A variational approach to ice stream flow
A variational approach to ice stream flow
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冰流流动的变分方法
DOI：
10.1017/s0022112006009591
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发表时间：
2006
影响因子：
3.7
通讯作者：
C. Schoof
中科院分区：
文献类型：
--
作者：
C. Schoof
冰盖很容易形成冰流，或快速流动的冰的狭窄带，其高速度是由冰和下伏床之间接触处的快速滑动引起的。最近的地球物理工作表明，冰流的滑动运动可以描述的库仑摩擦定律的基础上，我们调查如何冰流的位置取决于冰盖的几何形状和下伏床的力学性能。更一般地说，这个问题是有关流动的薄膜与库仑（或“固体”）摩擦定律适用于他们的基地。类比弹性摩擦问题，我们构造了一个变分公式的冰流之间的自由边界，发生床故障，和周围的冰脊，那里很少或根本没有滑动。这个变分问题的形式是一个非强制性的变分不等式，我们表明，解决方案存在提供的力和力矩平衡条件得到满足。在这种情况下，解决方案也是独特的，除非在某些特殊的情况下，这是不可能出现的真实的冰盖。此外，我们展示了如何变分公式的冰流问题可以利用计算数值解，并模拟的影响，改变冰的几何形状和床摩擦的位置和流速的流动。最后，我们研究了冰架支撑对冰流流动的影响，冰流的空间范围由河床的屈服应力分布决定。与以前的研究冰架扶壁，我们发现，冰架的去除可以导致冰流喂养冰架大大加快，这强调了重要的作用，冰架可能发挥控制海洋冰盖的动态。
Ice sheets are susceptible to the formation of ice streams, or narrow bands of fast-flowing ice whose high velocities are caused by rapid sliding at the contact between ice and the underlying bed. Based on recent geophysical work which has shown that the sliding motion of ice streams may be described by a Coulomb friction law, we investigate how the location of ice streams depends on the geometry of an ice sheet and on the mechanical properties of the underlying bed. More generally, this problem is relevant to the flow of thin films with Coulomb (or ‘solid’) friction laws applied at their base. By analogy with friction problems in elasticity, we construct a variational formulation for the free boundary between ice streams, where bed failure occurs, and the surrounding ice ridges, where there is little or no sliding. This variational problem takes the form of a non-coercive variational inequality, and we show that solutions exist provided a force and moment balance condition is satisfied. In that case, solutions are also unique except under certain specialized circumstances which are unlikely to arise for a real ice sheet. Further, we show how the variational formulation of the ice flow problem can be exploited to calculate numerical solutions, and to simulate the effect of changing ice geometry and bed friction on the location and velocities of streaming flow. Lastly, we study the effect of ice-shelf buttressing on the flow of ice streams whose spatial extent is determined by the yield stress distribution of the bed. In line with previous studies of ice-shelf buttressing, we find that the removal of an ice shelf can cause an ice stream feeding the ice shelf to speed up considerably, which underlines the important role ice shelves may play in controlling the dynamics of marine ice sheets.