Supplementary material from "Spatial heterogeneity in subglacial drainage driven by till erosion"

The distribution and drainage of meltwater at the base of glaciers sensitively affects fast ice flow. Previous studies suggest that thin meltwater films between the overlying ice and a hard-rock bed channelize into efficient drainage elements by melting the overlying ice. However, these studies do not account for the presence of soft deformable sediment observed underneath many West Antarctic ice streams, and the inextricable coupling that sediment exhibits with meltwater drainage. Our work presents an alternate mechanism for initiating drainage elements such as canals where meltwater films grow by eroding the sediment beneath. We conduct a linearized stability analysis on a meltwater film flowing over an erodible bed. We solve the Orr–Sommerfeld equation for the film flow, and we compute bed evolution with the Exner equation. We identify a regime where the coupled dynamics of hydrology and sediment transport drives a morphological instability that generates spatial heterogeneity at the bed. We show that this film instability operates at much faster time scales than the classical thermal instability proposed by Walder. We discuss the physics of the instability using the framework of ripple formation on erodible beds.