Ice constitutes physically, but not legally, a separate element of polar regions, alongside with land, water and air. Lack of clear legal regulations in this respect compells the practitioners to apply often inadequate analogies. The specific status of polar permanent and floating ice calls for urgent and comprehensive legal regulation under general international law, the law of the sea and the law of polar regions, on the ground of the principle of Arctic sectors in the Northern Hemisphere and the Antarctic Treaty System in the Southern Hemisphere, with reference to the relatively rich legal doctrine, discussed in detail below.
An axially symmetric, gravity driven, steady flow of a grounded polar ice sheet with a prescribed temperature field is considered. The ice is treated as an incompressible, non-linearly viscous, anisotropic fluid, the internal structure (fabric) of which evolves as ice descends from the free surface to depth in an ice sheet. The evolution of the ice fabric is described by an orthotropic constitutive law which relates the deviatoric stress to the strain-rate, strain, and three structure tensors based on the current (rotating) principal stretch axes. The solution of the problem is constructed as a leading-order approximation derived from asymptotic expansions in a small parameter that reflects the small ratio of stress and velocity gradients in the lateral direction of the ice sheet to those in the thickness direction. Numerical simulations of the flow problem have been carried out for various sets of rheological parameters defining the limit strength of the anisotropic fabric in ice. The results of calculations illustrate the influence of the ice anisotropy, basal melt conditions and temperature field in ice on the glacier thickness and lateral span, and on the depth profiles of the flow velocity.