On the Significance of Normal Stress Effects in the Flow of Glaciers

Abstract

McTigue and others (1985) identified a possible problem in the type of constitutive equation usually used for modeling the creep behaviour of polycrystalline ice. They pointed out that Glen’s flow law necessarily excludes the consideration of normal stress effects, which are of great significance in other disciplines that consider non-Newtonian fluids. Using the second-order fluid (with material parameters evaluated from laboratory data) as a tentative model for ice, they reached the conclusion that normal stress effects may be discernible in natural glacier flow. But, as noted by McTigue and others, the second-order fluid “fails to represent the non-linear rate dependence of ice in shear”; therefore it is in fact not a suitable constitutive model for glacier ice in shearing flow. In this note, parallel to what McTigue and others did for the second-order fluid, we present a similar analysis for (I) the modified second-order fluid and (II) the power-law fluid of grade 2, both of which are constitutive models recently proposed by Man as a tentative generalization of Glen’s flow law. Both models (I) and (II) can represent normal stress effects, and both agree with Glen’s flow law in the prediction of the depth profile of velocity in the steady laminar flow of glaciers. For ease of comparison, the same creep data of McTigue and others are used in quantifying the material parameters in these two models. Both models (I) and (II) predict far less pronounced normal stress effects in glaciers than those estimated by McTigue and others (whose data analysis in fact suffered from inconsistencies and over-parameterization).