Unconfined Ice-Shelf Flow

Abstract

The spreading of an unconfined ice shelf in two horizontal directions involves the variation of the two horizontal velocity components and the thickness in both directions. Exploiting the slow variation of physical quantities in both horizontal directions compared to vertical variation allows simple solution of the vertical momentum balance and the derivation of plane stress equilibrium equations for integrals of the horizontal stresses through the thickness, together with integrated traction conditions on a front contour defining the boundary of smooth flow. This contour, however, is not prescribed, but is part of the solution. Equilibrium of the region between this smooth contour and the sea margin determines the integrated front tractions in terms of the sea water pressure provided that restrictions on stresses in the margin region can be made. The resulting two-dimensional system of integropartial differential equations on the unknown domain is a complex problem.