A two-dimensional model of glacier flow is presented which includes periodical surging as a natural phenomenon for a certain class of glaciers. The input consists of the bedrock and balance profiles along the glacier, together with the ice flow properties and a frictional lubrication factor. The basal stress is determined from the condition of gross equilibrium for the whole glacier, together with the distribution of the frictional lubrication from energy dissipation along the glacier.
The difference between the basal stress and the down-slope stress of the glaciers produces longitudinal strain-rates which determine the basal sliding velocity. Since the velocity is also involved in the frictional lubrication, feed-back develops between the basal stress and sliding velocity.
For a given lubrication factor, a critical stage can be reached for which the velocity becomes sufficiently high to lower the basal stress, enough to cause very high velocities to develop. The model thus gives rise to three classes of glaciers with two modes of flow.
“Ordinary” glaciers do not have sufficient mass flux, for the given bedrock profile, to go beyond the “slow mode” in which the basal stress and velocity increase together as the glacier builds up to steady state.
“Fast” glaciers have sufficient flux to remain continuously in the “fast mode” with high velocities and relatively low basal stress.
“Surging” glaciers have sufficient flux to reach the fast mode but not sufficient to maintain it, and thus develop a periodically oscillating state between the fast and slow modes with gradual build up and rapid drainage.
Sample results are presented for models of a typical large valley surging glacier and for a very high-speed surging glacier.