A theory for ice‐till interactions and sediment entrainment beneath glaciers

The ice‐till interface beneath soft‐bedded glaciers can be marked by an abrupt transition from an ice layer above to unfrozen sediments below. Alternatively, the transition can be more gradual, with ice infiltrating the underlying sediments to form a fringe layer that contains a mixture of ice, liquid water, and sediment particles. The fringe thickness h is predicted to commonly be several decimeters to meters in scale, implying that significant sediment transport can occur when sliding occurs beneath. I adapt theories for the thermodynamic and mechanical balances that control freezing and melting in porous media to determine h as a function of effective stress N , the rate of basal heat flow, and key sediment properties. A fringe is expected only when N > p f ≈ 1.1 ( T m − T f ) MPa/°C, where T m − T f is the temperature drop below the pressure‐melting point that is needed for ice to infiltrate the pore space; p f increases with decreased grain size. For sediment properties that are within the typical range expected of the tills beneath glaciers, p f = O (10 4 ) Pa. The rate that water can be transported through the fringe and frozen onto or melted from the glacier base can achieve a steady state that is in balance with the rate that latent heat is transported to or from the basal interface. At constant N , when a gradual increase in heat flow from the glacier base causes the rate of melting to decrease, h increases and continues to do so when the heat flow is great enough to produce freezing. As freezing becomes more rapid and h increases further, the rate of fluid supply to the glacier base reaches a maximum when the effective permeability is sufficiently reduced by the partial ice saturation in the fringe. Larger h can be achieved with slower freezing at the glacier base, but steady states with larger h are unstable. The maximum rate of fluid supply to the glacier base is greater at lower N , higher temperature gradients, and for sediments with higher permeabilities. Unsteady behavior can lead to large changes in h when there is a mismatch between the rate that latent heat can be extracted and the rate that fluid is supplied to the glacier base. Transient behavior driven by abrupt changes in N is characterized by rapid variations in freezing rate, followed by slower adjustments to h that are limited by the timescale for the conduction of latent heat. The resulting patterns of sediment deformation are expected to commonly be distributed over finite depth ranges even when shear is perfectly localized at any single instant in time.