Ice Rheology

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Lecture Notes: Rheology Part I (Nina Kirchner)

The rheology lecture is scheduled with 2 hours. As with any other topic, there is *never* enough time to cover the subject in all its details, no matter how many hours you set aside for it. Thus, the "Rheology" that will be presented in these 2 hours reflects very much my personal preferences. In an attempt to at least sketch the broadness of the subject, Part I starts with the history of ice mechanics from a mechanicists point of view. We will see that from the earliest beginnings (dating in fact back to the ancient Greeks), the terms "ice" and "crystal" were intimately interlinked although the understanding (and modeling) of large natural ice masses as polycrystalline materials came only much later. Ice is very special for many reasons, among others because water has the greatest diversity (polymorphism) of solid phases over all known substances on Earth, and because it took well into the mid 20th century that the atomistic structure of of ice (Ih) was deciphered. Having the microstructure of ice at hand, it is tempting to believe that the mechanics of large natural ice masses such as contained in the ice sheets covering most of Greenland and Antarctica can be coped with provided that we have suitable tools of how the upscaling from the microscopic, discontinuous scale to the macroscopic, continuous scale takes place. "Homogenization and the continuum hypothesis " is thus the second issue addressed in this lecture. Inevitably, trouble comes along with the transition from the discrete to the continuous, and this is because of what can philosophically phrased as "the entire is more than the sum of its parts". The flow law that is used for idealized, macroscopic continuous ice masses fails to describe, by its very construction, processes which take place at the microscopic scale. Despite acting at the microscopic scale, processes such as e.g. fabric evolution and recrystallization manage to affect the large-scale macroscopic behavior of ice masses through a complex flow-structure-environment-interplay. Anisotropy, visible to the naked eye in thin cuts of ice cores under crossed polarizers, comes into play and demands attention in future modeling since nothing less that e.g. the depth-age relation for ice needed in climate reconstructions is affected by this phenomenon. Lecture Notes "Rheology" Part I can be found here: Media:Del 1 final 090720.pdf

Lecture Notes: Rheology Part II (Nina Kirchner)

On the long and stony path leading us eventually to an anisotropic flow law, we pass, in this Part II, the vast field of isotropic flow laws that have been developed and applied in the context of ice sheet modeling. The difficulty associated with ``the flow law is that there simply is no universally applicable one: ice can not be regarded as a material with a single unique constitutive response. Coarse classifications of the creep behavior of ice distinguish between three different creep regimes: primary (or: transient) creep, secondary (or: stationary) creep, and tertiary (or: accelerating) creep. ``The flow law in glaciology, namely the one named after Glen (and, to be correct, also Steinemann), is, strictly speaking, only valid for secondary creep (just as are all modifications derived from it) and has in its original formulation been derived for reduced dimensionality. A brief review of the consistent 3d extension of the Glen-Steinemann-law acquaints us with continuum mechanical concepts needed when turning to the description of tertiary creep: in this creep regime, the onset of ceaseless change in the microstructural configuration of the ice requires a theoretical framework that allows us to incorporate the effects of evolving fabric (denoting here changes in the behavior of the crystalline structure) and evolving texture (referring to grain size-related processes) into the flow law. A flow law capturing effects occurring during tertiary creep (and manifesting themselves in a up to 3fold enhancement of flow velocities) must be able to describe evolving (or: induced) anisotropy. Therefore, not only knowledge of the microstructure itself but also knowledge about its proper representation in a more macroscopic model description plays a fundamental role in the formulation of an anisotropic flow law. Lecture notes are here: Media:Del 2 final 090720.pdf

Lecture Notes: Rheology Part III (Nina Kirchner)

Finally, Part III of the rheology session goes beyond the discussion of secondary creep. The most comprehensive theoretical framework in which induced anisotropy can be treated and a corresponding flow law for ice can subsequently be formulated is given by the theory of Mixtures with Continuous Diversity (MCD). Using MCD, virtually all microstructural processes known, to date, to be of relevance in the deformational behavior of ice can be consistently described and accounted for in the formulation of a flow law which is sufficiently general to be able to describe tertiary creep in large ice masses. Currently, only a few specialists have applied MCD in ice sheet modeling, and the applications available employ a consistently reduced variant (the so-called CAFFE-model) derived from the general MCD-theory. Future modeling efforts including the effects of induced anisotropy in ice sheets will, hopefully, continue to incorporate flow laws deduced from the MCD theory: the flow-structure-interplay observed in-situ is best modeled within this framework. Get notes here: Media:Del 3 final090723.pdf