The role of membrane-like stresses in determining the stability and sensitivity of the Antarctic ice sheets: back pressure and grounding line motion
The role of membrane-like stresses in determining the stability and sensitivity of the Antarctic ice sheets: back pressure and grounding line motion
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DOI：
10.1098/rsta.2006.1797
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发表时间：
2006-07-15
期刊：
影响因子：
5
通讯作者：
Hindmarsh, Richard C. A.
中科院分区：
文献类型：
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作者：
Hindmarsh, Richard C. A.
膜应力作用于两个表面都相对润滑良好的薄体。它们之所以能在冰原上运行，是因为冰原底部要么在滑动，要么由于基底冰的应力和热软化，冰原的粘性比顶部小得多。冰流流过润滑良好的河床，并在河床两侧受到抑制。本文考虑了完全滑床的理想情况，并考虑了施加空间变化的水平体力沿冰流传播的力学效应。传播距离敏感地取决于流变指数，并且对于冰型流变来说可能非常大。提出了一种新的冰架剖面和接地无牵引力流剖面的解析解，该解析解表明，在通量不为零的位置，在上游有限距离处剖面会发生爆炸。这是早先关于浮动架的解析解的一个特征。通过尺度分析，研究了接地线膜应力衰减的长度尺度。在冰原中，这种效应在几十公里的距离上衰减，在冰原流和冰架流之间形成一个垂直边界层，在那里膜应力进行调节。有界的、物理上合理的稳定表面轮廓只在这个边界层中有条件地存在。在有界稳定剖面存在的地方，整个冰盖对应于不同接地区域的相邻剖面平衡出现（中性平衡）。如果边界层中不存在解，那么冰盖剖面必然会发生变化。存在的条件可以写成基本速率因子（滑动或内部变形）是否太大而不允许有稳定的解。临界值非常敏感地取决于冰速和接地线处施加的背应力。高冰速和高应力都有利于溶液的存在和稳定性。这些参数的变化会导致穿越稳定解存在判据，从而引起冰盖动力学的变化。提出了一种既代表中性平衡又代表动力跃迁的有限差分模型，并对其数值敏感性进行了初步研究。长波不稳定性存在的证据是通过一个数值特征问题的解决提出的，这将妨碍可预测性。
Membrane stresses act along thin bodies which are relatively well lubricated on both surfaces. They operate in ice sheets because the bottom is either sliding, or is much less viscous than the top owing to stress and heat softening of the basal ice. Ice streams flow over very well lubricated beds, and are restrained at their sides. The ideal of the perfectly slippery bed is considered in this paper, and the propagation of mechanical effects along an ice stream considered by applying spatially varying horizontal body forces. Propagation distances depend sensitively on the rheological index, and can be very large for ice-type rheologies.A new analytical solution for ice-shelf profiles and grounded tractionless stream profiles is presented, which show blow up of the profile in a finite distance upstream at locations where the flux is non-zero. This is a feature of an earlier analytical solution for a floating shelf.The length scale of decay of membrane stresses from the grounding line is investigated through scale analysis. In ice sheets, such effects decay over distances of several tens of kilometres, creating a vertical boundary layer between sheet flow and shelf flow, where membrane stresses adjust. Bounded, physically reasonable steady surface profiles only exist conditionally in this boundary layer. Where bounded steady profiles exist, adjacent profile equilibria for the whole ice sheet corresponding to different grounded areas occur (neutral equilibrium). If no solution in the boundary layer can exist, the ice-sheet profile must change.The conditions for existence can be written in terms of whether the basal rate factor (sliding or internal deformation) is too large to permit a steady solution. The critical value depends extremely sensitively on ice velocity and the back stress applied at the grounding line. High ice velocity and high stress both favour the existence of solutions and stability. Changes in these parameters can cause the steady solution existence criterion to be traversed, and the ice-sheet dynamics to change.A finite difference model which represents both neutral equilibrium and the dynamical transition is presented, and preliminary investigations into its numerical sensitivity are carried out. Evidence for the existence of a long wavelength instability is presented through the solution of a numerical eigenproblem, which will hamper predictability.