In many places, the Antarctic and Greenland ice sheets are fringed by tongues of ice floating on the ocean, called ice shelves. Recent observations and modelling suggest that melting and disintegration of the floating ice shelves can impact ice sheet flow, and hence have consequences for sea level rise. Of particular interest are observations of channels and undulations in the ice shelf base, for which the conditions for genesis remain unclear. To build insight into the potential for melting-driven instability of the ice shelf base, this talk will consider a free boundary problem with melting at the ice-ocean interface coupled to a buoyant plume of meltwater confined below a stationary ice shelf. An asymptotic model of turbulent heat transfer in the meltwater plume reveals that melting rates depend on ice-shelf basal slope, with potentially shocking consequences for the evolving ice-shelf geometry
