Elliptical Röthlisberger Channels: Modelling Flow, Heat and Evolution

Subglacial water flow plays a critical role in basal sliding and, consequently, in glacier and ice-sheet dynamics. However, modelling the coupled evolution of subglacial drainage and ice flow 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. The flow and temperature profiles in elliptical channels are solved for with 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. Our 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. These stable channels obey pressure-flux relationships that we use to explore the evolution and dynamics of hydrologically interacting channels in a wider subglacial drainage network, working towards a simplified and scalable subglacial hydrology model.