Glacier sliding over sinusoidal bed and the characteristics of creeping flow over bedrock undulations

The characteristics of creeping flow close to bed undulations, and the form of the sliding law, in the absence of friction, bed separation and regelation, are analyzed. This is done by an analytical and numerical treatment of a non-linear medium flowing over a sinusoidal bed. The main theoretical results of relevance obtained to date, which are usually only valid in the case of a linear rheology, are given, and emphasis is placed on what can be learned from them about flow behaviour close to the bed. An estimate of the pressure variation along the bed and of an effective viscosity is used to obtain a sliding law for a non-linear medium valid in the limit of small roughness and infinitely thick glaciers. Solutions based on a second order perturbation analysis of the velocity field are presented and examined for a sinusoidal bed. Numerical calculations are performed to extend the analytical results to the case of non-linear rheology and a strongly undulating bed.