Ice streams are bands of fast-flowing ice in ice sheets. We investigate their formation as an example of spontaneous pattern formation, based on positive feedbacks between dissipation and basal sliding. Our focus is on temperature-dependent subtemperate sliding, where faster sliding leads to enhanced dissipation and hence warmer temperatures, weak- ening the bed further, and on a similar feedback driven by basal melt water production. Using a novel thermomechanical model, we show that formation of a steady pattern of fast and slow flow can occur through the downstream amplification of noise in basal conditions. This process can lead to the establishment of a clearly defined ice stream separated from slowly flowing, cold-based ice ridges by narrow shear margins. Our model is also able to predict the downstream widening of ice streams due to dissipation and heat transport in these margins. We also show that downward advection of cold ice induced by accelerated sliding is the primary stabilizing mechanism that can suppress ice steam formation altogether, and give an approximate, analytical criterion for pattern formation.

冰流是冰盖中快速流动的冰带。我们基于耗散和基础滑动之间的正反馈，研究它们的形成，作为自发图案形成的一个例子。我们的重点是与温度相关的亚温带滑动，在这种情况下，更快的滑动会导致耗散量增加，从而使温度升高，进一步削弱床层，并关注由基础融水产生的类似反馈。使用一种新颖的热力学模型，我们证明了在基础条件下通过噪声的下游放大可以形成快速和缓慢流动的稳定模式。此过程可能导致建立清晰定义的冰流，并通过狭窄的剪切裕度将其与缓慢流动的基于冷的冰脊分开。我们的模型还能够预测由于这些边界处的耗散和热传递而导致的冰河下游扩展。我们还表明，由加速滑动引起的冷冰的向下平流是主要的稳定机制，可以完全抑制冰蒸汽的形成，并为模式形成提供了近似的分析标准。