A nonconforming hydroelastic triangle for ice shelf modal analysis

Abstract

© 2019 The Authors. Hydroelastic oscillations of ice shelves, induced by the action of ocean waves, produce deflection and stresses that could potentially lead to calving events. Due to the large horizontal span of several Antarctic ice shelves, like the Ross, Ronne or Larsen C, hydroelastic models for the ice shelf/ice shelf cavity configuration based on long wave approximations can be very effective. Such a model, based on the linearised Shallow Water Equations and the Kirchhoff–Love bending theory for slender plates is considered. For ice shelf modal analysis, in the framework of the specific model, a nonconforming hydroelastic finite element is developed. The new hydroelastic triangle is based on coupling Specht’s plate element with a linear triangle for the velocity potential approximation. It enables explicit computation of the hydroelastic coupling matrix and optimal convergence rates for the eigenpairs. The element efficiency is verified against a semi-analytical solution and the theoretically predicted convergence rates are validated for solutions with sufficient regularity. The SHEEL element (Specht HydroElastic ELement) can be used for cases of variable bathymetry and mild variations of the ice shelf thickness. The same element can be employed for time domain hydroelastic analysis with very slight modifications. A model of the Larsen C ice shelf is considered as a case study.