Stability of Sheet Flow of Water Beneath Temperate Glaciers and Implications for Glacier Surging

Abstract

Abstract A mathematical model is presented for the stability of sheet flow of water beneath a temperate glacier. Enhanced viscous heat dissipation in thick parts of the sheet tends to make sheet flow unstable, the instability increasing as sheet thickness and pressure gradient increase. However, incipient channels may be destroyed as the glacier slides over protuberances on its bed. Quasi-stable sheet flow may be possible for sheets up to several millimeters in thickness, especially beneath glaciers that have relatively gentle surface slopes and slide at moderate to high speeds. Such water sheets may somewhat reduce the effective roughness of glacier beds, but probably not enough to allow surge initiation. Furthermore, the presence of numerous water-filled cavities at the glacier bed will tend to reduce the sheet thickness and lessen the degree of “lubrication” of the glacier bed by the water sheet.