Anisotropic behavior of GRIP ices and flow in Central Greenland
Introduction
This paper deals with the influence of ice rheology on the flow of ice sheets. In particular, the effects of the anisotropic behavior of polar ices will be investigated by: (1) analysing results of several mechanical tests performed on deep ices of the GReenland Ice core Project (GRIP); (2) modelling the mechanical behavior of polar ice with a micro–macro approach; and (3) modelling the large-scale flow of ice in the vicinity of the GRIP drill site (present summit of the Greenland ice cap).
Polar ice, as found in large ice masses like Greenland and Antarctica, is a polycrystalline material, meaning that it consists of an arrangement of crystals (grains). The macroscopic (bulk) mechanical behavior of an ice sample is directly linked to the microscopic (local) behavior of individual grains. Thus, it directly depends on the orientation of the crystallographic axes of grains with respect to the prescribed macroscopic deformation. Ice crystals exhibit an extreme viscoplastic anisotropy (they deform essentially by shear in basal planes). This means that the magnitude and direction of the deformation rate is highly dependent on the orientation of the prescribed stress with respect to the crystallographic axes. This microscopic anisotropy induces a strong macroscopic anisotropy when the polycrystalline sample exhibits a preferred orientation of the c axes (called “texture” in materials science). This is for example the case for Vostok (Antarctica), Dye 3 and Law Dome (Greenland) deep ices 1, 2, 3 and also for GRIP deep ices as will be shown here. Textures develop by the rotation of crystallographic planes during the plastic deformation that the ice is subjected to, and also when polygonization and migration recrystallization mechanisms are active 4, 5. When polar ice does not exhibit a particular orientation of the crystallographic axes (randomly oriented texture), as is the case for example for ice from the surface of ice sheets, the sample behaves identically in all directions and is said to be macroscopically isotropic.
The present paper raises the question of how the observed anisotropy may affect the flow of ice in ice sheets. In particular, we will show that it can make the flow near an ice divide extremely sensitive to bedrock topography and texture pattern. This feature could explain (at least partially) why the stratigraphy of the last 300 m of both GRIP and GISP2 ice cores is disturbed [6], a question of importance when attempting to reconstruct past climate from the study of deep ice cores.
We will present here results of several mechanical tests performed on GRIP ice samples of different depths, therefore presenting different textures. These tests were carried out in two different laboratories (LGGE-Grenoble, France, and Kitami Institute of Technology, Japan) for different orientations of the samples, so that different steady-state (secondary creep) directional viscosities could be determined at each depth (tertiary creep behavior of GRIP ices was presented by Dahl-Jensen et al. [7]). The comparison of all tests will show the good correlation between texture pattern and mechanical response. To understand in a more general way how textures influence the behavior of samples, we apply the ViscoPlastic Self-Consistent (VPSC) model of Lebensohn and Tomé [8] to GRIP ices. This model, which has already been used by Castelnau et al. 9, 10, 11, calculates an approximate solution of the stress and strain rate fields within the whole polycrystal, and thus estimates the mechanical response of a polycrystal for any prescribed stress when only the texture of the material is known. Using the texture of our GRIP samples as input to the model, we will compare the modelled rheology of GRIP ices with that determined experimentally. This is to our knowledge the first time that a rheological model for anisotropic ices is tested quantitatively on mechanical tests performed in the laboratory. The VPSC model enables us also to investigate how the sample behavior is sensitive to specific texture parameters and in particular to texture symmetries, an important question as shown by Azuma and Goto-Azuma [12]. In the last part of this paper, we study how ice anisotropy may affect the large-scale flow of ice in Central Greenland. For this, we apply the large-scale ice flow model developed by Mangeney et al. 13, 14 to the GRIP–GISP2 flow line. This model takes into account an anisotropic constitutive relation which gives the rheology of the ice for a given texture [15]. At present, the model is restricted to textures that exhibit an axisymmetry around the in situ vertical axis (i.e. the vertical axis is a revolution axis for the texture). This is due to the fact that all analytical anisotropic constitutive relations for polar ice have so far been developed for ices presenting orthotropic transversally isotropic behavior. In fact, such a texture symmetry is found only approximately in natural samples [16]. We will show that this approximation should lead to significant inaccuracy in flow prediction. Consequently, the flow of ice near an ice divide cannot be realistically modelled unless a model is developed that precisely describes the development of texture with deformation and recrystallization.
The present paper is structured as follows. In Section 2, we present the results of mechanical tests. In Section 3, we compare the results of the VPSC model with those obtained experimentally, and we show in more detail how texture symmetries affect polycrystal behavior. In Section 4, we apply the large-scale ice flow model to Central Greenland to show how anisotropy influences the in situ flow.
Section snippets
Description
Several mechanical tests have been performed on GRIP ice samples taken from depths ranging from 1328 to 2868 m. The texture of GRIP ices, described in detail by Thorsteinsson et al. [17], changes along the core from a random orientation at the ice sheet surface to a strongly preferred orientation in the deeper parts, with c axes aligned approximately parallel to the in situ vertical direction. This vertical single maximum texture becomes pronounced at 2200 m and persists down to a depth of 2800 m.
Modelling mechanical behavior
Mechanical tests have been used to determine the response of GRIP ice samples for two different orientations of the stress state with respect to texture orientation. To understand in a more general way the relation between texture and rheology, we use a micro–macro model, i.e. a model that relates the behavior of the polycrystal to that of individual grains. We shall now concentrate on the comparison between the experimental rheology of our GRIP samples and that predicted by the model.
Influence on in situ flow
We will now use the large-scale ice flow model of Mangeney et al. 13, 14 to calculate the flow of ice in the vicinity of the GRIP drill site. This 2-dimensional model does not use the shallow ice approximation generally adopted in glaciology, which is based on the existence of a small aspect ratio in ice sheet geometry. The model presents the particularity of completely solving the set of stress equilibrium and incompressibility equations, which renders it applicable to any ice sheet and
Conclusions
We have presented results of several experimental tests performed in two different laboratories (LGGE-Grenoble and Kitami Institute of Technology) on GRIP ice samples. These tests make it possible to estimate the directional viscosities corresponding to a nearly vertical in situ compression and to an in situ horizontal shear combined with a horizontal uniaxial tension. We observe a gradually increasing anisotropy from 1000 down to 2600 m depth, and a slightly decreasing anisotropy below. A
Acknowledgements
This work is a contribution to the GReenland Ice-core Project, carried out at Summit, central Greenland. Financial support was provided by the national funding bodies of Belgium, Denmark, France, Germany, Iceland, Italy, Switzerland, and the United Kingdom, under the auspices of the European Science Foundation. This work was also supported by the PNEDC (Programme National d'Étude de la Dynamique du Climat) CNRS, and by the CEC (Commission of European Communities) Environment Program. We are
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