Is vertical shear in an ice shelf negligible?

Vertical shear stress in ice shelves cannot be precisely zero, since the upper and lower surfaces are generally not parallel. By performing stress balance on a vertical column in an ice shelf we calculate what its magnitude must be. This is done for an unconfined glacier tongue and for a confined bay ice shelf; first, using the assumption of constant temperature and density with depth, and secondly, using realistic data and profiles for Erebus Glacier tongue and for the Amery ice shelf. Shear stresses increase almost linearly with depth and are proportional to surface slope. For Erebus Glacier tongue the shear stress is at most 5% of the magnitude of the direct stress deviators and its action through the ice shell should result in differential movement of 1.8 cm a−1 between the top and bottom of the ice shelf. For the Amery ice shelf, the shear stress is at most 0.4% of the magnitude of the direct stress deviators and this should lead to differential movement of 2.5 cm a−1 between the top and bottom of the ice shelf. Shear stresses are therefore generally negligible in comparison with direct stress deviators and can be ignored when considering the overall dynamics of ice shelves. Differential movement is unlikely to be detectable.