Isothermal flow of an anisotropic ice sheet in the vicinity of an ice divide

Abstract

Simulations of glacier flow are commonly based on the assumption that ice has an isotropic viscosity. Here we examine the plane flow of ice in the special region of an ice divide using a constitutive relation for an anisotropic, incompressible viscous body that is orthotropic and transversally isotropic. Ice is assumed to be isotropic at the ice sheet surface, with the continuous development of a vertical single maximum c axis fabric with increasing depth. We consider the theoretical case of an isothermal ice sheet over a horizontal bedrock, with no slip at the ice‐bedrock interface. The ice sheet surface elevation is imposed, and the flow corresponding to the steady state is calculated, using a two‐dimensional finite difference model based on the resolution of a pressure‐Poisson equation. In this model, all components of the stress and strain rate tensor are calculated. The main conclusion is that for a fixed surface elevation, the general flow pattern accelerates when the anisotropic behavior of the ice is taken into account due to the greater fluidity with respect to shear stress. The downward motion of the ice is faster, despite a higher resistance to vertical deformation. As a result, the dominance of shear strain rate in the flow of polar ice is stronger in the anisotropic case than in the isotropic case. The shear stresses are slightly relaxed, while the longitudinal stresses are significantly increased in the anisotropic case.