Handle URI:
http://hdl.handle.net/10754/598366
Title:
Free-boundary models of a meltwater conduit
Authors:
Dallaston, Michael C.; Hewitt, Ian J.
Abstract:
© 2014 AIP Publishing LLC. We analyse the cross-sectional evolution of an englacial meltwater conduit that contracts due to inward creep of the surrounding ice and expands due to melting. Making use of theoretical methods from free-boundary problems in Stokes flow and Hele-Shaw squeeze flow we construct an exact solution to the coupled problem of external viscous creep and internal heating, in which we adopt a Newtonian approximation for ice flow and an idealized uniform heat source in the conduit. This problem provides an interesting variant on standard free-boundary problems, coupling different internal and external problems through the kinematic condition at the interface. The boundary in the exact solution takes the form of an ellipse that may contract or expand (depending on the magnitudes of effective pressure and heating rate) around fixed focal points. Linear stability analysis reveals that without the melting this solution is unstable to perturbations in the shape. Melting can stabilize the interface unless the aspect ratio is too small; in that case, instabilities grow largest at the thin ends of the ellipse. The predictions are corroborated with numerical solutions using boundary integral techniques. Finally, a number of extensions to the idealized model are considered, showing that a contracting circular conduit is unstable to all modes of perturbation if melting occurs at a uniform rate around the boundary, or if the ice is modelled as a shear-thinning fluid.
Citation:
Dallaston MC, Hewitt IJ (2014) Free-boundary models of a meltwater conduit. Phys Fluids 26: 083101. Available: http://dx.doi.org/10.1063/1.4892389.
Publisher:
AIP Publishing
Journal:
Physics of Fluids
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Aug-2014
DOI:
10.1063/1.4892389
Type:
Article
ISSN:
1070-6631; 1089-7666
Sponsors:
This publication was based on work supported in part by Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). We thank two anonymous reviewers for their helpful comments.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorDallaston, Michael C.en
dc.contributor.authorHewitt, Ian J.en
dc.date.accessioned2016-02-25T13:19:29Zen
dc.date.available2016-02-25T13:19:29Zen
dc.date.issued2014-08en
dc.identifier.citationDallaston MC, Hewitt IJ (2014) Free-boundary models of a meltwater conduit. Phys Fluids 26: 083101. Available: http://dx.doi.org/10.1063/1.4892389.en
dc.identifier.issn1070-6631en
dc.identifier.issn1089-7666en
dc.identifier.doi10.1063/1.4892389en
dc.identifier.urihttp://hdl.handle.net/10754/598366en
dc.description.abstract© 2014 AIP Publishing LLC. We analyse the cross-sectional evolution of an englacial meltwater conduit that contracts due to inward creep of the surrounding ice and expands due to melting. Making use of theoretical methods from free-boundary problems in Stokes flow and Hele-Shaw squeeze flow we construct an exact solution to the coupled problem of external viscous creep and internal heating, in which we adopt a Newtonian approximation for ice flow and an idealized uniform heat source in the conduit. This problem provides an interesting variant on standard free-boundary problems, coupling different internal and external problems through the kinematic condition at the interface. The boundary in the exact solution takes the form of an ellipse that may contract or expand (depending on the magnitudes of effective pressure and heating rate) around fixed focal points. Linear stability analysis reveals that without the melting this solution is unstable to perturbations in the shape. Melting can stabilize the interface unless the aspect ratio is too small; in that case, instabilities grow largest at the thin ends of the ellipse. The predictions are corroborated with numerical solutions using boundary integral techniques. Finally, a number of extensions to the idealized model are considered, showing that a contracting circular conduit is unstable to all modes of perturbation if melting occurs at a uniform rate around the boundary, or if the ice is modelled as a shear-thinning fluid.en
dc.description.sponsorshipThis publication was based on work supported in part by Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). We thank two anonymous reviewers for their helpful comments.en
dc.publisherAIP Publishingen
dc.titleFree-boundary models of a meltwater conduiten
dc.typeArticleen
dc.identifier.journalPhysics of Fluidsen
dc.contributor.institutionMathematical Institute, University of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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