A theoretical treatment of the sliding of glaciers in the absense of cavitation

Abstract

A model is proposed for the description of glacier sliding which includes the nonlinearity of the flow law for ice. The model describes coupled flow problems in the basal ice and a thin water film, together with a temperature problem in the underlying bedrock. To determine the sliding law relating basal velocity to basal stress, the sliding theory should be formulated as a boundary layer to the larger-scale bulk ice flow. Dimensional analysis indicates that the regelative component of ice velocity may be neglected, provided roughness is absent at the smallest wavelengths and then the ice flow effectively uncouples from the other problems. In this case, with the crucial ( but unrealistic) assumption that the flow law for temperate ice is independent of the moisture content, there exist complementary variational principles that describe the functional form of the sliding law and give bounds on the magnitude of the 'roughness' coefficient. These principles are valid for nonlinear stress-strain rate relations and for non-vanishing bedrock corrugation, and indicate how the basal velocity is determined by two parameters that together describe the degree of roughness of the bed. Specific estimates are then given. Finally, the main weakness in the model as a predictor of quantitatively accurate results is pointed out: that is, that the variation of moisture within the basal layer, and the resultant effect on the flow law, are neglected. A valid description of this phenomenon does not yet appear to be available.