Grain Growth in Polar Ice: I. Theory

Many observations regarding grain growth in ice sheets are glaciologically interesting but imperfectly understood. Here we develop the theory of grain growth in ice that is not deforming rapidly, and in the succeeding paper we use this theory to explain observations from glacial ice. In the absence of significant strain energy, the driving force for grain growth arises from grain-boundary curvature. Grain growth is slowed by the interaction of grain boundaries with extrinsic materials (microparticles, bubbles, and dissolved impurities). If the driving force for growth is not large enough to cause boundaries to separate from an extrinsic material, then the grain-boundary velocity is determined by the velocity characteristic of the extrinsic material (low-velocity regime). If the driving force is large enough to cause separation, then boundaries migrate more rapidly than the extrinsic material (high-velocity regime) but the net driving force is reduced through transient pinning by the extrinsic material. Polar ice is typically in the low-velocity regime relative to dissolved impurities and the high-velocity regime relative to microparticles and bubbles. Cross-sectional area of grains is predicted to increase linearly with time under most but not all circumstances.