Ice-shelf deflections modelled with a full 3D elastic model

Abstract:

Ice-shelf flexure modelling was performed using a full 3D finite-difference elastic model, which takes into account sub-ice-shelf seawater flow. The sub-ice seawater flow was described by the wave equation (Holdsworth and Glynn, 1978), so the ice-shelf flexures result from the hydrostatic pressure perturbations in sub-ice seawater. The modelling of ice-shelf vibrations was successfully performed in (Holdsworth and Glynn, 1978) by employing of the thin-plate approximation. The numerical simulation has shown that the modelling of the ice-shelf vibrations can be performed in the full model, which links well known momentum equations with the wave equation for non-viscous fluid, i.e. for sub-ice seawater. Nevertheless, the numerical simulation reveals that the numerical solution stability requires the application of an additional method in the numerical approximation. The aim of this work is in attempt to apply an additional approximation in the boundary conditions to improve the numerical stability of the model.The numerical experiments were carried out for the thin plate of ice with changing ice thickness (with trapezoidal profile along the center line) and with different spreads, and for harmonic temporal and spatial pressure perturbations. In contrariety to the Holdsworth & Glynn model (thin-plate model), ice-shelf vibrations not always follow for the incident wave in the full model. "Not always follow" means that incident ocean waves induce cyclical ice-shelf deflections with the same frequency, but the deflection amplitude (in non-resonance case) is not equal to the one in the incident wave. Evidently, the explanation can be given from the point of view of the elastic medium deformation theory. Exactly, the full model considers a common elastic medium deformation, which implies that there is a distinction in the deformations of different horizontal layers in the medium. Thus, the three stress components f_xz,f_yz, f_zz are non-zero. This forcing complementary hampers the deflections of the plate. In other words, the plate described by the full model is anticipated to be more rigid in comparison with the thin plate, which is described by the thin-plate approximation.