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The Cryosphere An interactive open-access journal of the European Geosciences Union
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© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

  14 Nov 2020

14 Nov 2020

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This preprint is currently under review for the journal TC.

The role of grain-size evolution on the rheology of ice: Implications for reconciling laboratory creep data and the Glen flow law

Mark D. Behn1, David L. Goldsby2, and Greg Hirth3 Mark D. Behn et al.
  • 1Dept. Earth & Environmental Sciences, Boston College, Chestnut Hill, MA 02467 USA
  • 2Dept. Earth & Environmental Science, University of Pennsylvania, Philadelphia, PA 19104 USA
  • 3Dept. Earth, Environmental & Planetary Sciences, Brown University, Providence, RI 02912 USA

Abstract. Viscous flow in ice is often described by the Glen flow law – a non-Newtonian, power-law relationship between stress and strain-rate with a stress exponent n ~ 3. The Glen law is attributed to grain-size-insensitive dislocation creep; however, laboratory and field studies demonstrate that deformation in ice can be strongly dependent on grain size. This has led to the hypothesis that at sufficiently low stresses, ice flow is controlled by grain boundary sliding, which explicitly incorporates the grain-size dependence of ice rheology. Experimental studies find that neither dislocation creep (n ~ 4) nor grain boundary sliding (n ~ 1.8) have stress exponents that match the value of n ~ 3 in the Glen law. Thus, although the Glen law provides an approximate description of ice flow in glaciers and ice sheets, its functional form is not explained by a single deformation mechanism. Here we seek to understand the origin of the n ~ 3 dependence of the Glen law by using the wattmeter to model grain-size evolution in ice. The wattmeter posits that grain size is controlled by a balance between the mechanical work required for grain growth and dynamic grain size reduction. Using the wattmeter, we calculate grain size evolution in two end-member cases: (1) a 1-D shear zone, and (2) as a function of depth within an ice-sheet. Calculated grain sizes match both laboratory data and ice core observations for the interior of ice sheets. Finally, we show that variations in grain size with deformation conditions result in an effective stress exponent intermediate between grain boundary sliding and dislocation creep, which is consistent with a value of n = 3 ± 0.5 over the range of strain rates found in most natural systems.

Mark D. Behn et al.

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Mark D. Behn et al.

Mark D. Behn et al.


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Latest update: 27 Nov 2020
Publications Copernicus
Short summary
Grain size is a key microphysical property of ice, controlling the rheological behavior of ice sheets and glaciers. In this study, we develop a new model for grain size evolution in ice and show that it accurately predicts grain size in laboratory experiments and in natural ice core data. The model provides a physical explanation for the power-law relationship between stress and strain rate known as the Glen Law, and can be used as a predictive tool for modeling ice flow in natural systems.
Grain size is a key microphysical property of ice, controlling the rheological behavior of ice...