A periodic visco-elastic model for crevasses propagation in marine ice shelves

<div class="ui-layout-east ui-layout-pane ui-layout-pane-east ui-layout-pane-hover ui-layout-pane-east-hover ui-layout-pane-open-hover ui-layout-pane-east-open-hover"> <div class="ng-scope"> <div class="pdf full-size"> <div class="pdf-viewer"> <div class="pdfjs-viewer pdfjs-viewer-outer"> <div class="pdfjs-viewer-inner" tabindex="0" role="tabpanel"> <div class="pdfViewer"> <div class="page" role="region" data-page-number="1" aria-label="Page 1" data-loaded="true" data-listening-for-double-click="true"> <div class="textLayer"><span dir="ltr" role="presentation">Calving is a key mechanism that controls the length of floating ice shelves, and therefore their</span><br role="presentation" /><span dir="ltr" role="presentation">buttressing effect on grounded ice. A fully process-based model for calving is currently still not</span><br role="presentation" /><span dir="ltr" role="presentation">available in a form suitable for large-scale ice sheet models. Here we build on prior work that</span><br role="presentation" /><span dir="ltr" role="presentation">treats crevasse growth in the run-up to calving as an example of linear elastic fracture growth.</span><br role="presentation" /><span dir="ltr" role="presentation">Purely elastic behaviour is confined to short time intervals, much less than a single Maxwell</span><br role="presentation" /><span dir="ltr" role="presentation">time (the ratio of viscosity to Young&#8217;s modulus) in duration: this is typically hours to a few days</span><br role="presentation" /><span dir="ltr" role="presentation">for cold polar ice shelves, depending on temperature and state of stress. We explicitly recognize</span><br role="presentation" /><span dir="ltr" role="presentation">that the elastic stresses occurring during fracture propagation act on an ice-mass subject to a</span><br role="presentation" /><span dir="ltr" role="presentation">pre-stress created by long-term viscous deformation. By coupling a boundary element solver</span><br role="presentation" /><span dir="ltr" role="presentation">for instantaneous elastic stress increments and the resulting fracture propagation with the</span><br role="presentation" /><span dir="ltr" role="presentation">Elmer/Ice Stokes flow solver that computes the pre-stress and is able to model the long-term</span><br role="presentation" /><span dir="ltr" role="presentation">evolution of the domain, we are able to show how viscous deformation end elastic fracture</span><br role="presentation" /><span dir="ltr" role="presentation">mechanics interact. We show that viscous deformation is in general an essential part of calving,</span><br role="presentation" /><span dir="ltr" role="presentation">and as a result, viscous deformation ultimately sets the time scale for calving. The geometric</span><br role="presentation" /><span dir="ltr" role="presentation">changes resulting from that deformation are necessary to cause continued growth to calving</span><br role="presentation" /><span dir="ltr" role="presentation">of fractures that initially propagate only part-way through the domain. We identify two distinct</span><br role="presentation" /><span dir="ltr" role="presentation">modes of fracture propagation: either fractures propagate episodically, the crack lengthening in</span><br role="presentation" /><span dir="ltr" role="presentation">each instance by a finite difference over short (elastic) time scales. Alternatively, fractures grow</span><br role="presentation" /><span dir="ltr" role="presentation">gradually in such a way as to keep the viscous pre-stress near the crack tip from becoming</span><br role="presentation" /><span dir="ltr" role="presentation">tensile, with elasticity playing a secondary role. Our results point to the purely instantaneous</span><br role="presentation" /><span dir="ltr" role="presentation">stress-based calving laws that have become popular in large-scale ice sheet mechanics being</span><br role="presentation" /><span dir="ltr" role="presentation">too simplistic.</span></div> <ul> <li class="textLayer"><span dir="ltr" role="presentation"><img src="" alt="" /></span></li> <li class="textLayer"><span dir="ltr" role="presentation">Figure1: ice shelf geometry evolution and crevasse propagation</span></li> </ul> </div> </div> </div> <div class="pdfjs-controls"> <div class="btn-group">&#160;</div> </div> </div> </div> </div> </div> </div> <div class="ui-layout-resizer-controls synctex-controls">&#160;</div>