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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