Realistic, yet simple bottom boundary conditions for glaciers and ice sheets
Realistic, yet simple bottom boundary conditions for glaciers and ice sheets
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冰川和冰盖真实而简单的底部边界条件
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发表时间：
1987
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通讯作者：
L. Lliboutry
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作者：
L. Lliboutry
在不可变形和不可渗透的河床上，滑动规律必须是底部剪应力τB、滑动速度u和有效压力N = pi - pw之间的关系，其中pi是冰荷载，pw是相互连通的水腔中的压力。三个水平尺度被识别：0.1米、10米和10公里。经典理论考虑的是最小尺度;它们的价值是可疑的，因为温带冰既不是干燥的，也不是完全不透水的。中间尺度产生滑动规律用于冰川建模，融化-再冻结过程可以忽略不计。对于模拟大的，寒冷的冰盖，在最大规模的滑动规律是必要的，它建议，滑动只发生在底部温带层存在。讨论了如何处理非牛顿流变学问题。在中间尺度上，由两个叠加的“凹凸轮廓”组成的微浮雕模型是有利的。如果较小的一个有相同高度的隆起，τB将是双倍值，但这个模型是不现实的（1965年阿拉林格莱彻的雪崩可以用另一种方式来解释）。因此，采用了具有不等高度的较小凸起的模型。它给出了一个在大滑动速度下的渐近滑动律τB =<$N + cuN 1 −n，其中以k和c为可调参数。第三个必须以低速引入。虽然这两种极端情况之间的正确插值函数仍然未知，但得到了一些关于运动波的定性结果。
Over a nondeformable and impermeable bed, the sliding law has to be a relationship between the bottom shear stress τb, the sliding velocity u, and the effective pressure N = pi — pw, where pi is the ice load and pw is the pressure in the interconnected water cavities. Three horizontal scales are recognized: 0.1 m, 10 m, and 10 km. Classical theories consider the smallest scale; they are of dubious value because temperate ice is neither dry nor totally impermeable. The intermediate scale yields sliding laws to be used in glacier modeling; melting-refreezing processes may then be ignored. For modeling large, cold ice sheets, the sliding law at the largest scale is needed; it is suggested that sliding occurs only when a bottom temperate layer exists. How to tackle non-Newtonian rheology is discussed. At the intermediate scale a microrelief model consisting of two superimposed “bumpy profiles” is favored. If the smaller one had bumps of equal height, τb would be double valued, but this model is unrealistic (the ice avalanche at the Allalingletscher in 1965 may be explained otherwise). Therefore a model with the smaller bumps of unequal height is adopted. It yields an asymptotic sliding law at large sliding velocities τb = ƒN + cuN1−n, with ƒ and c as adjustable parameters. A third one has to be introduced at low velocities. Although the correct interpolation function between both extreme cases remains unknown, some qualitative results about kinematic waves are obtained.