Modelling the Evolution of Elliptical Röthlisberger Channels

Isaac Brown , Katarzyna L P Warburton , Jerome Neufeld 

Subglacial water flow is critical to basal sliding and ice dynamics. Modelling the coupled evolution of subglacial drainage and ice flow remains challenging, however. 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 laminar–turbulent melt scheme captures heat generation and melting from both viscous and turbulent dissipation, while a viscous flow law models the creep closure of the surrounding ice. Whilst the flow of ice tends to increase the eccentricity of the channel, we find that elliptical channels tend toward a circular shape when laminar melting dominates due to differential melting between the roof and walls of the channel. Our hybrid melt model predicts the existence of stable, non-circular cross-sections. Unlike circular channels, these channels obey pressure-flux relationships that, beyond a critical volume flux threshold, suggest a preference for flux sharing, a behaviour characteristic of distributed drainage networks. This contrasts with circular channels, which undergo channelisation towards fewer, larger conduits. These idealised channels suggest potential simplifications to modelling subglacial drainage networks and the dynamics of evolving subglacial hydrological networks.