Ice fabrics in two-dimensional flows: beyond pure and simple shear

Abstract

Abstract. Ice fabrics – the distribution of crystal orientations in a polycrystal – are key for understanding and predicting ice flow dynamics. Despite their importance, the characteristics and evolution of fabrics produced outside of the deformation regimes of pure and simple shear flow has largely been neglected, yet they are a common occurrence within ice sheets. Here, we use a recently developed numerical model (SpecCAF) to classify all fabrics produced over a continuous spectrum of incompressible two-dimensional deformation regimes and temperatures. The model has been shown to accurately predict ice fabrics produced in experiments, where the ice has been deformed in either uniaxial compression or simple shear. Here we use the model to reveal fabrics produced in regimes intermediate to pure and simple shear, as well as those that are more rotational than simple shear. We find that intermediate deformation regimes between pure and simple shear result in a smooth transition between a fabric characterised by a girdle and a secondary cluster pattern. Highly rotational deformation regimes are revealed to produce a weak girdle fabric. Furthermore, we provide regime diagrams to help constrain deformation conditions of measured ice fabrics. We also obtain predictions for the strain scales over which fabric evolution takes place at any given temperature. The use of our model in large-scale ice flow models and for interpreting fabrics observed in ice cores and seismic anisotropy provides new tools supporting the community in predicting and interpreting ice flow in a changing climate.

Bridging the Gap Between Experimental and Natural Fabrics: Modeling Ice Stream Fabric Evolution and its Comparison With Ice‐Core Data

“…Within the context of the continuum theory, the orientation tensor (defined in a discrete sense in Equation 1) is given by $$${A}_{ij}=\langle {n}_{i}{n}_{j}\rangle ={\int }_{{S}^{2}}\frac{{\rho }^{\ast }}{\rho }{n}_{i}{n}_{j}\,\mathrm{d}\boldsymbol{n}$$$ We use the same values for the nondimensional parameters as determined in Richards et al. (2021, 2022), $$\tilde{\lambda }$$ and $$\tilde{\beta }$$, which were normalized by the strain rate $$\dot{\gamma }=\sqrt{{D}_{ij}{D}_{ij}/2}$$. The dimensional forms of these parameters are $$$\lambda =\tilde{\lambda }(T)\dot{\gamma },\quad \beta =\tilde{\beta }(T)\dot{\gamma }$$$ With the functions $$\tilde{\lambda }(T)$$ and $$\tilde{\beta }(T)$$ determined via regression against experiments, SpecCAF has been shown to give accurate predictions for fabrics produced in laboratory conditions ($$\dot{\gamma }\sim 1{0}^{-5}$$...…”

“…We use the same values for the nondimensional parameters as determined in Richards et al (2021Richards et al ( , 2022, 𝐴𝐴 λ𝜆 and 𝐴𝐴 β𝛽 , which were normalized by the strain rate 𝐴𝐴 𝐴𝐴𝐴 = √ 𝐷𝐷𝑖𝑖𝑖𝑖𝐷𝐷𝑖𝑖𝑖𝑖∕2 . The dimensional forms of these parameters are…”

“…The parameter 𝐴𝐴 𝐴𝐴 controls the magnitude of the effect. More details and explanation of the terms in the equations, alongside discussion of the model assumptions can be found in Placidi et al (2010) and Richards et al (2021Richards et al ( , 2022.…”

“…Thus, by applying the model and parameters to an ice stream, we are able to generate comparisons between fabrics produced under laboratory and ice-sheet conditions. This equation is solved using spherical harmonics as in Richards et al (2021Richards et al ( , 2022, however here we use the Specfab numerical solver .…”

“…To apply SpecCAF for fabric prediction at EGRIP, we must estimate the three-dimensional path, deformation, and temperature history of the ice along the vertical depth of the drilled ice core. This means that, unlike experiments, and the theoretical exploration of general two-dimensional flow regimes in Richards et al (2022), the ice parcel undergoes a changing history of deformations as it moves through the ice sheet.…”