Comparing the effects of Temperature, Fabrics and Stress exponentThrostur Thorsteinsson
1 IntroductionMany factors can affect the effective viscosity of ice,![]() 2 The Physics2.1 Glens flow lawGlen's Flow Law [Glen (1958)] has for a long time been widely accepted as the constitutive relation for ice. It is given by the relationwhere
and We will throughout this paper assume that Glen's flow law is the correct law for isotropic ice. We define
2.2 Temperature effectsThe temperature effects are described through the Arrhenius factorwhere Q is the activation energy for creep (0.68e V), k is the Boltzmann constant and T is the temperature in Kelvin.
where V is the activation volume for creep ( The relation (eq. 3) holds for temperatures lower than -10 degrees Celsius. Above that one must use a different relation. Good data on the value of A are given by Paterson [Paterson (1994)], here tabulated in Table 1. Table 1.
2.3 FabricWe choose to look at the fabric dependence by using Azuma's [Azuma (1994)] flow law for anisotropic polycrystalline ice.It is assumed that all the crystals deform only by glide in the basal plane and that the stress is homogeneous. Using these definitions one can calculate the enhancement that happens when the ice is anisotropic. 2.4 Power law for creep or a Newtonian fluid ?In ice streams the deviatoric stresses vary from about 1 bar at the edges to 0.1 bar at the center. This is just at the suggested threshold for n=1 instead of n=3 in Glen's flow law, equation(1).3 Ice StreamsIn ice streams the temperature gradient near the surface is small and most of the temperature variation happens in the bottom![]()
Similarly for the whole temperature range we get
For the fabric dependence we get, according to Azuma's [Azuma (1994)] flow
law, that the ratio of
For the stress dependence we have that the stresses are predominantly shear
stresses. The magnitude is changing from the center (0.1 bar) to the edge (1
bar) of the ice stream. For a power fluid (n=3) this results in changes in
If ice were a Newtonian fluid (n=1) there would be no change in 4 ConclusionTemperature, fabric and stress dependence are all important factors for flow calculations of ice.If we were to assume that the ice in the ice streams were isothermal at (-25
C) and isotropic, we could be off, close to the bed, by a factor of 650.
Ignoring the nonlinearity of the ice could cost us a factor of 100. So all these
factors are important and should be accounted for in flow calculations.
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