Abstract
We study creeping, isothermal free surface flows of a non-linear power law fluid subject to gravity along straight or curved inclined basal surfaces and having a free surface that is subject to prescribed accumulation/ablation sources. The boundary-layer approximation of the Stokes equations corresponds to the equations in the Shallow-Ice Approximation (SIA), but here they are presented in a Cartesian co-ordinate setting as well as in topography-following orthogonal coordinates. Under isothermal conditions the govering equations, using Glen-type power law rheology, allow semi-analytical representation of the solutions of the three-dimensional ice flows. For plane flow explicit analytic solutions can be constructed. These solutions depend on the slope angle and the mass flux, the integrated accumulation/ablation function. We graphically represent depth profiles, streamwise and normal velocity components and shear stresses and illustrate how these quantities react to variations in the two parameters.
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Savvin, A.A., Hutter, K., Dorfmann, A.A. (1999). Three-dimensional isothermal boundary layer solutions of slow creeping ice flows based on the shallow ice approximation. In: Hutter, K., Wang, Y., Beer, H. (eds) Advances in Cold-Region Thermal Engineering and Sciences. Lecture Notes in Physics, vol 533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0104192
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DOI: https://doi.org/10.1007/BFb0104192
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