We present a theoretical framework that integrates the dynamics of glaciers with and without the topographic confinement. This Part 1 paper concerns the former, which may exhibit surge cycles when subjected to thermal switches associated with the bed condition. With the topographic trough setting the glacier width and curbing the lateral drainage of the meltwater, the problem falls under the purview of the undrained plastic bed (UPB) formalism. Employing the UPB, we shall examine the external controls of the glacial behavior and test them against observations. Through our non-dimensionalization scheme, we construct a 2-D regime diagram, which allows a ready prognosis of the glacial properties over the full range of the external conditions, both climate- and size-related. We first discern the boundaries separating the glacial regimes of steady-creep, cyclic-surging and steady-sliding. We then apply the regime diagram to observed glaciers for quantitative comparisons. These include the Svalbard glaciers of both normal and surge types, Northeast Greenland Ice Stream characterized by steady-sliding, and Hudson Strait Ice Stream exhibiting cyclic surges. The quantitative validation of our model containing no free parameters suggests that the thermal switch may unify the dynamics of these diverse glaciers.

中文翻译：

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冰川动力学和不稳定性理论第 1 部分：受地形限制的冰川

我们提出了一个理论框架，整合了有和没有地形限制的冰川动力学。第 1 部分文件涉及前者，当受到与床条件相关的热开关时，它可能会出现浪涌循环。由于地形槽设置了冰川宽度并抑制了融水的横向排水，这个问题属于不排水塑料床 (UPB) 形式主义的范围。使用 UPB，我们将检查冰川行为的外部控制，并根据观察对其进行测试。通过我们的无量纲化方案，我们构建了一个二维状态图，它可以在与气候和大小相关的所有外部条件下对冰川特性进行现成的预测。我们首先辨别出稳定蠕变、循环涌动和稳定滑动的冰川状态之间的界限。然后，我们将状态图应用于观察到的冰川进行定量比较。其中包括正常和浪涌类型的斯瓦尔巴冰川、以稳定滑动为特征的格陵兰岛东北部冰流和表现出周期性浪涌的哈德逊海峡冰流。我们的模型不包含自由参数的定量验证表明，热开关可以统一这些不同冰川的动力学。