A Glacier Flow Model Incorporating Longitudinal Deviatoric Stresses

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Abstract
A model for glacier flow is developed which incorporates longitudinal deviatoric stress contributions to the field equations. The underlying assumptions may be applied to develop models for various situations. Here, they are developed for steady-state and non-steady-state sliding glaciers in plane flow. The models reduce to a proper generalization of plane-flow pseudo-hydrostatic theory if longitudinal deviatoric stresses are neglected in comparison to basal shear stresses. Solution of this simpler reduced model allows an estimate to be made of the magnitude of the longitudinal deviatoric stress to test if it is negligible or, more generally, investigate under what conditions it can be neglected. The steady-state model predicts that longitudinal deviatoric stresses are negligible for very arbitrary non-uniform sliding-law distributions provided that the following conditions exist: the region must be distant from an ice divide or terminus and subject to normal (not extreme) accumulation or ablation. On the other hand, examples are produced where, under non-steady conditions, longitudinal deviatoric stresses are important and even dominant.