Meander formation in supraglacial streams

Meandering streams on the surface of glaciers are similar in planform geometry to meanders in alluvial and bedrock rivers, despite fundamental differences in the mechanisms and timescales of incision. We develop depth-averaged conservation equations for flow in such supraglacial channels with erodible boundaries and solve the linear stability problem for harmonic perturbations to an initially straight channel. Meander formation in supraglacial streams is driven by channel curvature, which enhances heat production and heat transfer to the surrounding ice at bend apexes. This leads to enhanced melting and lateral channel migration, with near constant channel width maintained by the competition of lateral erosion and broadscale ablation of the glacier surface. We find that meandering occurs for a wide but finite range of hydraulic and thermal parameters in both subcritical and supercritical flows and that meanders usually propagate downstream. Predicted meander wavelengths are in general agreement with an empirical scaling between supraglacial channel width and meander wavelength derived from glacial environments worldwide.