Röthlisberger channels with finite ice depth and open channel flow

Abstract

Abstract The theoretical basis of subglacial channel dynamics can be traced back to the work of Röthlisberger (1972) and Nye (1953). Röthlisberger (1972) considered the channels’ behaviour to be governed by a mix between water friction melting back the channel walls and the viscous closure of the surrounding ice; Nye (1953) derived a viscous closure rate for the ice. While their modelling is evidently well constructed, two aspects of their work have gone undeveloped. The first is the consideration of a finite glacier depth within the viscous closure law, instead of the assumption of an infinite glacier depth. The second is the allowance of a region of open channel flow, so that a channel’s water may transition from a region of closed channel flow to one where the water is exposed to the atmosphere. This paper helps close these two gaps, showing how Nye’s equation for the rate of ice closure can be modified, and how the point of transition between closed and open channel flow may be determined.