loading time: 0 Render date: 2024-07-17T01:30:03.393Z Has data issue: false hasContentIssue false
  • English
  • Français

The dynamics of confined extensional flows

Published online by Cambridge University Press:  31 August 2016

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

Abstract

I present a theoretical and experimental study of floating viscous fluid films introduced into a channel of finite length, motivated by the flow of glacial ice shelves. The dynamics are characterized by a mixture of viscous extensional stresses, transverse shear stresses and a driving buoyancy force. A theory based on a width-integrated model is developed and investigated using analytical, asymptotic and numerical methods. With fluid introduced at a constant rate, the flow is found to approach a steady state with two possible asymptotic forms depending on the length of the channel. For channel lengths less than half the width, the flow is similar to a purely extensional one-dimensional flow, characterized by concave surface profiles and being insensitive to the position of the channel exit (or calving front). Greater lengths result in a more complex asymptotic structure in which the flow adjusts over a short distance towards a prevailing flow of universal dimensionless form. In complete contrast to the extensional regime, the prevailing flow is controlled by the position of the channel exit. Data from a new laboratory experiment involving particle velocimetry of a floating fluid film compares well with the predicted along-channel velocity. Motivated by glaciological application, the analysis is generalized to power-law rheologies and the results used to classify the flow regimes of a selection of ice shelves. The prediction for the frontal speed is in good agreement with geophysical data, indicating that the universal profile predicted by the theory is common in nature.

JFM classification

Waves/Free-surface Flows: Channel flow Geophysical and Geological Flows: Ice sheets Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 804 , 10 October 2016 , pp. 24 - 57
Check for updates
Copyright
© 2016 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. & 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
Bird, R. B., Armstrong, R. C. & Hassager, O. 1987 Dynamics of Polymeric Liquids, Volume 1: Fluid Mechanics. Wiley.Google Scholar
Copley, A. & McKenzie, D. 2007 Models of crustal flow in the India–Asia collision zone. Geophys. J. Intl 169, 683–698.Google Scholar
Cuffey, K. M. & Paterson, W. S. B. 2010 The Physics of Glaciers, 4th edn. Academic.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
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
Griggs, J. A. & Bamber, J. L. 2011 Antarctic ice-shelf thickness from satellite radar altimetry. J. Glaciol. 57 (203), 485–498.Google Scholar
Gudmundsson, G. H., Krug, J., Durand, G., Favier, L. & Gagliardini, O. 2012 The stability of grounding lines on retrograde slopes. Cryosphere 6, 1497–1505.Google Scholar
Hindmarsh, R. C. A. 2012 An observationally validated theory of viscous flow dynamics at the ice-shelf calving front. J. Glaciol. 58, 375–387.Google Scholar
Howell, P. D.1994 Extensional thin layer flows. PhD thesis, University of Oxford.Google Scholar
Kowal, K. N., Pegler, S. S. & Worster, M. G. 2016 Dynamics of laterally confined marine ice sheets. J. Fluid Mech. 790, R2.Google Scholar
Lister, J. R. & Kerr, R. C. 1989 The propagation of two-dimensional and axisymmetric viscous gravity currents at a fluid interface. J. Fluid Mech. 203, 215–249.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
MacAyeal, D. R. & Barcilon, V. 1988 Ice-shelf response to ice-stream discharge fluctuations: I. Unconfined ice tongues. J. Glaciol. 34, 121–127.Google Scholar
MacAyeal, D. R., Rommelaere, V., Huybrechts, P., Hulbe, C. L., Determann, J. & Ritz, C. 1996 An ice-shelf model test based on the Ross Ice Shelf. Ann. Glaciol. 23, 46–51.Google Scholar
Morland, L. W. 1987 Unconfined ice-shelf flow. In Dynamics of the West Antarctic Ice Sheet: Proceedings of a Meeting held in Utrecht, May 6–8, 1985, Reidel.Google Scholar
Morland, L. W. & Shoemaker, E. M. 1982 Ice shelf balances. Cold Reg. Sci. Technol. 5 (3), 235–251.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 an 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
Pegler, S. S. & Worster, M. G. 2013 An experimental and theoretical study of the dynamics of grounding lines. J. Fluid Mech. 728, 5–28.Google Scholar
Rignot, E., Mouginot, J. & Scheuchl, B. 2011 MEaSUREs InSAR-Based Antarctica Ice Velocity Map. NASA DAAC at the National Snow and Ice Data Center.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
Tanner, R. I. 2000 Engineering Rheology. Oxford University Press.Google Scholar
Van der Veen, C. J.1983 A note on the equilibrium profile of a free floating ice shelf. IMOU Rep. V83(15), State University Utrecht.Google Scholar
Van der Veen, C. J. 1999 Fundamentals of Glacier Dynamics. CRC Press.Google Scholar
Wearing, M. G., Hindmarsh, R. C. A. & Worster, M. G. 2015 Assessment of ice flow dynamics in the zone close to the calving front of Antarctic ice shelves. J. Glaciol. 61, 1194–1206.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

Pegler supplementary movie

This movie illustrates the initial stages of a laboratory experiment in which glucose syrup (dyed red and seeded with particles of polyvinyl carbonate) is introduced along the surface of a dense salt solution (clear). It is sped up by a factor of 25. The movie illustrates the development of an `under-thick' input, for which the flow thickens in the vicinity of the input.

Download Pegler supplementary movie(Video)
Video 2.3 MB