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Dynamics of a viscous layer flowing radially over an inviscid ocean

Published online by Cambridge University Press:  09 March 2012

Samuel S. Pegler
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
Corresponding
E-mail address:

Abstract

We present a theoretical and experimental study of a viscous fluid layer spreading over a deep layer of denser, inviscid fluid. Specifically, we study an axisymmetric flow produced by a vertical line source. Close to the source, the flow is controlled viscously, with a balance between radial compressive stresses and hoop stresses. Further out, the flow is driven by gradients in the buoyancy force and is resisted by viscous extensional and hoop stresses. An understanding of these different fluid-mechanical relationships is developed by asymptotic analyses for early times and for the near and far fields at late times. Confirmation of the late-time, far-field behaviour is obtained from a series of laboratory experiments in which golden syrup was injected into denser solutions of potassium carbonate. We use our mathematical solutions to discuss a physical mechanism by which horizontal viscous stresses in a spreading ice shelf, such as those in West Antarctica, can buttress the grounded ice sheet that supplies it.

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Copyright
Copyright © Cambridge University Press 2012

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References

1. Davis, S. H. 2000 Interfacial fluid dynamics. In Perspectives in Fluid Dynamics: A Collective Introduction to Current Research, (ed. Batchelor, G. K., Moffatt, H. K. & Worster, M. G. ), pp. 152. Cambridge University Press.Google Scholar
2. 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
3. Howell, P. D. 1994 Extensional thin layer flows. PhD thesis, University of Oxford.Google Scholar
4. 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
5. Huppert, H. E. 2006 Gravity currents: a personal perspective. J. Fluid Mech. 554, 299322.CrossRefGoogle Scholar
6. 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, 215249.CrossRefGoogle Scholar
7. 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
8. 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, doi:10.1017/jfm.2012.91.Google Scholar
9. 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.CrossRefGoogle Scholar
10. Robison, R. A. V., Huppert, H. E. & Worster, M. G. 2010 Dynamics of viscous grounding lines. J. Fluid Mech. 648, 363380.CrossRefGoogle Scholar
11. Schoof, C. 2007 Marine ice sheet dynamics. Part 1 The case of rapid sliding. J. Fluid Mech. 573, 2755.CrossRefGoogle Scholar
12. Smith, G. D. & Morland, L. W. 1981 Viscous relations for the steady creep of polycrystalline ice. Cold Reg. Sci. Technol. 5, 141150.CrossRefGoogle Scholar
13. Weertman, J. 1957 Deformation of floating ice shelves. J. Glaciol. 3, 3842.CrossRefGoogle Scholar
14. Wilchinsky, A. V. & Chugunov, V. A. 2000 Ice stream–ice shelf transition: theoretical analysis of two-dimensional flow. Ann. Glaciol. 30, 153162.CrossRefGoogle Scholar
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