IACS Working group
Division on Planetary and other Ices of the Solar System

Flow law for polycrystalline ice
(2010 – 2014)

WG Chair: Ilka Weikusat
WG participants: Nobuhiko Azuma, Paul Duval, Sepp Kipfstuhl, Luca Placidi, Denis Samyn, Adam Treverrow, Roland Warner.
Advisor: Jo Jacka.

As a simple first step, we propose to reassess the traditional form of "flow law". Later activities could explore in greater detail the range of more sophisticated flow relations, including micro/grain scale models, and general descriptions involving an effective tensor viscosity.
The deformation of ice is usually modelled by using a constitutive law called Glen’s flow law, which relates the strain rate tensor to the stress tensor (usually with a nonlinear dependence on stress) by a scalar factor. This factor is commonly split into a temperature-dependent part, the so called rate factor A(T), an overall proportionality constant, and an enhancement factor E, which parameterises all other physical influences, like impurities, damage, grain size, crystal orientation patterns, etc., usually with respect to the proportionality observed at minimum (secondary) creep rate associated with pure, isotropic, polycrystalline ice under the corresponding temperature and stress conditions.
A first parameterisation of the rate factor assumed an Arrhenius relation, depending on temperature and activation energy (e.g. Cuffey and Paterson, 2010). This relation has most often been used in numerical simulations. Hooke (1981) presented a parameterisation that extended the Arrhenius relation. This is the most recent widely used fit of laboratory measurements to a function of temperature. Since then many new deformation experiments have been carried out. A re-analysis of all stress-strain rate datasets as a function of temperature and the assessment of the previously proposed parameterisations are thus initial tasks the working group will perform.
Beyond the temperature dependence of the rate factor, the question arises whether the Glen-type constitutive relation requires an extension or reformulation. The working group will evaluate the need for a new flow law and survey the prospects available in the literature.
We propose to begin by building a database of flow rates from field and laboratory studies with artificial and natural ice samples, discriminating between secondary and tertiary creep. Related to that, a bibliography of experimental papers, with an accompanying glossary to promote consistent definitions and terminology, as well as a bibliography of theoretical works on flow laws, will be assembled.
Call for contributions: In case you have performed laboratory deformation experiments, please get in contact with us (iacs_flowlaw(at)awi.de).
Hooke, R.LeB. Flow law for polycrystalline ice in glaciers: comparison of theoretical predictions, laboratory data, and field measurements, Reviews of Geophysics and Space Physics, 19(4), 664-672, 1981.
Cuffey, K.M. and Paterson, W.S. B. The Physics of Glaciers, 4th edition, Elsevier, Amsterdam, 2010.