Local Friction Laws for Glaciers: A Critical Review and New Openings

Abstract “Sliding velocity” and “friction law” are precisely defined. Different scales for tackling glacier dynamics are introduced. The energy balance in the melting-refreezing process is clarified. The validity of a Glen body as a model for ice rheology is discussed. The assumed model for subglacial water is a very slightly pervious ice, and a not absolutely watertight ice-bedrock interface, owing to glacial striae and rock joints. Then autonomous hydraulic regimes and cavities at water vapour pressure have a negligible influence on the drag, and only the interconnected regime has to be considered. A more rigorous treatment of Weertman’s model (independent knobs) gives quite different numerical factors. In general a term increasing with Terzaghi’s effective pressure N has to be added to the drag. The double-valued friction law found by Weertman is shown to have been an error. Kamb’s relations for the model with a vanishing microrelief are considerably simplified. His conjectural solution cannot be extended to slopes actually found in the microrelief. The author’s (Lliboutry, 1968) treatment is unsatisfactory and includes an error. With a model consisting of irregular bumps of similar length, a new friction law is given. The pertinent measure of the bedrock roughness is then the shadowing function, not the spectral power density.