Radially symmetric ice sheet flow

Abstract
The evolution equations for a radially symmetric grounded ice sheet flowing under gravity are formulated on the basis that the ice is an incompressible nonlinearly viscous heat conducting fluid with temperature–dependent rate factor. The reduced model, which comprises the leading order balances when longitudinal gradients are small compared with gradients through the sheet thickness, is derived. Steady flow is analysed when the temperature field is prescribed, uncoupled from the energy balance or satisfying energy balance with the addition of an appropriate heat source. The problem reduces to a second–order differential equation for the thickness with boundary conditions at the divide (axis of symmetry) and margin, with the margin radius unknown. Asymptotic analysis yields an expression for the surface slope at the margin. Numerical algorithms for both non–slip and sliding at the base are constructed and tested against solutions of special cases. A variety of examples are solved to demonstrate the influence of the viscous law, surface accumulation distribution, sliding and the bed form for different prescribed temperature fields; including evaluation of the heat source distribution necessary to maintain the temperature field.

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