Many problems in glaciology require an understanding of the flow field in a glacier. For example, the way in which flow redistributes mass determines the shape of a glacier, and also the rapidity with which glaciers respond to climatic change. Flow also redistributes energy and thus affects the temperature distribution. This, in turn, has important implications for the nature of the coupling with the glacier bed. Spatial variations in speed, or strain rates, are of concern to structural geologists using glaciers as analogs for deformation of rocks. From a geomorphic perspective, the entrainment of debris and the character of moraines constructed from this debris are dependent upon the flow field. In short, understanding the flow field is fundamental to the analysis of many problems in glacier mechanics.

For a full description of the flow field in a glacier, we need the horizontal and vertical components of the velocity at every point. By making several assumptions, we can obtain approximate solutions to this problem that will give insights into certain characteristics of glaciers and the landforms they produce. Initially, we will limit the analysis to two dimensions and also assume a steady state.

We will begin by studying the distribution of horizontal velocity. Given the pattern of accumulation and ablation over a glacier, we can use conservation of mass to determine the mean (depth-averaged) horizontal velocity.