Full Stokes ice sheet model Elmer/Ice, and its application to regional drainage systems in Greenland and Antarctica
For decades, approximations to the full Stokes equations – the set of partial differential equations describing ice dynamics have been the standard in numerical glaciology in applications to ice sheets. In particular, the shallow ice approximation (SIA) for grounded ice sheets and the shallow shelf...
| Main Authors: | , , , , |
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| Format: | Conference Object |
| Language: | English |
| Published: |
2016
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| Subjects: | |
| Online Access: | https://nipr.repo.nii.ac.jp/?action=repository_uri&item_id=14022 http://id.nii.ac.jp/1291/00013955/ https://nipr.repo.nii.ac.jp/?action=repository_action_common_download&item_id=14022&item_no=1&attribute_id=16&file_no=1 |
| Summary: | For decades, approximations to the full Stokes equations – the set of partial differential equations describing ice dynamics have been the standard in numerical glaciology in applications to ice sheets. In particular, the shallow ice approximation (SIA) for grounded ice sheets and the shallow shelf approximation (SSA) for the floating ice shelves have been deployed in many applications (e.g., Greve and Blatter 2009). Based on the assumption of shallowness of the geometry, these approximations lead to simplifications of the Stokes equations that are numerically very efficient, i.e., easy to solve and economical in memory consumption. Induced by these simplifications, the SIA and SSA are not valid in particular at places of pronounced interest (see Fig. 1): ice domes, ice streams and marine ice sheets (transition from grounded to floating ice). Ice flow is governed by the conservation laws (aka balance equations) of mass, linear momentum and energy. Under the assumption of incompressibility (mass density ȡ = const), conservation of mass is equivalent to conservation of volume, expressed by a vanishing divergence of the velocity field, div u = 0.Conservation of linear momentum, which, due to the low Froude number, reduces to a balance between the Cauchy stress tensor, ı (which usually is split into its deviatoric part, IJ, and the isotropic pressure, p) and the acceleration due to gravity, g, yields the actual Stokes equation, div τgrad p + ρg= 0.Besides the, compared to the SIA and SSA, increased size of the problem, the major difficulty is introduced by the closure relation that expresses the deviatoric stress components in terms of the velocities. The standard approach in ice sheet modeling is to use the isotropic Norton-Hoff law for a shear-thinning fluid, in glaciology also known as Glen’s flow law. In particular at ice domes, where slow velocities and vertical compression prevail, anisotropic effects of the ice fabric (i.e., the arrangement of crystal axes in grains) need to be taken into account. Based on the ... |
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