Stability of Sheet Water Flow Under a Glacier

Abstract

Abstract Walder recently analyzed the initial instability of water flow in a sheet under a glacier that is produced by greater heat production in the flowing water and thus the larger rate of ice melting where a perturbation has increased the water sheet thickness. We have looked at the problem from the other presumed final state. We assume that instabilities have finally caused all the water to flow in channels (R-channels) at the bed. We investigated whether these channels can collect enough of the water that is produced by the geothermal heat and the heat sliding to remain in existence. When a basal shear stress is present, the distance out to which a channel can collect water is not that much greater than the channel radius itself. It is concluded that it is not likely for the channel to be able to collect appreciable amounts of water that is produced at the bed . Hence despite the indication that an instability initially might grow in a water sheet, this instability either cannot develop to the point when the water flow is primarily in channels or else the water flow alternates cyclically between a state primarily of sheet flow and a state of channel flow. It would appear that the channels that do exist under a glacier have their primary origin in the melt water from the upper surface that pours down moulins and thus is already channelized by the time it reaches the bed.