Sayag Roiy, Worster M Grae
Institute of Theoretical Geophysics, Department of Applied Mathemnatics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Sep;84(3 Pt 2):036111. doi: 10.1103/PhysRevE.84.036111. Epub 2011 Sep 19.
An ice sheet that spreads into an ocean is forced to bend owing to its buoyancy and detaches from the bedrock to form a floating ice shelf. The location of the transition between the grounded sheet and the floating shelf, defined as the grounding line, behaves as a free boundary. We develop a model of an elastic grounded sheet resting on a deformable elastic bed and coupled to an elastic floating shelf. We find that the grounding-line position is determined by the geometry of the bed and the bending-buoyancy length scale of the system. These two contributions depend on the reaction modulus of the bed in opposite ways. We show that the structure of the floating shelf depends on the bending-buoyancy length scale only, allowing us to calculate the bending stiffness of the elastic sheet independently of the properties of the bed. Relations between the structure of the floating shelf and the grounding-line position are also developed. Our theoretical predictions agree with laboratory experiments made using thick elastic sheets and a dense salt solution. Our findings may provide new insights into the dynamics near grounding lines, as well as methods to infer the bending stiffness of ice sheets and the grounding-line position from satellite altimetery that can be applied to elastic sheets in general.
延伸至海洋的冰盖由于其浮力而被迫弯曲，并与基岩脱离形成漂浮的冰架。陆地冰盖与漂浮冰架之间的过渡位置，即接地线，表现为一个自由边界。我们建立了一个弹性陆地冰盖模型，该冰盖位于可变形的弹性基底上，并与弹性漂浮冰架相连。我们发现，接地线的位置由基底的几何形状和系统的弯曲 - 浮力长度尺度决定。这两个因素对基底反应模量的依赖方式相反。我们表明，漂浮冰架的结构仅取决于弯曲 - 浮力长度尺度，这使我们能够独立于基底特性来计算弹性冰盖的弯曲刚度。还建立了漂浮冰架结构与接地线位置之间的关系。我们的理论预测与使用厚弹性板和浓盐溶液进行的实验室实验结果一致。我们的研究结果可能为接地线附近的动力学提供新的见解，以及从卫星测高数据推断冰盖弯曲刚度和接地线位置的方法，这些方法通常可应用于弹性板。
