Plane ice-sheet flow with evolving orthotopic fabric

Abstract

A plane, gravity-driven, steady flow of an isothermal ice sheet over a horizontal bedrock, with no-slip basal conditions, is considered. The ice is modelled as a linearly viscous, incompressible and anisotropic fluid, with evolving orthotropic fabric that depends on local strain rates and deformations. For a fixed, free-surface elevation, the ice-accumulation rates necessary to maintain the prescribed geometry are calculated by using the finite-element method, together with the velocities and stresses. Numerical simulations have been carried out for different combinations of enhancement factors for compression and shear in order to investigate their effect on the rate of flow. The results obtained have shown that, apart from the near-divide region, the global flow rate is nearly proportional to the magnitude of the shear-enhancement factor and is very little sensitive to the value of the compression enhancement factor. Normalized velocity-depth profiles have been compared for the anisotropic and isotropic ice and it has been found that significant differences occur only in a region near the ice divide. Direct shear stresses are little affected by the ice anisotropy, but the longitudinal deviatoric stresses in a part of the ice sheet are significantly increased compared to the isotropic ice flow.

Enhancement factors for grounded ice and ice shelves inferred from an anisotropic ice-flow model

“…Results for the grounded part are shown in Figure 3. As expected (Mangeney and Califano, 1998; Gagliardini and Meyssonnier, 1999; Staroszczyk and Morland, 2000), the surface velocity, u s , for the anisotropic fabric is greater than that of the isotropic fabric, which confirms that the anisotropy makes the ice softer in the grounded part, where shear stress dominates. The enhancement factor evolution along x is calculated using Equation (15) for both with basal sliding and no basal sliding.…”

“…These last developments indicate that the above conclusion of Mangeney and Califano (1998) is only valid in the restricted case of a vertical material symmetry axis. For a grounded ice-flow regime, all the applications indicate that anisotropic ice flows faster than isotropic ice (Mangeney and Califano, 1998; Gagliardini and Meyssonnier, 1999; Staroszczyk and Morland, 2000), with an enhancement of the flow depending on the anisotropic polycrystal models. To our knowledge, the comparison of isotropic and anisotropic flows for an ice shelf has never been addressed, so the effect of anisotropy on ice-shelf flows remains unclear.…”

“…These small values are explained by the uniform-stress polycrystal model used in their approach, which had a limited anisotropy factor, k s < 2.5. With k s = 5, Staroszczyk and Morland (2000) obtained an enhancement factor of 4. We recall that in our work Ks is set to its experimental value of 10.1.…”

A user-friendly anisotropic flow law for ice-sheet modeling

“…Morland and Staroszczyk (1998) propose an anisotropic flow law that depends on a ‘fabric response function’ (a function of the current strain) fitted to laboratory and field data. This approach has the major quality of being easy to implement into an ice-sheet model (Staroszczyk and Morland, 2000), it is, however, essentially phenomenological.…”

Ice-divide flow at Hans Tausen Iskappe, North Greenland, from surface movement data

“…a single-maximum fabric increasing in strength with depth as observed in the Greenland Ice-core Project (GRIP) core from Summit, central Greenland, by Thorsteinsson and others (1997)). Modelling based on anisotropic flow laws shows that anisotropy significantly affects longitudinal stretching close to the ice divide (Mangeney and others, 1996, 1997; Staroszczyk and Morland, 2000). These studies were based on orthotropic and transversely isotropic flow laws.…”