A continuum-mechanical model for the flow of anisotropic polar ice

TL;DR

The paper introduces the CAFFE model, a continuum-mechanical framework for anisotropic polar ice that integrates an anisotropic flow law with a fabric-evolution equation based on an orientation mass balance. Anisotropy enters via a deformation-dependent enhancement factor $\hat{E}(\mathcal{A})$, with the deformability $\mathcal{A}$ computed from a polycrystal orientation distribution, while fabric evolution is governed by grain-rotation, recrystallization, and migration terms. The model remains computationally tractable for ice-flow simulations and is demonstrated through a detailed EDML ice-core case study, showing that fabric orientation relative to the flow direction can markedly alter deformation and velocity profiles, including large bottom-enhancement effects. The results underscore the importance of incorporating anisotropy and fabric evolution in glacier and ice-sheet models, and the work lays the groundwork for broader 3D implementations (e.g., in Elmer/Ice) to capture real-world polar-ice mechanics. Overall, CAFFE provides a practical yet physically grounded approach to linking microscopic crystal orientation to macroscopic ice flow.

Abstract

In order to study the mechanical behaviour of polar ice masses, the method of continuum mechanics is used. The newly developed CAFFE model (Continuum-mechanical, Anisotropic Flow model, based on an anisotropic Flow Enhancement factor) is described, which comprises an anisotropic flow law as well as a fabric evolution equation. The flow law is an extension of the isotropic Glen's flow law, in which anisotropy enters via an enhancement factor that depends on the deformability of the polycrystal. The fabric evolution equation results from an orientational mass balance and includes constitutive relations for grain rotation and recrystallization. The CAFFE model fulfills all the fundamental principles of classical continuum mechanics, is sufficiently simple to allow numerical implementations in ice-flow models and contains only a limited number of free parameters. The applicability of the CAFFE model is demonstrated by a case study for the site of the EPICA (European Project for Ice Coring in Antarctica) ice core in Dronning Maud Land, East Antarctica.

Figures (4)

• Figure 1: Dansgaard-Johnsen type distributions of the vertical strain rate (left panel) and the temperature at the EDML site (right panel). The depth of the kinks is at two-thirds of the local ice thickness. The strain rate at the surface has been chosen such that the downward vertical velocity equals the accumulation rate, and the surface and basal temperatures match the ice-core data.
• Figure 2: Sketch of the rotation of the girdle fabrics in order to align with the $x$-axis (case "R13") and with the $y$-axis (case "R23") in the Schmidt projection.
• Figure 3: Variation of the enhancement factor (left panel), the ice fluidity (middle panel) and the horizontal velocity (right panel) along the EDML ice core. "Data R13" and "Data R23" represent the solutions obtained with the measured girdle fabrics rotated to align with the $x$- and $y$-direction, respectively, and "Isotropy" represents isotropic conditions.
• Figure 4: Variation of the enhancement factor (left panel) and the horizontal velocity (right panel) along the EDML ice core. "Model" represents the solutions based on the fabric evolution equation (\ref{['eq_tranverse']}) for transverse isotropy. For "Data R13", "Data R23" and "Isotropy" see the caption of Fig. \ref{['fig_enh_flui_vel']}.