Numerical Model of Penelope Ice Viscometer Flows

Summary

The plane flow of ice over a bump as observed with the so-called Penelope ice viscometer has been calculated. The cavity which forms in the lee of the bump is included as an initial condition. The deformation of the ice is assumed to be the sum of the linear elasticity an the non-linear viscosity resulting from the Glen creep law.

A finite difference method based on orthogonal curvilinear co-ordinates is used to determine the stresses and deformation from unit ε ₀ and σ ₀, which are computed at the end of the procedure from the experimentally measured strains and torque. The model yields a very low Young’s modulus (E = 1250 bar) and a fluidity parameter B = T^-3 y^-1 = 0.079 bar^-3 year^-1. However, the fact that the outer ice remains bubbly makes the computed radial velocities unrealistic.