Flotation and free surface flow in a model for subglacial drainage. Part 2. Channel flow

We present a new model of subglacial drainage incorporating flow in a network of channels and a porous sheet, with water exchange between the two determined by pressure gradients. The sheet represents the average effect of many linked cavities, whilst the channels emerge from individual cavities that enlarge due to dissipation-induced melting. The model distinguishes cases when the water pressure drops to zero, in which case it allows for the drainage space to be only partially filled with water (free surface flow), and when the pressure reaches the ice overburden pressure, in which case it allows for uplift of the ice to whatever extent is needed to accommodate the water (flotation). Numerical solutions are found for a one-dimensional flow-line version of the model. The results capture typically observed or inferred features of subglacial drainage systems, including open channel flow at the ice margin, seasonal channel evolution, and high water pressures and uplift of the ice surface driven by rapid changes in water supply.