Subglacial water flow plays a critical role in basal sliding and, consequently, in glacier and ice-sheet dynamics. However, modelling subglacial drainage elements and coupling these to the ice motion remains challenging. This study investigates the evolution of the basal ice–water interface by analysing heat and fluid flow in idealised englacial channels. We extend the classical Röthlisberger model for circular channels to elliptical channel geometries. A hybrid turbulent–laminar melt scheme captures heat generation from both viscous and turbulent dissipation, while a viscous flow law models the creep closure of the surrounding ice. We solve for the flow and temperature profiles in elliptical channels, finding differential melting between the roof and walls of the channel. We find that elliptical channels tend towards a circular shape when laminar melting dominates, whilst the flow of ice tends to increase the eccentricity of the channel. A hybrid laminar-turbulent melt model permits variations in the distribution of melting along the ice-water boundary and the existence of stable, non-circular cross-sections. The analysis of these idealised channels hints at possible simplifications to modelling subglacial drainage networks, and the dynamics of the evolving subglacial hydrological network.
